Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene

Abstract

The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carrier-carrier interactions and carrier-phonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of observed signals within phenomenological frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated experimental and theoretical programme, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modelling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amounts of disorder and with either high or low doping levels. The theory reproduces the observed dynamics quantitatively without the need to invoke any fitting parameters, phenomenological models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efficient carrier-carrier scattering, which maintains a thermalized carrier distribution, and carrier-optical-phonon scattering, which removes energy from the carrier liquid.

ARTICLE

Received 5 Feb 2016 | Accepted 14 Apr 2016 | Published 25 May 2016

Momchil T. Mihnev1,2,*, Faris Kadi3,*, Charles J. Divin1,2, Torben Winzer3, Seunghyun Lee1,4, Che-Hung Liu1, Zhaohui Zhong1, Claire Berger5,6, Walt A. de Heer5,7, Ermin Malic3,8, Andreas Knorr3 & Theodore B. Norris1,2

The ultrafast dynamics of hot carriers in graphene are key to both understanding of fundamental carriercarrier interactions and carrierphonon relaxation processes in two-dimensional materials, and understanding of the physics underlying novel high-speed electronic and optoelectronic devices. Many recent experiments on hot carriers using terahertz spectroscopy and related techniques have interpreted the variety of observed signals within phenomenological frameworks, and sometimes invoke extrinsic effects such as disorder. Here, we present an integrated experimental and theoretical programme, using ultrafast time-resolved terahertz spectroscopy combined with microscopic modelling, to systematically investigate the hot-carrier dynamics in a wide array of graphene samples having varying amounts of disorder and with either high or low doping levels. The theory reproduces the observed dynamics quantitatively without the need to invoke any tting parameters, phenomenological models or extrinsic effects such as disorder. We demonstrate that the dynamics are dominated by the combined effect of efcient carriercarrier scattering, which maintains a thermalized carrier distribution, and carrieropticalphonon scattering, which removes energy from the carrier liquid.

1 Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan 48109, USA. 2 Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, Michigan 48109, USA. 3 Institut fr Theoretische Physik, Nichtlineare Optik und Quantenelektronik, Technische Universitat Berlin, D-10623 Berlin, Germany. 4 Department of Electronics and Radio Engineering, Kyung Hee University, Gyeonggi 446-701, South Korea. 5 School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA. 6 Institut Neel, CNRS UJF-INP, Grenoble 38042, Cedex 6, France. 7 King Abdulaziz University, Jeddah 22254, Saudi Arabia. 8 Department of Applied Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to T.B.N. (email: mailto:[email protected]

Web End [email protected] ).

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 1

DOI: 10.1038/ncomms11617 OPEN

Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617

a

In graphene, a linearly polarized ultrafast optical pulse excitation gives rise to an initially anisotropic distribution of carriers at high energies1,2. Efcient carriercarrier and

carrierphonon interactions quickly relax the hot carriers to an isotropic thermal distribution, which is then followed by carrier cooling as energy is transferred from the carrier population to the lattice37. A schematic illustration of these processes is given in Fig. 1 (see Supplementary Note 1). A variety of dynamical phenomena, such as the appearance of signicant carrier multiplication and transient optical gain, have been theoretically predicted6,810 and experimentally demonstrated6,11,12. The dynamics observed by a time-domain terahertz (THz) probe pulse, however, exhibit a number of features that have been interpreted in the framework of phenomenological models, but as yet have not been understood quantitatively or qualitatively in terms of fundamental microscopic many-particle processes. For example, the observed photoinduced THz conductivity may be either positive or negative. The positive photoinduced THz conductivity has been viewed in the context of simple Drude models as stemming from enhanced free-carrier intraband absorption upon photo-excitation13,14, while the negative photoinduced THz conductivity has been attributed variously to stimulated THz emission15, enhanced carrier scattering with optical phonons, surface optical phonons or charge impurities1618 and carrier heating1921.

It is generally understood that the initial cooling of hot thermalized carriers proceeds via the emission of high-energy optical phonons (:oopE200 meV). Once the carrier temperature is sufciently below the optical phonon energy, the cooling should proceed via the emission of low-energy acoustic phonons (:oacE4 meV). For graphene samples with low doping density, the cooling of hot carriers near the Dirac point is expected to be very slow due to the vanishing density of states, the energetic mismatch with the energy of optical phonons, and the weak scattering with acoustic phonons4,22,23. The slowest observed cooling times, however, have been on the order of hundreds of picoseconds14, much shorter than the few nanoseconds expected from carrieracousticphonon scattering in ideal graphene22,23, leading to proposals that the cooling is dominated by disorder-assisted electronphonon (supercollision) scattering24. The central role of disorder in these models implies that the underlying enhancement of carrieracousticphonon scattering should strongly depend on the quality and the degree of disorder of the particular graphene sample. Hence, both a methodical experimental investigation and a microscopic theoretical treatment are markedly needed to provide a rigorous foundation for understanding the THz dynamics of hot carriers in graphene.

In the following, we present the results of a systematic experimental study of the THz carrier dynamics in a wide variety of graphene samples, using ultrafast time-resolved THz spectroscopy25, in which we vary the graphene fabrication method, the number of graphene layers and their stacking orientation, the degree of disorder, the Fermi level, the carrier temperature, the substrate temperature and the type of underlying substrate to determine the dominant mechanisms responsible for the hot-carrier relaxation and cooling dynamics for different graphene material parameters and under different experimental conditions. The experimental programme is complemented by the development of a theoretical model26,27 based on the density-matrix formalism that provides microscopic access to the time-and momentum-resolved dynamics of the carrier occupation, the phonon population for different optical and acoustic phonon modes, and the microscopic polarization determining the optical excitation of a disorder-free graphene system. An essential component of the theory is that it incorporates explicitly the time-dependent response of the system to the THz probe pulse; the macroscopic intraband current density induced by the THz

probe, and hence the resulting dynamic THz response, is calculated by microscopically accounting for the full time- and momentum-dependent carriercarrier and carrierphonon interactions. We nd that this rst-principles microscopic

I II III IV

I II III IV

I II III IV

b

c

Figure 1 | Hot-carrier relaxation and cooling dynamics in graphene with various doping densities. (a,b) Hot-carrier relaxation and cooling dynamics in n-type (a) and p-type (b) highly doped graphene (step I). Initially, the optical pump pulse injects hot non-equilibrium carriers at high energies (step II). The hot electrons and holes thermalize within the conduction and valence bands, respectively, due to very efcient intraband carriercarrier scattering processes (step III). As the hot carriers relax to lower energies, interband Auger recombination processes become allowed that quickly merge the separate electron and hole quasi-Fermi levels and lead to a single uniform hot-carrier Fermi-Dirac distribution within B100200 fs after photoexcitation3,6,7 (step IV). The hot carriers cool further via optical

phonon emission facilitated by very efcient carriercarrier rethermalization in highly doped graphene. (c) Hot-carrier relaxation and cooling dynamics in undoped (very lightly doped) graphene (step I). Initially, the optical pump pulse injects hot non-equilibrium carriers at high energies (step II). In contrast to a and b interband impact ionization processes are possible and lead for a moderate excitation regime to signicant carrier multiplication in the conduction band. Similar to a and b as the hot carriers relax to lower energies, interband Auger recombination processes become allowed (stepIII) that lead to a single uniform hot-carrier Fermi-Dirac distribution within B100200 fs after photoexcitation3,6,7 (step IV). The hot carriers cool further via optical phonon emission, which becomes increasingly inefcient at low carrier temperatures due to the small phase space near the Dirac point as the high-energy tail of the hot-carrier distribution diminishes asymptotically. At low carrier temperatures, acoustic phonon emission and/or other slow cooling processes can also have a contribution to hot-carrier cooling in some graphene samples2225.

