Emergence of coherence in the charge-density wave state of 2H-NbSe2

Abstract

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature T_cdw . Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe₂ intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at T_cdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in 'pseudogap' states.

ARTICLE

Received 28 May 2014 | Accepted 19 Jan 2015 | Published 17 Feb 2015

U. Chatterjee1,2, J. Zhao2,3, M. Iavarone4, R. Di Capua4, J.P. Castellan1,5, G. Karapetrov6, C.D. Malliakas1,7, M.G. Kanatzidis1,7, H. Claus1, J.P.C. Ruff8,9, F. Weber1,5, J. van Wezel1,10, J.C. Campuzano1,3, R. Osborn1,M. Randeria11, N. Trivedi11, M.R. Norman1 & S. Rosenkranz1

A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a nite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We nd that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-dened amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks

the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase uctuations in strongly coupled CDW systems and provide insights into the signicance of phase incoherence in pseudogap states.

1 Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA. 2 Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA. 3 Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA. 4 Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA. 5 Institute of Solid State Physics, Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany.

6 Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA. 7 Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA. 8 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA. 9 CHESS, Cornell University, Ithaca, New York 14853, USA. 10 Institute for Theoretical Physics, University of Amsterdam, Tyndall Avenue, 1090 GL Amsterdam, The Netherlands. 11 Department of Physics, Ohio State University, Columbus, Ohio 43210, USA. Correspondence and requests for materials should be addressed to U.C. (email: mailto:[email protected]

Web End [email protected] ) or to S.R. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms7313 OPEN

Emergence of coherence in the charge-density wave state of 2H-NbSe2

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The formation of charge-density waves (CDWs) and superconductivity are archetypical examples of symmetry breaking in materials, which are characterized by a

complex order parameter. In clean weak-coupling systems, the formation of the amplitude and the establishment of macroscopic phase coherence are known to occur simultaneously at the transition temperature1,2, but the situation may be dramatically different at strong coupling or in the presence of disorder39. Such systems generally exhibit short correlation lengths and a transition temperature that is greatly suppressed from the expected mean-eld value. This opens the possibility for a gap in the electronic spectra to persist in the absence of long-range order over a large temperature range and the opportunity to study this so-called pseudogap behaviour, which has been observed in a wide range of systems from high-temperature super-conductors1012 to disordered superconducting thin lms13 and cold atoms14, in a simple system.

In the CDW state below the transition temperature Tcdw, a

modulation appears in the density of conduction electrons that is accompanied by a periodic lattice distortion1. Although this lattice distortion leads to an increase in the elastic energy, there is a net gain in the free energy of the system due to a reduction in the energy of the electrons via the opening of an energy gap D.

The CDW state is characterized by the order parameter dr(r) r(r) rav(r) r0cos[q.r f(r)], where q is the CDW

wave vector, rav the average charge density, r0 the amplitude of

the CDW order parameter, which is proportional to the energy gap D, and f the phase of the CDW, that is, the location of the charge modulation with respect to the underlying lattice. It is straightforward to realize that there are two ways to destroy the order parameter(i) by reducing the amplitude r0 through excitations across the energy gap and/or (ii) by randomization of the phase f either through thermal or quantum uctuations.

Similar to the case of Bardeen-Cooper-Schrieffer (BCS) transitions in clean superconductors, the expectation value, of dr in weakly coupled CDW systems vanishes via (i), as, in general, (ii) is not relevant due to the large magnitude of the phase stiffness energy1,3. However, strongly coupled CDW systems can be susceptible to strong phase uctuations due to their shorter coherence lengths1,47.

To explore this systematically as a function of disorder in a material with a simple electronic and crystal structure, we investigate pristine and intercalated (with Co and Mn ions) 2H-NbSe2 samples, where CDW ordering involves strong electronphonon coupling15,16. In our investigations, we employ a combination of experimental probes. Scanning tunnelling microscopy (STM) and X-ray diffraction (XRD) are used to measure the real and momentum space structure of the CDW order, respectively. Angle-photoemission spectroscopy (ARPES) is employed to investigate the presence of an energy gap in the electronic spectra, which is proportional to the amplitude of the order parameter, and to infer the existence or

x=0 x=0.0045 Mn

x=0

X-ray intensity (a.u.)