2 NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617 ARTICLE

approach explains completely all results without the need for any tting parameters, phenomenological models or extrinsic effects such as disorder, which strongly suggests that the role of supercollisions in the hot-carrier dynamics has been largely overstated in the literature24,28,29. Moreover, the theory allows us to go beyond idealized Drude models for the dynamic THz response, and determine the limitations of such simplied models1321. This work establishes that the hot-carrier dynamics are governed by the coupling of extraordinarily efcient carriercarrier and carrieropticalphonon interactions. This is in sharp contrast to electrical transport, which in some graphene samples is dominated by interactions with defects, charge impurities, breaks and ripples (that is, extrinsic effects) since carriers move at the Fermi energy3033.

ResultsGraphene samples. The specic graphene samples in this study include multilayer epitaxial graphene (MEG), which is grown on the C-face of single-crystal 4H-SiC(000 1) substrates by thermal decomposition of Si atoms34,35, single-crystal chemical-vapor-deposited (CVD) graphene (sCVDG), which is grown on oxygen-rich copper foil into large individual single crystals exceeding hundreds of micrometres in size36, and polycrystalline CVD graphene (pCVDG), which is grown on regular copper foil into large continuous layers with domain sizes on the order of hundreds of nanometres37. The as-grown CVD graphene samples are transferred to various substrates for the THz measurements. Because the different graphene samples are synthesized using completely different techniques, their doping density and degree of disorder are also very different (see Methods section), which allows us to observe the possible impact of the Fermi level and the degree of disorder on the dynamic THz response.

Ultrafast time-resolved THz spectroscopy experiment. To study the dynamic THz response of graphene, we utilize ultrafast time-resolved THz spectroscopy25,38,39, which has established itself as a powerful all-optical experimental technique for directly probing the relaxation and cooling dynamics of photoexcited carriers (see Methods section). A 60-fs ultrafast optical pump pulse at 800 nm wavelength injects hot carriers into the graphene sample. The dynamic THz response is monitored by a single-cycle THz probe pulse at a variable time delay after the optical pump. The transmitted THz probe is detected using time-domain electro-optic sampling and frequency-domain THz spectra are obtained via Fourier transformation of the time-domain THz electric eld. The THz carrier dynamics are acquired by monitoring the THz transmission only at the peak of the THz probe pulse, while varying the pumpprobe delay. The differential THz transmission signal, Dt/t, is the change in the THz probe transmission through the graphene sample due to photoexcitation by the optical pump, normalized to the THz transmission without photoexcitation.

We begin by summarizing the main features of the data. First, we consider MEG, sCVDG and pCVDG samples having high doping density ( eF

j jB100400 meV). Figure 2a,b shows repre

sentative differential THz transmission signals as a function of pumpprobe delay, for variable pump uence and for variable substrate temperature, respectively, for a MEG sample with three layers. The secondary peak in the Dt/t signal at B7 ps is due to a round-trip reection of the optical pump inside the substrate that photoexcites additional carriers. Similar results are obtained for the other two types of graphene samples (see Supplementary Figs 15, Supplementary Table 1 and Supplementary Notes 24). Based on extensive measurements on many graphene samples under various experimental conditions, we nd that the THz carrier dynamics in all highly doped graphene samples are

strikingly similar. The Dt/t signal is positive under all experimental conditions, which corresponds to a pump-induced increase of the THz transmission or a decrease of the THz absorption.

Phenomenological ts to the data in Fig. 2a,b (dashed black lines) reveal that the differential THz transmission follows closely a mono-exponential relaxation under all experimental conditions. A summary of the extracted carrier relaxation times as a function of pump uence and substrate temperature for the highly doped graphene samples is presented in Fig. 3a,b. We note that the relaxation times of all highly doped graphene samples are weakly dependent on the pump uence and completely independent of the substrate temperature. In addition, they are very similar in value and in the range of B13 ps with sample-to-sample variation within B2030% despite the wide range of disorder present in the array of samples studied. On average, MEG samples exhibit slightly longer relaxation times than sCVDG and pCVDG samples, which can be attributed to a degree of disorder arising from charge impurities, substrate roughness, wrinkling and breaking of the transferred CVDG samples that can provide additional parallel channels for carrier cooling. We note, however, that the relaxation times of some CVDG samples can approach or exceed these of MEG samples, indicating that disorder-assisted electronphonon (supercollision) cooling24,28,29 is not the dominant cooling mechanism in our high-quality graphene samples, but generally provides at most only a modest correction.

Figure 2c,d shows the THz carrier dynamics calculated within the microscopic theory for disorder-free highly doped graphene ( eF

j j 300 meV) under similar experimental conditions

(see Methods section) and Fig. 3c,d shows the calculated carrier relaxation times to directly compare with the experiments. We observe that the theory is in excellent agreement with experiment, and reproduces the weak pump uence dependence and the complete substrate temperature independence. In sharp contrast, the supercollision model24,28,29 totally fails to capture the substrate temperature independence. The measured THz carrier dynamics can be completely reproduced neglecting carrier acousticphonon scattering in the microscopic theory. Hence, the hot-carrier dynamics are directly the result of an interplay between efcient carriercarrier and carrieropticalphonon scattering; optical phonon emission removes energy from the high-energy tail of the hot-carrier distribution, which is maintained by efcient carriercarrier rethermalization. The physical reason the differential THz transmission of highly doped graphene is independent of the substrate temperature is that the equilibrium THz transmission itself is insensitive to it, when the substrate temperature is far below the Fermi temperature. The slight increase of the relaxation times with increasing pump uence is due to the re-absorption of hot optical phonons generated during the initial carrier thermalization.

The THz carrier dynamics in graphene samples having very low doping density are very different. We consider specically MEG samples in which only the rst few layers closest to the underlying SiC substrate have high doping density ( eF

j jB100400 meV) and the large number of top layers have

very low doping density ( eF

j jB10 meV). In these MEG samples,

the many top lightly doped layers completely dominate the measured THz carrier dynamics. Figure 4a,b shows representative differential THz transmission signals for variable pump uence and for variable substrate temperature, respectively, for a MEG sample with 63 layers. The secondary dip in the Dt/t signal at B7 ps is again due to a round-trip substrate reection of the optical pump. In sharp contrast to the high doping case, the Dt/t signal is negative under all experimental conditions, which corresponds to a pump-induced decrease of the THz transmission or an increase of the THz absorption.

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 3

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617

a b

0.04

90 J cm2

80 J cm2

70 J cm2

60 J cm2

50 J cm2

40 J cm2

30 J cm2

20 J cm2

10 J cm2

5 J cm2

2 J cm2

1 J cm2

0.03

0.03

10 K30 K50 K 100 K 150 K 200 K 250 K 290 K

0.02

0.02

t / t

t / t

0.01

0.01

0

0

5 0 5 10 15 20

5 0 5 10 15 20

Pumpprobe delay (ps)

Pumpprobe delay (ps)

c d

0.3

80 J cm2

50 J cm2

25 J cm2

12.5 J cm2

0.3

50 K 100 K 200 K 300 K

t / t (a.u.)