ARPES intensity (a.u.)

Intercalation

26 K30 K35 K40 K45 K50 K60 K

Tcdw

Tcdw

x=0, T=26 K x=0.0009, T=23 K x=0.0045, T=18 K x=0.0165, T=18 K x=0.0192, T=18 K

10

20

30

40

0.10 0.00

0.10 0.00

T (K) Energy (eV)

Energy (eV)

T (K) x

X-ray intensity (a.u.)

x=0, T=1.5 K x=0.0045,

T=1.5 K (X 235)

x=0, T=35 K (X 30)

1.0

0.0

x=0

Spectral weight

1.0

0.0

Tcdw

xc

4.28

4.32

4.36

4.40

30

50

0.000

0.010

0.020

K (RLU)

Figure 1 | CDW phase transition for pure and intercalated 2H-NbSe2 samples. (a) Intensity of the CDW superstructure peak as a function of T for an x 0 (green) and x 0.0045 (Mn-intercalated, red). Dotted lines are guides to the eye, indicating the growth of the CDW order parameter.

Arrows mark the estimated Tcdw, which is the interpolation of the linear part to zero. (b) FF divided EDCs for various temperatures at the momentum location shown by the red dot in Fig. 2d. (c) FF divided EDCs for different x at the lowest measured temperatures. The sample with x 0.0165 is

intercalated with Co, the others are intercalated with Mn. The corresponding momentum location is shown by the pink dot in Fig. 2d. The red dashed line in b and c shows the energy location of the peak (for ToTcdw and xoxc) and kink (for T4Tcdw or x4xc) in the EDCs, while the black line is the chemical

potential. (d) Intensity prole of CDW superstructure peaks along (0,K,0) for x 0, 0.0045 (intercalated with Mn) at 1.5 K and for x 0 at T 35 K.

The intensities have been normalized to that of the (0,4,4) Bragg peak and have subsequently been multiplied by the factors displayed in the legend to make them all visible on the same scale. (e,f) Normalized spectral weight associated with the coherence peak, following the procedure as described below, as a function of T for x 0 and as a function of x at the lowest measured temperature. The black dots correspond to Tcdw for x 0 and xcB0.013,

respectively. For x 0, the coherent spectral weight was obtained as the remaining integrated spectral intensity after subtracting the highest measured

temperature (60 K) as background and dividing by the value obtained at the lowest measured temperature. We adopt the same procedure, as for the normalized spectral weight as a function of T, for its x dependence by considering the spectrum at the highest value of x as the background and dividing the coherent spectral weight at the lowest measured temperature for each x by the one for x 0.

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disappearance of phase coherence of the order parameter through the presence or absence of sharp coherence peaks in the ARPES spectra. Furthermore, Tcdw is determined by tracking the onset of the CDW order parameter in XRD and the CDW-induced anomaly in transport measurements. Our main results from this extensive set of measurements are as follows. First, the temperature Tcdw, above which CDW phase coherence is destroyed, is suppressed with intercalation x and vanishes at a quantum phase transition (QPT) at xc. Second, the CDW state below Tcdw(x) and xoxc has an energy gap and sharp electronic

excitations. Finally, the CDW energy gap survives above Tcdw(x)

and x4xc in the state, which has only short-range CDW correlations, but the electronic excitations are no longer well-dened.

ResultsXRD and transport. Previous investigations of the CDW transition in 2H-NbSe2 using neutron and XRD have shown that a superstructure with incommensurate wave vector q (1 d)a*/3,

where a* 4p/O3a, lattice parameter a 3.44 and dB0.02,

appears below Tcdw 33 K (ref. 17). However, the origin of the

CDW and the exact nature of the Nb atom motion involved were only recently established using inelastic X-ray scattering16 and superspace crystallography18, respectively. To explore the evolution of the CDW transition with increasing disorder, we use synchrotron XRD and transport measurements on a number of intercalated samples (for details, see Methods section and Supplementary Fig. 1). Figure 1a shows the intensity of the incommensurate superstructure peaks, which is proportional to the square of the CDW order parameter. For the undoped compound, the superstructure intensity increases continuously from the temperature-independent background present above Tcdw, as expected for a second-order phase transition. Moreover, the width of this superstructure peak, which is a measure of the inverse of the CDW correlation length, becomes resolution limited below Tcdw, implying the presence of long-range order (Fig. 1d). For intercalated samples, the XRD superstructure peak exhibits a reasonably sharp onset of intensity (Fig. 1a) as a

function of temperature, but its width (Fig. 1d) is not resolution limited even at our lowest measured temperature. This suggests that the process of intercalation gives rise to disorder that has impacts on the CDW state, consistent with previous work on 2H-NbSe2 and other dichalcogenide systems1922. We can nevertheless still identify a CDW transition temperature, even in the intercalated, disordered samples, from a linear extrapolation of the temperature dependence of the superstructure intensity, as indicated in Fig. 1a.

From our XRD data on samples with different concentrations x of intercalant ions, we observe that Tcdw is quickly suppressed (Fig. 1a), as x is increased and beyond xc the superstructure peaks become very broad, indicating that the CDW order becomes of short range. Qualitatively, similar attributes have been identied in resistivity measurements as well: the CDW-induced anomaly in the resistivity becomes weaker with increasing x, shifts to lower temperatures and eventually disappears beyond xc (see ref. 22,

Supplementary Note 1 and Supplementary Fig. 2). We note that the effect of doping on the CDW is the same irrespective of whether the intercalating ion is Mn or Co as observed by STM, discussed later. The disappearance of Tcdw naturally points to the existence of a QPT at xc. Although our measurements show clear signatures of the change in the CDW order across xc, as expected at a QPT, we have not been able to characterize this QPT in greater detail due to the difculty in synthesizing samples with dense-enough x-values around xc.

Angle-resolved photoemission. To elucidate the evolution of the electronic structure across Tcdw and xc, we now focus on the

T- and x-dependent ARPES measurements. We have taken data over a large region of momentum space in the rst Brillouin zone (Supplementary Note 2 and Supplementary Fig. 3a). However, we will predominantly be concerned with ARPES data as a function of energy at specic momentum values close to the high-symmetry KM line (Fig. 2d). The reason for choosing this particular direction is that the CDW gap is maximum along it and hence easily detectable by ARPES23,24. The Fermi function (FF) at corresponding temperatures is divided out to better

0.08 0.04 0.00

[afii9796]

K y

ARPES intensity (a.u.)

Cut 2

Cut 1

K

M

Kx

x=0, T=26 K Tcdw=32.2 K

x=0, T=50 K Tcdw=32.2 K

x=0.0165T=18 K,Tcdw=0 K

Co intercalation

0.10 0.00 0.10 0.00

Figure 2 | Electronic dispersion exhibiting back bending. (a,b) FF divided EDCs as a function of momentum k along cut 1 (dened in d), which is close to the KM line, for x 0, and at T 26 K and T 50 K, respectively. Red EDCs are associated with momenta k inside the inner Fermi surface

(centred around the K point) starting from the brown dot (shown in d) to the red dot along cut 1, green ones to the remaining k points along cut 1 between the red and black dots. (c) FF divided EDCs for x 0.0165 (Co intercalation) at T 18 K, along cut 2, which is along KM, as shown in d. Red EDCs

correspond to k starting from the brown dot inside the inner Fermi surface (centred around the K point) to the pink dot along cut 2, green ones tothe remaining k points between the pink and black dots. Blue curves indicate EDCs at the Fermi momentum, the black dots show the locations of the peak and kinks of the EDCs and the black dashed lines are at the chemical potential. The method for locating the black dots is described in Supplementary Note 5 and Supplementary Fig. 7. (d) Fermi surface plot based on the tight-binding t to the band structure of 2H-NbSe2 in ref. 24. Black and red arrows denote outer and inner Fermi surface barrels.