0.2

0.2

t / t (a.u.)

0.1

0.1

0 0 1 2 3 4 5

0 0 1 2 3 4 5

Pumpprobe delay (ps)

Pumpprobe delay (ps)

Figure 2 | THz carrier dynamics in graphene with high doping density. (a,b) Experimental differential THz transmission, Dt/t, as a function of pump probe delay recorded at a substrate temperature of 300 K for a few different pump uences (a) and at a pump uence of 60.0 mJ cm 2 for a few different substrate temperatures (b) for a highly doped MEG sample with three layers. The THz carrier dynamics follow a fast mono-exponential relaxation at all substrate temperatures and all pump uences (dashed black lines). (c,d) Theoretical differential THz transmission, Dt/t, as a function of pumpprobe delay calculated within the microscopic theory at a substrate temperature of 300 K for a few different pump uences (c) and at a pump uence of 12.5 mJ cm 2 for a few different substrate temperatures (d) for disorder-free highly doped graphene ( eF

j j 300 meV). Experiment and theory are in excellent agreement

under all conditions.

Phenomenological ts to the data in Fig. 4a,b (dashed black lines) reveal that the differential THz transmission evolves from a faster mono-exponential relaxation at room temperature to a slower bi-exponential relaxation at cryogenic temperatures. A summary of the extracted carrier relaxation times as a function of pump uence at room temperature for two MEG samples with 35 and 63 layers is presented in Fig. 5a. We note that the relaxation times at room temperature do not depend on the number of layers, which supports the interpretation that the measured THz carrier dynamics are dominated by the many top lightly doped layers. This conclusion is further supported by the fact that the maximum Dt/t signal scales roughly linearly with the number of layers (see Supplementary Figs 35 and Supplementary Notes 34). In addition, the relaxation times of lightly doped graphene samples are in the range of B47 ps, which is longer than the relaxation times of highly doped graphene samples (see Fig. 3a); this is due to a reduced efciency of carriercarrier scattering, which scales with carrier density. For cryogenic temperatures, we extract both short and long carrier relaxation times from the bi-exponential ts, which we associate with two distinct cooling mechanisms. As explained below, the fast carrier relaxation component on a timescale of tens of picoseconds is fully accounted for by the combined effect of carriercarrier and carrieropticalphonon scattering in the absence of disorder. Figure 5b shows the short relaxation times as a function of substrate temperature for variable pump uence for the MEG sample with 63 layers. We note that the short relaxation times of

all lightly doped graphene samples are weakly dependent on the pump uence, but strongly dependent on the substrate temperature.

Figure 4c,d shows the THz carrier dynamics calculated within the microscopic theory for disorder-free undoped graphene ( eF

j j 0 meV) under similar experimental conditions

(see Methods section) and Fig. 5c,d shows the calculated carrier relaxation times. The theory captures again all trends observed in the experiments. As in the high-doping case, the hot-carrier relaxation occurs via the interplay between efcient carrier carrier and carrieropticalphonon scattering. In contrast to the high-doping case, however, the relaxation times increase signicantly with decreasing substrate temperature. This behaviour for undoped graphene is due to the substrate temperature dependence of the equilibrium THz transmission and not the dynamic non-equilibrium part of the differential THz transmission; that is, the initial Fermi surface, where the THz probe pulse acts on the carriers, strongly depends on the substrate temperature, when it is comparable to the Fermi temperature. Similar to the high-doping case, the theory shows a slight increase of the relaxation times with increasing pump uence that can be traced back to hot phonon effects.

At low substrate temperatures, the THz carrier dynamics in the MEG samples with many lightly doped layers relax on a timescale exceeding hundreds of picoseconds, corresponding to the slow carrier relaxation component in the bi-exponential decay. As the high-energy tail of the hot-carrier distribution diminishes

4 NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617 ARTICLE

a b

2.5

2.5

Relaxation time (ps)

Relaxation time (ps)

2

2

1.5

1.5

MEG 3 layers sCVDG 1 layer pCVDG 1 layer pCVDG 1 layer

MEG 3 layers sCVDG 1 layer pCVDG 1 layer

1 0 20 40 60 80

1

0 50 100 150 200 250 300

Pump fluence (J cm2)

Pump fluence (J cm2)

Substrate temperature (K)

c d

3

3

Relaxation time (ps)

Relaxation time (ps)

2.5

2.5

2

2

80 J cm2

50 J cm2

25 J cm2

12.5 J cm2

50 K 100 K 200 K 300 K

1.5

1.5

0 20 40 60 80

0 50 100 150 200 250 300

Substrate temperature (K)

Figure 3 | THz carrier relaxation times in graphene with high doping density. (a,b) Carrier relaxation times extracted from ts to experimental differential THz transmission, Dt/t, as a function of pump uence at a substrate temperature of 300 K (a) and as a function of substrate temperature at a pump uence of 60.0 mJ cm 2 (b) for highly doped MEG, sCVDG and pCVDG samples. (c,d) Carrier relaxation times extracted from ts to theoretical differential THz transmission, Dt/t, as a function of pump uence for a few different substrate temperatures (c) and as a function of substrate temperature for a few different pump uences (d) for disorder-free highly doped graphene ( eF

j j 300 meV). The theory accurately reproduces the magnitude of the

relaxation times and the trends with pump uence and substrate temperature observed in the experiments.

asymptotically, a different cooling mechanism becomes dominant below B200 K. We have analysed the physical origin of this mechanism in a separate publication25. In particular, the THz carrier dynamics become dependent on the number of layers in the MEG sample, indicating that interlayer thermal coupling effects are important.

Microscopic theory. We now turn to a discussion of the theoretical approach used to calculate the dynamic THz response described above (see Methods section, Supplementary Fig. 6 and Supplementary Note 5). The theory is an extension of the methods developed previously by some of the authors1,2,5,9,11,12,26,27, and is extended in this work to rigorously include the effect of the time-dependent THz probe electric eld. By selectively switching on and off the different scattering processes in the model, we nd that the acoustic phonon modes have negligible contribution to the observed THz carrier dynamics on the timescale of tens of picoseconds; the observed dynamics are fully accounted for by the combined effect of carrieropticalphonon scattering (which transfers energy from the carrier liquid to the lattice) and carriercarrier scattering (which continuously rethermalizes the carrier population as high-energy carriers lose their energy to the lattice). As seen in the comparisons between experiment and theory above, this rst-principles microscopic approach explains completely all experimental results without the need for any tting

parameters, phenomenological models or extrinsic effects such as disorder.