Energy (eV)

Energy (eV)

Energy (eV)

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visualize the existence of the gap D from such energy distribution curves (EDCs)25,26. In Fig. 1b, we display the spectral function obtained from the FF-divided EDCs as a function of T for x 0

(raw data, shown in the Supplementary Fig. 3b,c, agree with previous ARPES studies23,24). At the lowest temperature (T 26 KoTcdw 33 K), the spectrum exhibits a coherence peak

at an energy below the chemical potential m, signalling a non-zero value of the gap. Unlike superconducting or one-dimensional CDW systems, we nd that this gap is centred at positive energies, that is, above m. This particlehole asymmetry is clearly evident from the FF-divided ARPES data shown in Fig. 1b, which has a negative slope at m. Consequently, the estimation of the energy gap based on the leading edge or by symmetrizing the spectra around m23,24 underestimates the size of the gap. Given that the minimum of the FF-divided ARPES intensity occurs above m, we can not determine the exact magnitude of the energy gap, but can only establish its existence and that, in agreement with recent STM data27, it is larger than estimated by symmetrization and leading-edge analysis in previous ARPES studies. The presence of a particlehole asymmetric gap is an indication that Fermi surface nesting is not important for driving the CDW in 2H-NbSe2. This is supported by recent measurements of soft phonon modes using inelastic X-ray scattering16. However, differing conclusions about the role of nesting have been offered in previous ARPES studies2830.

With increase in temperature, the intensity of the coherence peak is reduced, but its energy remains the same. Finally, above Tcdw, this peak disappears and remarkably, the spectra become almost T independent. Although the spectra for T4Tcdw do not

have a discernable peak, they do have a well-dened kink, that is, a sharp change of slope. Closer inspection of Fig. 1b reveals that the location of this kink in the spectra above Tcdw is similar to that of the coherence peaks below Tcdw, as shown by the red

dotted line. Although we cannot obtain the exact magnitude of the energy gap as a function of T through Tcdw, the fact that peak/

kink structure of the ARPES spectra lies below the chemical potential clearly demonstrates that the energy gap persists for T4Tcdw. On the other hand, there is a loss of phase coherence as indicated by the absence of a peak in these spectra. Our ARPES data on 2H-TaS2 exhibits similar features (Supplementary Note 3 and Supplementary Fig. 5), which in turn suggests that these features are generic to quasi two-dimensional (2D) CDW systems. We have also seen similar results for other values of x as well in 2H-NbSe2 (Supplementary Fig. 4). Therefore, Tcdw can be identied as the transition from an incoherent, gapped electronic state to a coherent one. This implies that although the CDW order parameter vanishes above Tcdw, its amplitude

does not.

In Fig. 1e, we display the normalized spectral weight as a function of T (the details of the normalization procedure is described in the caption of Fig. 1). One can clearly observe that it decays monotonically with T and vanishes above Tcdw. The x

dependence of the spectra (Fig. 1c) through xc resembles the T dependence through Tcdw, for example, the spectrum at the lowest measured temperature progressively loses its peak with increasing x and eventually becomes featureless for x4xc. It can

readily be seen (Fig. 1f) that the x dependence of the normalized coherent spectral weight follows a similar trend as the T dependence, that is it steadily goes down with increasing x and vanishes above xc. However, a nite energy gap persists for all x, even beyond xc. In other words, there exists an extended region in the (x,T) phase plane of 2H-NbSe2 systems where the spectral function has an energy gap but no coherence.