The standard Drude model, which is often employed as a phenomenological basis for the interpretation of graphene transport and optical data, can be obtained by assuming a constant time- and momentum-independent scattering rate in the microscopic theory (see Methods section and Supplementary Note 6). It is thus interesting to consider to what extent the Drude model can account for the observed dynamics. Figure 6a shows the pump-induced temporal evolution of the carrier temperature T(t) and the Fermi level eF(t) obtained by solving the full graphene Bloch equations within this approximation for low(12.5 mJ cm 2 (red line)) and high (80 mJ cm 2 (blue line)) photoexcitation, for disorder-free highly doped graphene ( eF

j j 300 meV). For very high carrier temperature, as one has

at early time delay and high uence, the calculated Dt/t signal is negative, in contradiction to the experimental observation that the Dt/t signal is positive at all time delays for highly doped graphene samples. Only after the carrier temperature drops below

B2,200 K does the Dt/t signal become positive. If one makes the further approximation (as is often done in Drude models) that the only effect of the optical pump is to heat the carriers, that is, the Fermi level is assumed to remain constant, than the calculated Dt/t signal is negative at all time delays (dashed black line in

Fig. 6a). The full microscopic theory including the transient carrier temperature T(t), the transient Fermi level eF(t) and the

explicitly time- and momentum-dependent scattering rates

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 5

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617

a b

0

0

0.04

0.1

t / t

t / t

60 J cm2

40 J cm2

20 J cm2

10 J cm2

5 J cm2

2 J cm2

1 J cm2

10 K20 K40 K80 K 120 K 160 K 200 K 240 K 280 K

0.08

0.2

0.12

0.3

0.16 5 0 5 10 15 20

0 10 20 30 40 50

Pumpprobe delay (ps)

Pumpprobe delay (ps)

c d

0

0

0.01

0.01

0.02

t / t (a.u.)

t / t (a.u.)

0.02

0.03

25 J cm2

6 J cm2

1.5 J cm2

0.5 J cm2

0.04

50 K 100 K 200 K 300 K

0.03

0 2 4 6 8 10

0 2 4 6 8 10

Pumpprobe delay (ps) Pumpprobe delay (ps)

Figure 4 | THz carrier dynamics in graphene with low doping density. (a,b) Experimental differential THz transmission, Dt/t, as a function of pumpprobe delay recorded at a substrate temperature of 300 K for a few different pump uences (a) and at a pump uence of 23.4 mJ cm 2 for a few different substrate temperatures (b) for a lightly doped MEG sample with 63 layers. The THz carrier dynamics evolve from a faster mono-exponential relaxation at room temperature to a slower bi-exponential relaxation at cryogenic temperatures (dashed black lines). (c,d) Theoretical differential THz transmission,

Dt/t, as a function of pumpprobe delay calculated within the microscopic theory at a substrate temperature of 300 K for a few different pump uences (c) and at a pump uence of 1.5 mJ cm 2 for a few different substrate temperatures (d) for disorder-free undoped graphene ( eF

j j 0 meV). Experiment and

theory are in excellent agreement under all conditions.

Gin=outlk t

, on the other hand, completely reproduces all the

features of the experimental data under all conditions. Drude models are not sufcient to consistently explain all the data, particularly the behaviour at higher pump uence, for which the short time dynamics would exhibit a negative Dt/t signal, unless ad hoc phenomenological parameters such as a carrier heating efciency19,20 or a non-monotonic carrier-temperature-dependent Drude weight21 are added to the model. We conclude that a Drude model approximation to the full microscopic theory can provide only a semi-qualitative framework for interpreting experimental data in highly doped and undoped graphene samples at low photoexcitation; however, the full microscopic theory is required to explain the data consistently for all photoexcitation levels.

The microscopic theory also allows us to address an important question in hot-carrier physics, namely, the energy dependence of the carrier scattering rate (inverse time), dened here as the exponential decay of the carrier occupation (see Methods section). For weak THz probe excitations (as is the case here), the Boltzmann equation reveals a direct relation between the microscopic scattering rates and the exponential decay of the carrier occupation. By tting the numerically calculated hot-carrier dynamics, we obtain the energy relaxation time of the photoexcited carriers, named the carrier scattering time. Figure 6b shows the calculated carrier scattering time t e

as a function of the excess carrier energy e for disorder-free undoped graphene ( eF

j j 0 meV) at a substrate temperature of

300 K. We observe that the carrier scattering time is precisely

inverse to the carrier energy, t e

b= e

j j (with bE0.9 eV ps),

over a very broad energy range ( e

j jB0.21.5 eV) in agreement

with previous experimental studies on MEG40 and graphite41,42. This behaviour is a direct consequence of the linear density of states and is therefore independent of the substrate temperature. For highly doped graphene, a deviation from the strictly inverse relation can be expected for eEeF. However, our microscopically determined energy dependence of the carrier scattering time is in sharp contrast with the linear relation on the carrier energy, t e

a ej j (refs 30,31), that has been inferred

from electrical transport measurements in some graphene samples. This is attributed to the fact that in electrical transport measurements carriers have energies close to the Fermi energy, and carrier scattering in these graphene samples is dominated by extrinsic mechanisms such as defects, charge impurities, breaks and ripples32,33 likely introduced during the multistep synthesis, transfer and fabrication processes. Transferred graphene (for example, on SiO2) has local spatial charge inhomogeneities under overall charge-neutral conditions due to disorder, charge impurities or surface corrugation4345, which obscure the low-energy graphene band structure and prevent one from studying the true graphene physics near the Dirac point. Such effects can be minimized by placing the graphene on ultra-smooth substrates such as hexagonal BN (h-BN)46 or by suspending it47. The lightly doped layers in MEG are naturally protected, which makes them an ideal graphene system for studying the carrier dynamics within a few meV of the Dirac point.

6 NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617 ARTICLE

a b

7.5

40

7

35

6.5

30

Relaxation time (ps)

Relaxation time (ps)

6

25

5.5

20

5

15

23.4 J cm

8.8 J cm3.0 J cm1.2 J cm

4.5

10

4

MEG 35 layers MEG 63 layers

5

3.5 0 10 20 30 40 50 60 70 80

0 0 50 100 150 200 250 300

Pump fluence (J cm2)

Substrate temperature (K)

c d

6

20

18

5.8

16

14

Relaxation time (ps)

5.6

12

10

5.4

8

25 J cm2

6 J cm2

1.5 J cm2

0.5 J cm2

5.2

6

4

5

2

0 5 10 15 20 25

0 0 50 100 150 200 250 300

Pump fluence (J cm2)

Relaxation time (ps)

Substrate temperature (K)

Figure 5 | THz carrier relaxation times in graphene with low doping density. (a,b) Carrier relaxation times extracted from ts to experimental differential THz transmission, Dt/t, as a function of pump uence at a substrate temperature of 300 K (a) and as a function of substrate temperature for a few different pump uences (b) for lightly doped MEG samples. (c,d) Carrier relaxation times extracted from ts to theoretical differential THz transmission, Dt/t, as a function of pump uence at a substrate temperature of 300 K (c) and as a function of substrate temperature for a few different pump uences (d) for disorder-free undoped graphene ( eF

j j 0 meV). The theory accurately reproduces the magnitude of the relaxation times and the trends with pump uence

and substrate temperature observed in the experiments.

Finally, we consider the correlation between the differential THz transmission and the carrier temperature dynamics. In the microscopic theory, the dynamic THz response depends on the transient carrier temperature, the transient Fermi level and the time- and momentum-dependent scattering rates (see Methods section). The inset of Fig. 6b shows a direct comparison between the differential THz transmission and the differential carrier temperature (where the substrate temperature is subtracted) calculated within the microscopic theory for disorder-free undoped graphene ( eF

j j 0 meV) at a substrate

temperature of 300 K and a pump uence of 1.5 mJ cm 2. We see that the differential THz transmission does not exactly follow the carrier temperature dynamics and, in particular, the relaxation times extracted from the decay of the Dt/t signals are not exactly equal to the electronic cooling times. In sharp contrast, a simple Drude model, in which only the carrier temperature is assumed to be time-dependent, would predict incorrectly that the two quantities are proportional13,14,24. Hence, our microscopic approach clearly reveals that the transient carrier temperature, the Fermi level shifts and the time- and momentum-dependent scattering rates are all essential to capture the dynamic THz response correctly.