We now look at the details of the (x,T) phase plane in the context of pairing. As a direct consequence of particlehole coupling, the electronic dispersion, that is, the relation between

electronic energy and momentum, is altered from the one in the normal state. In the CDW state with ordering wave vector q, an electronic state with momentum k gets coupled to another with momentum k q, and the dispersion is modied to Ek (ek

ek q)[14(ek ekq)2 Dk2], where Dk is the energy gap and ek

is the normal-state dispersion1,6. The dispersion of the lower branch deviates from ek, as ek approaches ek q, reaches a

maximum when ek ek

q and then bends back to follow ek q

instead (Supplementary Fig. 6 and Supplementary Note 4). This bending back effect, commonly known as the Bogoliubov dispersion2, occurs in the superconducting state due to electronelectron pairing and has been directly observed by ARPES in cuprates3133. As shown in Fig. 2a, by monitoring the peak positions and kinks of the EDCs (see Supplementary Note 5 and Supplementary Fig. 7 for details), it is easy to see that the electronic dispersion below Tcdw for x 0 has the expected

bending back behaviour. In addition, quite remarkably, the bending back of the dispersion is visible even when the CDW is short ranged(i) in the x 0 sample at TB50 K4Tcdw in Fig. 2b

and (ii) an intercalated sample with xB0.01654xc at T 18 K in

Fig. 2c. The presence of a CDW gap below and above Tcdw along

with the persistence of a back bending feature in the electronic dispersion naturally suggests that the electronhole pairs induced by the CDW persist above Tcdw and beyond xc. We point out that similar observations have been made in the pseudogap phase of cuprates where, just as in the superconducting state, a Bogoliubov dispersion was found to exist above Tc, which was considered as evidence for pairing without phase coherence34. Taking into consideration of all these observations, one can realize that for T4Tcdw or x4xc in the (x,T) phase plane of 2H-NbSe2, there are

electronhole pairs without coherence, which in turn implies that CDW order parameter vanishes because of phase incoherence.

Scanning tunnelling microscopy. So far, we have concentrated on the structure and the relevant electronic excitations associated with the CDW order in momentum space. To visualize them in real space, we have performed high-resolution STM measurements as a function of T and x as shown in Fig. 3, where the upper panels are STM topographic images, each of which covers an area of 18.5 nm by 18.5 nm, the second row shows Fourier-ltered images and the bottom panels are 2D-Fourier transform (FT) images. Figure 3a corresponds to the x 0 sample at

T 4.2 K. The almost perfect hexagonal lattice pattern conrms

that our pristine samples are of very high quality and practically defect free. A close inspection of the topographic image clearly reveals the presence of a locally commensurate CDW pattern that repeats after every third lattice spacing; however, phase slips lead to the slight incommensuration observed in XRD as well as in the FT of the STM image shown in Fig. 3i35. The long-range order of both the lattice as well as the CDW is reected in the sharp peaks observed in the FT image, where the outermost set of the six strong peaks correspond to the Bragg peaks of the underlying lattice, and the innermost ones at B1/3 the wave vector correspond to the lowest-order CDW superlattice peaks (Figs 3 and 4). Our topographic as well as FT images of pure samples are consistent with earlier STM measurements27,3638. Although the CDW order is well visible in the topographic image of the pure sample, the CDW corrugation in NbSe2 is very small, and to enhance the subtle features due to CDW modulations we show Fourier-ltered images in the middle row, panels eh of Fig. 3. These images are obtained by applying a mask to the FT image that only retains the region around the lowest-order CDW peaks, for example, the region between the dash-dotted circles shown in Fig. 3i, and transforming back to real space. This results in images of the CDW maxima and allows a direct visualization of the phase

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x=0 T=4.2 K

x=0.0045Mn intercalation T=4.2 K

x=0.0045Mn intercalation T=77 K

x=0.04Co intercalation T=4.2 K

5 nm

Figure 3 | STM data on pristine and intercalated 2H-NbSe2 samples. STM topographic images of (a) x 0 at 4.2 K, (b,c) x 0.0045 (Mn intercalated) at

4.2 and 77 K, respectively, and (d) x 0.04 (Co intercalated) at 4.2 K. The scan areas are 18.5 nm 18.5 nm. The images have been acquired at

V 50 mV and I 100 pA. The total z-deection is 0.6 in a,c, 1.0 in b and 1.2 in d. (eh) Fourier-ltered images obtained by retaining only the

region around the lowest-order CDW peak in the FT images, for example, the region 0.2qBRAGGoqo0.45qBRAGG indicated by the white dash-dotted

circles in i, and transforming back to real space. The dashed white circles in these ltered images show examples of patches with well-dened CDW structures in the intercalated samples. (il) 2D-FTs of the topographic images in ad. The white circles indicate the position of one of the lowest-order Bragg peaks at qBRAGG; blue circles in ik atB1/3 qBragg indicate the position of the lowest-order CDW superlattice peaks. In samples with high CDW disorder, the FT does not show clear CDW peaks but rather a ring-like structure, as indicated by the blue circles in l for Co0.04NbSe2.

x=0.0045

(Mn intercalation) x=0.04

(Co intercalation)

1.0

3

x=0, T=4.2 K x=0.0045, T=4.2 K x=0.0045, T=77 K x=0.04, T=4.2 K

Normalized FT intensity

x=0, T=4.2 K

x=0.0045, T=4.2 K

x=0.0045, T=77 K

x=0.04, T=4.2 K

Normalized FT intensity

0.5q/qBRAGG q/qBRAGG

1.0 0.20 0.25 0.30 0.35 0.40 0.45

2

0.5

1

0

0.0

Figure 4 | STM FT proles. (a) Line proles of the FT images in Fig. 3il along one of the lattice wave vector directions. The curves have been shifted for clarity. The intensity of each prole has been normalized to the intensity of the Bragg peak. The CDW peak at q q

BRAGG/3 has been tted with a Gaussian and the t is superimposed on the FT line prole for each curve. (b) Gaussian ts of the CDW peaks in a normalized to the CDW peak of pure NbSe2.

and CDW domain structure. To ensure that the ltered images are free from possible artefacts due to the ltering procedure, we compared images obtained using different sizes of the ltering mask. The main features of the ltered images remain the same regardless of the lter used. The long-range order and phase coherence of the CDW in the pure sample is clearly reected in its Fourier-ltered image, where an almost perfect CDW lattice is obtained (Fig. 3e). STM topographic images of intercalated samples reveal the presence of defects, both at the surface and beneath the surface, as bright spots. In the sample with nominal doping x 0.0045 (Fig. 3b), the local density of defects in the

topographic image is in the range 0.006oxo0.0075. In contrast to the pure sample, the Fourier-ltered image (Fig. 3f) reveals that coherent CDW order does not exist uniformly over the entire sample, but only in the form of patches. As a demonstration, we have indicated one such region with locally well-dened CDW order in the Fourier-ltered image (Fig. 3f) by a dashed circle. In other words, CDW order in the intercalated sample with x 0.0045 lacks long-range translational order, which in turn

supports the observation, as in Fig. 1, that the CDW order in this intercalated sample is not long range. Consistent with this, the CDW peaks of the FT image in Fig. 3j are broader than those of

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Peak and gap (ARPES) Gap (ARPES)

FT peak in LR CDW state (STM) FT peak in SR CDW state (STM)

Tcdw (transport)

T(K)

60

50

40

30

20

10

0

TCDW

xC

0.000

0.005

0.010

0.015

Intercalation concentration x

Figure 5 | Intercalation versus temperature diagram of CDW correlations in 2H-NbSe2. Overview plot of the results from ARPES, STM, transport and

XRD measurements. ARPES data points are shown by red squares. Filled squares correspond to the simultaneous presence of the coherence peak and an energy gap, empty ones to the presence of only an energy gap. STM data points are shown by blue circles, indicating the presence of a CDW. Bow ties denote Tcdw, obtained from transport measurements, marking the transition from a long-range-ordered CDW state to a short-range-ordered state as a function of x and T. Extrapolation of this phase line leads to xcB0.013, beyond which there is only short-range order at all measured temperatures. The superconducting transitions, observed for all samples except the very highest doping as listed in Supplementary Table 1, are not shown in this diagram.