DiscussionIn summary, we have studied the hot-carrier relaxation and cooling dynamics in highly doped and undoped (very lightly doped) graphene samples synthesized using a wide array of methods, using ultrafast time-resolved THz spectroscopy

combined with microscopic modelling. The THz carrier dynamics depend critically on the Fermi level, and are quantitatively explained using a microscopic density-matrix theory of carriercarrier and carrierphonon interactions, without the need to invoke any free tting parameters, phenomenological models or extrinsic effects such as disorder; the theory accounts explicitly for the time-dependent response of the hot carriers to the THz probe eld. The hot-carrier dynamics are governed by the interplay of efcient carriercarrier and carrier opticalphonon scattering, while carrieracousticphonon scattering is found not to be important on picosecond timescales.

Methods

Graphene samples synthesis, fabrication and characterization. To date a number of techniques have been demonstrated for the synthesis of high-quality graphene including exfoliation, epitaxial and CVD growth methods. We report here comprehensive experiments on graphene synthesized using three different methods. The rst type is MEG, which is grown on the C-face of single-crystal 4HSiC(000 1) substrates by thermal decomposition of Si atoms34,35. The MEG grows conformally across atomic terraces on the SiC substrate resulting into large continuous layers with domain sizes exceeding hundreds of micrometres in size. By carefully tuning the chemical recipe, MEG samples having from a few up to a hundred layers can be reliably grown, and the uctuations in the homogeneity of the MEG samples are estimated not to exceed one layer. The individual layers in MEG are electronically decoupled due to their unique rotational stacking, and each layer exhibits a single graphene layer Dirac cone near the Dirac point, so that MEG behaves in essence as multilayer graphene48,49. The second type is sCVDG, which is grown on oxygen-rich copper foil into large individual single crystals exceeding hundreds of micrometres in size36. The third type is pCVDG, which is grown on regular copper foil into large continuous layers with domain sizes on the order of hundreds of nanometres37.

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 7

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617

a

0.35

0.3

0.25

0.2

0.15

0.10 500 1,000 1,500 2,000 2,500 3,000 3,500

Carrier temperature (K)

1

0.5

0

0.5

1

t /t (T, [afii9830] F) (a.u.)

12.5 J cm2

80 J cm2

5.7 ps

Fermi level (eV)

t = 0.5 ps

0.2 ps

Time

b

5

1

Differential THz transmission Differential carrier temperature

0.8

Quantity (a.u.)

0.6

0.4

0.2

0 0 2 4 6 8 10

Pumpprobe delay (ps)

4

Scattering time (ps)

3

2

1

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Energy (eV)

Figure 6 | Microscopic theory calculation of the carrier dynamics and the carrier scattering time in graphene. (a) Differential THz transmission,

Dt/t, expected from a Drude model with a constant scattering rate for an initial carrier temperature of 300 K and a Fermi level of 300 meV as a function of the transient carrier temperature T(t) and the transient Fermi level eF(t). The solid black line separates regions of positive and negative

Dt/t signal. The dashed black line shows the possible differential THz transmission under the assumption that the Fermi level remains constant.

The solid red (blue) line shows the path through the T(t)-eF(t)-map for a pump uence of 12.5 mJ cm 2 (80 mJ cm 2) obtained from the solution of the full graphene Bloch equations for the pump-induced dynamics. The rst point reects the system 0.2 ps after the optical pump pulse, when the carrier distribution can be represented by a single uniform hot-carrier Fermi-Dirac distribution. The time delay between two points is 0.5 ps, respectively. The gure illustrates the fact that the full microscopic theory is required to explain the experimental data consistently for all photo-excitation levels. (b) Carrier scattering time t e

as a function of excess

carrier energy e calculated within the microscopic theory for disorder-free undoped graphene ( eF

j j 0 meV) at a substrate temperature of 300 K. The

calculated values are precisely inverse to the carrier energy, t e

b= e

j j

(with bE0.9 eVps). Inset: comparison between the normalized differential THz transmission and the normalized differential carrier temperature dynamics calculated within the microscopic theory for disorder-free undoped graphene ( eF

j j 0 meV) at a substrate temperature of 300 K and

a pump uence of 1.5 mJ cm 2. The two time-dependent quantities relax on similar, but not exactly equal timescales.

By carefully tuning the chemical recipe, both mono- and bi-layer pCVDG samples can be reliably grown.

The as-grown CVD graphene samples are transferred from the copper foils to various substrates including C-cut single-crystal sapphire (Alfa Aesar) and amorphous polyethylene (TOPAS cyclic olen copolymer, TOPAS Advanced

Polymers) for the ultrafast time-resolved THz spectroscopy measurements. The exact same transfer process is used for both sCVDG and pCVDG samples. One side of the copper samples is spin coated with 950PMMA A2 (MicroChem) photoresist as a protection layer and the other side is exposed to oxygen plasma to etch away the undesired graphene. The samples are left in ammonium persulfate solution (0.025 g ml 1) for 12 h to dissolve the copper foil underneath. Then, the graphene lms with PMMA coating are transferred onto the prepared clean substrates and are left to dry for 12 h. The nal step is to use acetone for removing the PMMA coating on top and isopropyl alcohol for rinsing the samples.

Because the different graphene samples are synthesized using completely different techniques, their doping density and degree of disorder are also very different, which allows us to study the dynamic THz response for different Fermi levels and different degrees of disorder. The MEG samples have a gradient doping density prole, where the rst few layers closest to the underlying SiC substrate are highly n-doped ( eF

j jB100400 meV) due to electron transfer from the interface,

and the Fermi level in subsequent layers decreases exponentially away from the substrate to around eF

j jB10 meV (refs 34,35,50,51). The CVDG samples are highly

p-doped ( eF

j jB200400 meV) due to water vapour adsorption from the

environment52. Thus, we can directly compare the dynamic THz response of graphene with Fermi level far above, far below and very close to the Dirac point.

The graphene degree of disorder is in general not straightforward to quantify, but it can be estimated from various characterization techniques including high-resolution angle-resolved photoemission spectroscopy (ARPES), high-resolution scanning tunnelling microscopy, Raman spectroscopy and electrical transport measurements. Raman spectroscopy measurements of all three types of our graphene samples show negligible D peaks suggesting extremely low disorder36,37,53,54. The width of the Dirac cone in the graphene band structure directly measured by ARPES can provide a more sensitive measure for the long-range coherence of graphene55. Epitaxial graphene exhibits a very sharp, narrow and well-dened Dirac cone indicating very smooth and homogenous graphene lms with extremely high quality. On the other hand, exfoliated and especially CVD graphene transferred to an arbitrary substrate exhibits a rather smeared and broad Dirac cone indicating wrinkled and non-homogenous graphene lms. From the width of the Dirac cone, we can extract a correlation length, which for epitaxial graphene exceeds B50 nm, limited only by the instrument resolution, but is expected to be much longer55. The correlation length for exfoliated and CVD graphene is B13 nm (ref. 55). A similar disparity in the long-range coherence is inferred also from electrical transport and magneto-optical spectroscopy measurements of the graphene carrier mobility. The carrier mobility of epitaxial graphene has been reported to exceed B250,000 cm2 V 1 s 1 close to the theoretical value for disorder-free graphene34,35. On the other hand, the carrier mobilities of exfoliated and CVD graphene transferred to an arbitrary substrate range from a few thousands to tens of thousands dominated by interactions with defects, charge impurities, breaks and ripples. The highest values of up to B200,000 cm2 V 1 s 1 are achieved by minimizing these extrinsic scattering mechanisms including placing the graphene on ultra-smooth substrates such as h-BN46 or suspending it47. Thus, we can also directly investigate the impact of disorder on the dynamic THz response of graphene.

Ultrafast time-resolved THz spectroscopy on graphene. To study the dynamic THz response of graphene, we utilize ultrafast time-resolved THz spectroscopy25,38,39. Our laser system consists of a Ti:Sapphire oscillator (Mira 900-F, Coherent) followed by a Ti:Sapphire regenerative amplier (RegA 9050, Coherent) and produces ultrafast optical pulses with a centre wavelength of 800 nm, a pulse width of B60 fs and a repetition rate of 250 kHz. A portion of the laser beam is quasi-collimated at the sample position with an intensity spot size diameter of

B1,600 mm, and optically injects hot carriers in the graphene sample. A second portion of the laser beam illuminates a low-temperature-grown GaAs photoconductive emitter (Tera-SED 3/4, Gigaoptics)56,57 generating a broadband single-cycle THz pulse which is collimated and focused on the graphene sample with an intensity spot size diameter of B500 mm to probe the dynamic THz response. The transmitted portion of the THz probe is detected by using time-domain electro-optic sampling in a 1-mm-thick ZnTe crystal5860 and a pair of balanced Si photodiodes. The electrical signal is modulated by a mechanical chopper, placed in either the optical pump or the THz probe arm, and recorded by using a conventional lock-in amplier data acquisition technique. The graphene sample is mounted inside a liquid helium continuous ow cryostat (ST-100, Janis) to vary the substrate temperature from 10 to 300 K. The time delays between the optical pump, the THz probe and the sampling pulse are controlled by two motorized stages. All THz optics is surrounded by an enclosure purged with puried nitrogen gas to minimize water vapour absorption. The detection bandwidth of the system is in the range of B0.22.5 THz and the temporal resolution of the measurements is limited by the duration of the THz probe pulse to the sub-picosecond timescale. The experimental error is due primarily to long-term drift of the optomechanical components and the ultrafast Ti:Sapphire laser system, and is estimated not to exceed B5%.

Microscopic theory calculation of the dynamic THz response of graphene. The dynamic THz response due to an optical excitation can be microscopically addressed by evaluating the graphene Bloch equations, which describe the coupled

8 NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617 ARTICLE

where we dene:

tlk:

dynamics of the carrier occupation rlk at the wave vector k in conduction (l c)

and valence band (l v), the microscopic polarization pk, and the phonon

population njq at the momentum q for different optical and acoustic phonon modes j (ref. 5):

ddt rlk

e0 E rkrlk 2I Ovc kpk

1Ginlk Goutlk

: 9

The term tlkGinlk can be written as:

tlkGinlk

Ginlk 1 rlk

Goutlkrlk; 1

Ginlk

Ginlk Goutlk

1 : 10

By accounting only for weak excitations, the scattering rates can be approximated with the equilibrium scattering rates Gin=out;0lk fullling the principle of detailed balance (D.B.):

Goutlk

Ginlk

Gout;0lk

Gin;0lk

D:B: e e e =k T: 11

Thus, equation (10) represents the initial Fermi distribution rl;0k tlkGinlk and the

Boltzmann equation yields the relaxation-time model:

ddt rlk

ddt pk iDok gk

pk iOvck rck rvk

: 2

An optical excitation of the system is considered via the Rabi-frequency Okvc

accounting for interband transitions, where Dok vFk is the transition frequency

and vF is the Fermi velocity. Compared to previous work5, we include a drift term E rkrlk expressing the light-induced intraband transitions, which are crucial for

the THz dynamics driven by the probe pulse. The carriercarrier and carrier phonon interactions are taken into account by a Boltzmann-like equation with time- and momentum-dependent scattering rates Gin=outlk for the carrier occupation and by the diagonal dephasing gk 12 Pl Ginlk Goutlk for the microscopic

polarization. The explicit form of the many-particle contributions and the equation for the phonon dynamics can be found elsewhere5,26,27, for example, in ref. 5 in equations 2224.

The differential THz transmission is given by:

Dt=t t; o

/ a t o

a p;t o

; 3 with the absorption coefcient a(p,t)(o) including both the pump and theprobe pulse and a(t)(o) including only the probe pulse. The absorption a o

I j o

= E0o2A o

is determined by the macroscopic current

density26,27,61:

j o

4e0

m0L2

rlk rl;0ktlk : 12

Within the approximation in equation (11), equation (12) clearly reveals a direct relation between the microscopic scattering rates and the exponential decay of the carrier occupation. However, by tting the numerical data stemming from the full scattering equation (equation (7)), our method for the determination of the carrier scattering time (see Fig. 6b) goes beyond the relaxation-time approximation.

Drude model as an approximation of the microscopic theory. To obtain a simple Drude model from our microscopic approach (equations (1)(6)), we approximate the scattering rate as a constant: G0lk t

G, that is, we neglect the time

and the momentum dependence. By assuming a d-shaped perturbation for the THz probe pulse, the Fourier transform of equation (6) yields:

drlk o

ioex

e0A0

X

k

MvckI pk o

2e0

im0L2

X

k;l

Mllkrlk o

; 4

where Mllk is the optical matrix element, m0 is the free electron mass and L2 is the structure area of the system that cancels out after performing the summation over k. The current contains an interband contribution that is driven by the microscopic polarization pk(o) and an intraband contribution that is determined by the carrier occupation rlk o

. While the interband term has the dominant contribution for

probe pulses at optical frequencies, we consider in this work the intraband term, which has the dominant contribution for probe pulses at THz frequencies. Assuming a weak THz probe pulse, rlk o

can be treated perturbatively:

rlk t

rl;0k t

drlk t

; 5

where rl;0k t

is the pump-induced carrier occupation, while drlk t

describes the

1io G rk

rl;0k: 13

The intraband current density is given by:

j o

2e0

im0L2

X

k;l

Mllkdrlk o

: 14

By assuming a uniform hot-carrier Fermi-Dirac distribution for the carrier occupation, the gradient yields:

rkrlk slek

vF

4kBT sech2 sl kvF eF

=2kBT

; 15

where sl is 1 ( 1) for l c (l v) and eF is the Fermi level. For a constant

scattering rate G and with the optical intraband matrix element Mllk islMek

(sc 1 and sv 1), the intraband current can be evaluated analytically using

equations (13) and (14):

j o

e MA km pc i

weak carrier occupation excited by the THz probe pulse.