the pure sample (Figs 3i and 4). As x is increased to 0.04, the size of the patches with coherent CDW order (Fig. 3d,h) is further reduced and the peaks in the FT become even broader, leading to a ring-like structure (Fig. 3l). In Fig. 4a, we present the line proles of the FT in Fig. 3il along the atomic wave vectors as a function of doping, and in Fig. 4b we display the Gaussian ts to these CDW peaks (Supplementary Note 6), from which we clearly see the broadening of the CDW peak with doping. These results simply relate to the fact that the CDW coherence length decays with increasing x and eventually becomes short range, consistent with our ARPES and XRD observations. We note that these observations are independent of the intercalating ion, see Supplementary Note 7 and Supplementary Figs 8 and 9. STM observations of domain-like structures having well-dened CDW order, similar to those shown in Fig. 3f, have been reported in a number of disordered dichalcogenide systems39,40.

We now focus on STM data for T4Tcdw (Fig. 3c,g,k) corresponding to the x 0.0045 sample at T 77 K4Tcdw 20

K. Although weak in intensity, well-dened CDW modulations survive in various regions, as best seen in the Fourier-ltered image Fig. 3g, and the FT image (Fig. 3k) still clearly shows broad CDW peaks, indicating the persistence of short-range CDW correlations to temperatures well above Tcdw. In the pure sample,

we observe very weak CDW modulations localized around the impurities up to 45 K (Supplementary Fig. 10a). Given the small amount of defects and the weak modulation, only very weak CDW peaks are observed in the 2D-FT images. We do not observe any sign of CDW modulations in real space or in 2D-FT at 77 K (Supplementary Fig. 10b). This can be understood by realizing that the STM images represent a time-averaged view of the sample, and that in regions far from any pinning defects the signatures of short-range order are averaged out by dynamic uctuations.

DiscussionThe phase diagram of the CDW correlations in intercalated 2H-NbSe2 shown in Fig. 5 summarizes our results (for simplicity, the superconducting transition observed in all but the very highest doped sample are not shown in this gure). The squares are based on the ARPES spectra that are: (1) coherent and gapped (solid squares) within the triangular region where the CDW order is present; and (2) incoherent and gapped (empty squares) outside of this triangle, indicating short-range CDW order instead. The circles correspond to FTSTM datasolid ones within the triangular region where long-range CDW order exist and empty ones outside where CDW order is of short range. The bow ties indicate the CDW transition temperature determined from transport measurements and are included for completeness.

This phase diagram closely resembles that of the transition from the superconducting to the pseudogap state in cuprates41, and that of the superconducting to insulating transition in disordered systems9,13,42. The experimental observation of the persistence of an energy gap and the disappearance of single-particle coherence across classical or QPTs seems to be a common feature of these entirely different systems. The enigmatic pseudogap phase of cuprates is in many ways the most complicated of these examples, with close proximity to a Mott insulator and various competing orders. In this respect, the simplicity of 2H-NbSe2 studied in this paper makes it possible to focus on a single-order parameter, associated with CDW formation, and examine in detail how the spectroscopic signatures evolve across the QPT where this ordering is destroyed.

Methods

Intercalated 2H-NbSe2 samples. Cobalt (Co) and manganese (Mn) have been intercalated in pristine 2H-NbSe2 single crystals by adopting the procedures explained in refs 43,44. XRD patterns show that our intercalated samples have the same structure as the pristine 2H-NbSe2 samples. The concentration of Co and Mn were determined from energy-dispersive X-ray microprobe analysis measurements. While performing energy-dispersive X-ray microprobe analysis on intercalated samples, we have randomly chosen different regions of the samples and found that the atomic concentrations of Co and Mn remain almost the same, meaning there is no evidence for clustering on the length scale of 100 nm. This is substantiated by previous extended x-ray absorption ne structure (EXAFS) measurements45.