To obtain the dynamic THz response from the differential THz transmission spectra, we exploit the fact that ultrafast carriercarrier scattering in graphene forms a uniform hot-carrier Fermi-Dirac distribution within the rst tens of femtoseconds after the excitation3,6,7 and the subsequent dynamics is fully characterized by the temporal evolution of the transient carrier temperature T(t) and the transient Fermi level eF(t). Thus, by iteratively evaluating T(t) and eF(t) on the basis of the numerically calculated carrier dynamics at each time step, we obtain the pump-induced carrier occupation rl;0k t

. For the dynamics of the

probe-induced carrier occupation, we derive from equation (1) and with the ansatz in equation (5) a separate equation of motion yielding:

ddt drlk t

e0 E rkrl;0k t

G0lk t

drlk t

; 6

h i

T ln 1 ee =k T

ln 1 e e =k T

GG o

oG o

16

which corresponds to the Drude model. For a constant scattering rate G and an arbitrary THz frequency, the resulting Drude-like differential THz transmission (see Fig. 6a) is given by:

Dt=t t

pj T0; eF;0

j T t

; eF t

;

; 17 where T0 and eF,0 denote the initial carrier temperature and Fermi level before the arrival of the optical pump pulse at time t 0.

We note that in principle a k-dependent Gk could also be considered in equations (13) and (14) to obtain a more advanced Drude model. However, this would require also an approximate analytical model for Gk. We again emphasize that we go beyond the approximation by using the numerically calculated microscopic scattering rates for the evaluation of the current.

References

1. Malic, E., Winzer, T. & Knorr, A. Efcient orientational carrier relaxation in optically excited graphene. Appl. Phys. Lett. 101, 213110 (2012).

2. Mittendorff, M. et al. Anisotropy of excitation and relaxation of photogenerated charge carriers in graphene. Nano Lett. 14, 15041507 (2014).

3. Breusing, M. et al. Ultrafast nonequilibrium carrier dynamics in a single graphene layer. Phys. Rev. B 83, 153410 (2011).

4. Winnerl, S. et al. Carrier relaxation in epitaxial graphene photoexcited near the dirac point. Phys. Rev. Lett. 107, 237401 (2011).

5. Malic, E., Winzer, T., Bobkin, E. & Knorr, A. Microscopic theory of absorption and ultrafast many-particle kinetics in graphene. Phys. Rev. B 84, 205406 (2011).

6. Brida, D. et al. Ultrafast collinear scattering and carrier multiplication in graphene. Nat. Commun. 4, 1987 (2013).

where G0lk t

Gin;0lk t

Gout;0lk t

is the diagonal contribution stemming from the

Boltzmann-like scattering terms (equation (1)) which are independent of the probe pulse as denoted by the index 0. Non-linear contributions in the probe pulse and non-diagonal terms have been neglected here. Finally, we numerically evaluate the Fourier transform of drlk t

from equation (6) and, thereby, we account for the

fully microscopically determined carrier dynamics in terms of rl;0k t

and G0lk t

.

Thus, our microscopic approach provides access to the Coulomb- and phonon-assisted dynamics induced by the THz probe pulse and is used to obtain the results shown in Figs 25.

Microscopic theory calculation of the carrier scattering time in graphene.

Here, we derive an analytic relation between the microscopic scattering rates and the exponential decay of the carrier occupation. The collision part of the Boltzmann equation, which is given by:

ddt rlk Ginlk 1 rlk

Goutlkrlk; 7

can be rewritten as:

ddt rlk

rlk tlkGinlktlk ; 8

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 9

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617

7. Gierz, I. et al. Snapshots of non-equilibrium Dirac carrier distributions in graphene. Nat. Mater. 12, 11191124 (2013).

8. Winzer, T., Knorr, A. & Malic, E. Carrier multiplication in graphene. Nano Lett. 10, 48394843 (2010).

9. Winzer, T., Mali, E. & Knorr, A. Microscopic mechanism for transient population inversion and optical gain in graphene. Phys. Rev. B 87, 165413 (2013).

10. Song, J. C. W., Tielrooij, K. J., Koppens, F. H. L. & Levitov, L. S. Photoexcited carrier dynamics and impact-excitation cascade in graphene. Phys. Rev. B 87, 155429 (2013).

11. Li, T. et al. Femtosecond population inversion and stimulated emission of dense dirac fermions in graphene. Phys. Rev. Lett. 108, 167401

2012:

12. Pltzing, T. et al. Experimental verication of carrier multiplication in graphene. Nano Lett. 14, 53715375 (2014).

13. George, P. A. et al. Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene. Nano Lett. 8, 42484251 (2008).

14. Strait, J. H. et al. Very slow cooling dynamics of photoexcited carriers in graphene observed by optical-pump terahertz-probe spectroscopy. Nano Lett. 11, 49024906 (2011).

15. Docherty, C. J. et al. Extreme sensitivity of graphene photoconductivity to environmental gases. Nat. Commun. 3, 1228 (2012).

16. Jnawali, G., Rao, Y., Yan, H. & Heinz, T. F. Observation of a transient decrease in terahertz conductivity of single-layer graphene induced by ultrafast optical excitation. Nano Lett. 13, 524530 (2013).

17. Shi, S.-F. et al. Controlling graphene ultrafast hot carrier response from metal-like to semiconductor-like by electrostatic gating. Nano Lett. 14, 15781582 (2014).

18. Frenzel, A. J. et al. Observation of suppressed terahertz absorption in photoexcited graphene. Appl. Phys. Lett. 102, 113111 (2013).

19. Tielrooij, K. J. et al. Photoexcitation cascade and multiple hot-carrier generation in graphene. Nat. Phys. 9, 248252 (2013).

20. Jensen, S. A. et al. Competing ultrafast energy relaxation pathways in photoexcited graphene. Nano Lett. 14, 58395845 (2014).

21. Frenzel, A. J., Lui, C. H., Shin, Y. C., Kong, J. & Gedik, N. Semiconducting-to-metallic photoconductivity crossover and temperature-dependent Drude weight in graphene. Phys. Rev. Lett. 113, 056602 (2014).

22. Bistritzer, R. & MacDonald, A. H. Electronic cooling in graphene. Phys. Rev. Lett. 102, 206410 (2009).

23. Tse, W.-K. & Das Sarma, S. Energy relaxation of hot Dirac fermions in graphene. Phys. Rev. B 79, 235406 (2009).

24. Song, J. C. W., Reizer, M. Y. & Levitov, L. S. Disorder-assisted electron-phonon scattering and cooling pathways in graphene. Phys. Rev. Lett. 109, 106602 (2012).

25. Mihnev, M. T. et al. Electronic cooling via interlayer Coulomb coupling in multilayer epitaxial graphene. Nat. Commun. 6, 8105 (2015).

26. Malic, E., Winnerl, S. & Knorr, A. Graphene and Carbon Nanotubes: Ultrafast Optics and Relaxation Dynamics (Wiley-VCH, 2013).

27. Knorr, A., Hughes, S., Stroucken, T. & Koch, S. W. Theory of ultrafast spatio-temporal dynamics in semiconductor heterostructures. Chem. Phys. 210, 2747 (1996).

28. Graham, M. W., Shi, S.-F., Ralph, D. C., Park, J. & McEuen, P. L. Photocurrent measurements of supercollision cooling in graphene. Nat. Phys. 9, 103108 (2013).

29. Betz, A. C. et al. Supercollision cooling in undoped graphene. Nat. Phys. 9, 109112 (2013).

30. Ando, T. Screening effect and impurity scattering in monolayer graphene.J. Phys. Soc. Jpn 75, 074716 (2006).31. Das Sarma, S., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407 (2011).

32. Tan, Y.-W. et al. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 99, 246803 (2007).

33. Chen, J.-H. et al. Charged-impurity scattering in graphene. Nat. Phys. 4, 377381 (2008).

34. Berger, C. et al. Electronic connement and coherence in patterned epitaxial graphene. Science 312, 11911196 (2006).

35. de Heer, W. A. et al. Large area and structured epitaxial graphene produced by connement controlled sublimation of silicon carbide. Proc. Natl Acad. Sci. USA 108, 1690016905 (2011).

36. Hao, Y. et al. The role of surface oxygen in the growth of large single-crystal graphene on copper. Science 342, 720723 (2013).

37. Lee, S., Lee, K. & Zhong, Z. Wafer scale homogeneous bilayer graphene lms by chemical vapor deposition. Nano Lett. 10, 47024707 (2010).

38. Schmuttenmaer, C. A. Exploring dynamics in the far-infrared with terahertz spectroscopy. Chem. Rev. 104, 17591779 (2004).

39. Baxter, J. B. & Guglietta, G. W. Terahertz spectroscopy. Anal. Chem. 83,

43424368 (2011).

40. Orlita, M. et al. Carrier scattering from dynamical magnetoconductivity in quasineutral epitaxial graphene. Phys. Rev. Lett. 107, 216603 (2011).

41. Xu, S. et al. Energy dependence of electron lifetime in graphiteobserved with femtosecond photoemission spectroscopy. Phys. Rev. Lett. 76, 483 (1996).

42. Gonzlez, J., Guinea, F. & Vozmediano, M. A. H. Unconventional quasiparticle lifetime in graphite. Phys. Rev. Lett. 77, 3589 (1996).

43. Martin, J. et al. Observations of electron-hole puddles in graphene using a scanning single-electron transistor. Nat. Phys. 4, 144148 (2008).

44. Zhang, Y. B., Brar, V. W., Girit, C., Zettl, A. & Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Nat. Phys. 5, 722726 (2009).

45. Jung, S. Y. et al. Evolution of microscopic localization in graphene in a magnetic eld from scattering resonances to quantum dots. Nat. Phys. 7, 245251 (2011).

46. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722726 (2010).

47. Du, X., Skachko, I., Barker, A. & Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nat. Nanotechnol. 3, 491495 (2008).

48. Hass, J. et al. Why multilayer graphene on 4H-SiC(0001) behaves like a single sheet of graphene. Phys. Rev. Lett. 100, 125504 (2008).

49. Sprinkle, M. et al. First direct observation of a nearly ideal graphene band structure. Phys. Rev. Lett. 103, 226803 (2009).

50. Sun, D. et al. Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy. Phys. Rev. Lett. 101, 157402 (2008).

51. Sun, D. et al. Spectroscopic measurements of interlayer screening in multilayer epitaxial graphene. Phys. Rev. Lett. 104, 136802 (2010).

52. Chang, Y.-C., Liu, C.-H., Liu, C.-H., Zhong, Z. & Norris, T. B. Extracting the complex optical conductivity of mono- and bilayer graphene by ellipsometry. Appl. Phys. Lett. 104, 261909 (2014).

53. Faugeras, C. et al. Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study. Appl. Phys. Lett. 92, 011914 (2008).

54. Kunc, J., Hu, Y., Palmer, J., Berger, C. & de Heer, W. A. A method to extract pure Raman spectrum of epitaxial graphene on SiC. Appl. Phys. Lett. 103, 201911 (2013).

55. Baringhaus, J. et al. Exceptional ballistic transport in epitaxial graphene nanoribbons. Nature 506, 349354 (2014).

56. Katzenellenbogen, N. & Grischkowsky, D. Efcient generation of 380 fs pulses of THz radiation by ultrafast laser pulse excitation of a biased metal-semiconductor interface. Appl. Phys. Lett. 58, 222224 (1991).

57. Tani, M., Matsuura, S., Sakai, K. & Nakashima, S. Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs. Appl. Opt. 36, 78537859 (1997).

58. Wu, Q. & Zhang, X. C. Free-space electro-optic sampling of terahertz beams. Appl. Phys. Lett. 67, 35233525 (1995).

59. Wu, Q. & Zhang, X. C. Ultrafast electro-optic eld sensors. Appl. Phys. Lett. 68, 16041606 (1996).

60. Nahata, A., Weling, A. S. & Heinz, T. F. A wideband coherent terahertz spectroscopy system using optical rectication and electro-optic sampling. Appl. Phys. Lett. 69, 23212323 (1996).

61. Kira, M., Hoyer, W. & Koch, S. W. Microscopic theory of the semiconductor terahertz response. Phys. Stat. Sol. (b) 238, 443450 (2003).

Acknowledgements

We appreciate Xiaohan Wang and Rodney S. Ruoff for providing the single-crystal CVD graphene (sCVDG) samples. M.T.M. and C.J.D. thank Steve Katnik for technical assistance with the ultrafast laser system. F.K., T.W., E.M. and A.K. thank Roland Jago (Research Training Group 1558) for fruitful discussions. The work at the University of Michigan and the Georgia Institute of Technology was supported in part by the National Science Foundation (NSF) Materials Research Science and Engineering Center (MRSEC) under grant DMR-0820382. The work at the University of Michigan was also supported in part by the NSF Center for Photonic and Multiscale Nanomaterials (CPHOM) under grant DMR-1120923 and the NSF CAREER Award (ECCS-1254468). T.W. and A.K. acknowledge partial nancial support from the Deutsche Forschungsgemeinschaft (DFG) through SPP-1459 and Sfb 787. E.M. acknowledges partial nancial support from the European Commission (EC) under the Graphene Flagship programme (contract No. CNECT-ICT-604391) and the Swedish Research Council (VR). C.B. acknowledges partial nancial support from the EC under the Graphene Flagship programme (contract No. CNECT-ICT-604391). This work was performed in part at the Lurie Nanofabrication Facility (LNF), a member of the National Nanotechnology Infrastructure Network (NNIN), which is supported in part by the NSF.

Author contributions

M.T.M. and C.J.D. performed and analysed the ultrafast time-resolved THz spectroscopy experiments. F.K., T.W., E.M. and A.K. developed the microscopic theory. S.L., C.-H.L. and Z.Z. provided the polycrystalline CVD graphene (pCVDG) samples. C.B. and

10 NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications

NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11617 ARTICLE

How to cite this article: Mihnev, M. T. et al. Microscopic origins of the terahertz carrier relaxation and cooling dynamics in graphene. Nat. Commun. 7:11617doi: 10.1038/ncomms11617 (2016).

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecommons.org/licenses/by/4.0/

W.A.d.H. provided the multilayer epitaxial graphene (MEG) samples. M.T.M. and T.B.N. with input from other authors wrote the paper. All authors discussed the results.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

Web End =http://www.nature.com/ http://www.nature.com/naturecommunications

Web End =naturecommunications

Competing nancial interests: The authors declare no competing nancial interests.

Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/

Web End =http://npg.nature.com/ http://npg.nature.com/reprintsandpermissions/

Web End =reprintsandpermissions/

NATURE COMMUNICATIONS | 7:11617 | DOI: 10.1038/ncomms11617 | http://www.nature.com/naturecommunications

Web End =www.nature.com/naturecommunications 11