The superconducting critical temperature (Tc) for pristine 2H-NbSe2 samples is B7.2 K and it was previously shown that Tc gets suppressed due to intercalation46. Our magnetization versus temperature measurements for different samples show sharp superconducting transitions (Supplementary Fig. 1), which further support that our intercalated samples are homogeneous. Supplementary Table 1 lists details of all the samples used in this study.

Transport measurements. The temperature-dependent resistivity of the single crystals was measured using regular four-terminal transport measurement technique performed with a Physical Property Measurement System by Quantum Design equipped with external device control option. Keithley 6220 current source and Keithley 2182 nanovoltmeter were used to apply a DC current and measure the voltage drop, respectively.

XRD measurements. Synchrotron XRD experiments were performed at the Advanced Photon Source, Argonne National Laboratory. Data were taken in transmission geometry with 22.3 keV X-rays on the 11-ID-D beamline, using a Ketek Silicon Drift point detector, and on the high-energy station of beamline 6-ID-D, with 80 keV X-rays and a Pilatus 100 K area detector. In both setups, the samples were mounted on the cold head of a closed-cycle helium displex refrigerator and sealed inside a Be-can with He exchange gas.

ARPES measurements. ARPES measurements were carried out at the PGM beamline of the Synchrotron Radiation Center, Stoughton, WI, and at the SIS beamline of the Swiss Light Source, Paul Scherrer Institut, Switzerland, using Scienta R4000 analysers and 22 eV photons for all the measurements. Typical spot sizes of the synchrotron beam on the samples surface is B50150 mm times300 mm.

STM measurements. Low-temperature STM measurements have been performed using a Unisoku UHV STM system (Unisoku USM-1300 combined with RHK Electronics), with a base pressure of 1.0 10 10 Torr. The samples were cleaved

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just before cooling down. Atomically resolved images were acquired in the constant current mode with a constant voltage between sample and tip. We used Pt-Ir tips in all of our experiments.

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Acknowledgements

Work at Argonne (U.C., J.Z., J.P.C., C.D.M., M.G.K., H.C., J.P.C.R., F.W., J.C.C, R.O., M.R.N., S.R.) was supported by the Materials Science and Engineering Division, Basic Energy Sciences, Ofce of Science, U.S. Department of Energy. Work at Temple University (M.I) and Drexel University (G.K.) was supported as part of the Center for the Computational Design of Functional Layered Materials, an Energy Frontier Research Center funded by the U.S. DOE, BES under Award DE-SC0012575. J.v.W. acknowledges support from a VIDI grant nanced by the Netherlands Organization for Scientic Research (NWO). M.R. was supported by the DOE-BES grant DE-SC0005035. N.T. was supported by the U.S. DOE, Ofce of Science, Grant DE-FG02-07ER46423. The Synchrotron Radiation Center is supported by the University of Wisconsin, Madison. Synchrotron X-ray scattering experiments were carried out at the Advanced Photon Source, which is supported by the DOE, Ofce of Science, BES. We thank Ming Shi for his support with the experiments at the Swiss Light Source, Paul Scherrer Institut, Switzerland, and D. Robinson and K. Attenkofer for their support with the XRD measurements at the Advanced Photon Source, Argonne National Laboratory.

Author contributions

U.C. and S.R. proposed the research project. U.C. and J.Z. carried out the ARPES measurements and analysis of the ARPES data. J.P.C., J.P.C.R., F.W., R.O. and S.R. carried out the XRD measurements and analysis of the XRD data. M.I., R.D.C. and G.K. carried out the STM, transport measurements and analysis of STM and transport data. M.I., G.K., C.D.M. and M.G.K. synthesized high-quality pristine and intercalated NbSe2 samples. H.C. conducted the superconducting SQUID measurements on the samples, to determine their superconducting critical temperatures. U.C., J.v.W., M.R., N.T., M.R.N. and S.R. wrote the manuscript. All authors discussed the results and contributed to the manuscript.

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How to cite this article: Chatterjee, U. et al. Emergence of coherence in the charge-density wave state of 2H-NbSe2. Nat. Commun. 6:6313 doi: 10.1038/ncomms7313 (2015).

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