Negative magnetoresistance in Dirac semimetal Cd3As2

Abstract

A large negative magnetoresistance (NMR) is anticipated in topological semimetals in parallel magnetic fields, demonstrating the chiral anomaly, a long-sought high-energy-physics effect, in solid-state systems. Recent experiments reveal that the Dirac semimetal Cd₃ As₂ has the record-high mobility and positive linear magnetoresistance in perpendicular magnetic fields. However, the NMR has not yet been unveiled. Here we report the observation of NMR in Cd₃ As₂ microribbons in parallel magnetic fields up to 66% at 50 K and visible at room temperatures. The NMR is sensitive to the angle between magnetic and electrical fields, robust against temperature and dependent on the carrier density. The large NMR results from low carrier densities in our Cd₃ As₂ samples, ranging from 3.0 × 10¹⁷ cm^-3 at 300 K to 2.2 × 10¹⁶ cm^-3 below 50 K. We therefore attribute the observed NMR to the chiral anomaly. In perpendicular magnetic fields, a positive linear magnetoresistance up to 1,670% at 14 T and 2 K is also observed.

ARTICLE

Received 16 Jul 2015 | Accepted 27 Nov 2015 | Published 8 Jan 2016

Hui Li1,*, Hongtao He2,*, Hai-Zhou Lu2,*, Huachen Zhang1, Hongchao Liu1, Rong Ma1, Zhiyong Fan3, Shun-Qing Shen4 & Jiannong Wang1

A large negative magnetoresistance (NMR) is anticipated in topological semimetals in parallel magnetic elds, demonstrating the chiral anomaly, a long-sought high-energy-physics effect, in solid-state systems. Recent experiments reveal that the Dirac semimetal Cd3As2 has the record-high mobility and positive linear magnetoresistance in perpendicular magnetic elds. However, the NMR has not yet been unveiled. Here we report the observation of NMR in Cd3As2 microribbons in parallel magnetic elds up to 66% at 50 K and visible at room temperatures. The NMR is sensitive to the angle between magnetic and electrical elds, robust against temperature and dependent on the carrier density. The large NMR results from low carrier densities in our Cd3As2 samples, ranging from 3.0 1017 cm 3 at 300 K to

2.2 1016 cm 3 below 50 K. We therefore attribute the observed NMR to the chiral anomaly.

In perpendicular magnetic elds, a positive linear magnetoresistance up to 1,670% at 14 Tand2 K is also observed.

DOI: 10.1038/ncomms10301 OPEN

Negative magnetoresistance in Dirac semimetal Cd3As2

1 Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. 2 Department of Physics, South University of Science and Technology of China, Shenzhen, Guangdong 518055, China. 3 Department of Electronics and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. 4 Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to S.S. (email: mailto:[email protected]

Web End [email protected] ) or to J.W. (email: mailto:[email protected]

Web End [email protected] ).

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Searching for the signature of the Adler-Bell-Jackiw chiral anomaly13 in three-dimensional topological semimetals is one of the focuses in condensed matter physics. The

topological semimetals have a band structure with the conduction and valence energy bands touching at a nite number of paired Weyl nodes46 (Fig. 1a). In each pair, the two Weyl nodes carry opposite chirality, and paired monopoles and anti-monopoles of Berry curvature in momentum space7 (Fig. 1b). The nontrivial Berry curvature can couple an external magnetic eld (B) to the velocity of electrons, leading to a chiral current that is linearly proportional to the eld. The correlation of chiral currents further contributes to an extra conductivity that quadratically grows with increasing magnetic eld, in a magnetic eld and an electric eld applied parallel to each other. This B2-positive conductivity in weak parallel magnetic elds, or negative magnetoresistance (negative MR), is rare in non-ferromagnetic materials, thus can serve as one of the transport signatures of the topological semimetals. More importantly, because of its relation to the chiral charge pumping between paired Weyl nodes, the negative magnetoresistance is also believed to be a signature of the chiral anomaly8,9.

Among the recently identied candidates for topological semimetals (for example, HgCr2Se4 (refs 10,11), (Bi1 xInx)2Se3

(ref. 12), Na3Bi (refs 1315), TlBiSSe (ref. 16) and TaAs (refs 1721)), the Dirac semimetal Cd3As2 (refs 2227) has peculiar transport properties, such as a giant MR in perpendicular magnetic elds and record-high mobility2833, thus is of great potential in device applications. The negative MR possibly associated with the chiral anomaly has been claimed in several topological semimetals, including BiSb alloy34, ZrTe5 (ref. 35),

TaAs (refs 36,37), Na3Bi (ref. 38) and TaP (ref. 39). However, the chiral anomaly in Cd3As2 is not yet observed. One of the reasons is that the carrier density in earlier samples was too high (over 1018 cm 3). The chiral anomaly arises because of the nontrivial

Berry curvature, which diverges at the Weyl nodes, so the Fermi energy EF has to be as close to the Weyl nodes as possible for a clear signal of the negative MR.

In this work, we systematically investigate the magneto-transport properties of Cd3As2 microribbons, in which the carrier density is found to obey an Arrheniuss law, decreasing from3.0 1017 cm 3 at 300 K to 2.2 1016 cm 3 below 50 K. In

perpendicular magnetic elds, the ribbon exhibits a very large non-saturating positive linear MR (linear MR) up to 300 K. In contrast, when the magnetic eld is applied in parallel with the

measurement electric eld, a negative MR is observed. It is sensitive to the angle between magnetic and electrical eld, and shows a parabolic dependence on the low magnetic elds (o1 T)

and persists up to 300 K. More importantly, our analysis reveals a characteristic carrier density dependence of the observed negative MR that is in agreement with the semiclassical theory about the chiral anomaly in topological semimetals. All the experimental evidence makes us believe that the chiral anomaly induced negative MR is indeed realized in our Cd3As2 ribbons with low carrier density. By studying the carrier density dependence of the observed linear MR in perpendicular magnetic elds, possible physical origins are also discussed. Our work shows that the carrier density plays an important role in the observation of the negative and linear MR and their magnitudes.

ResultsDevice characteristics. Figure 2a shows the scanning electron microscopy image of the four-terminal Cd3As2 devices studied in this work. The width w and inter-voltage-probe distance l are 1,210 and 1,600 nm, respectively. According to the atomic force microscopy measurement shown in Fig. 2b, the ribbon thickness t is about 327 nm (Fig. 2c). Figure 2d shows the measured temperature (T) dependence of the resistance (R) of the Cd3As2 ribbon. With decreasing temperature, the ribbon changes from an insulating behaviour to a metallic one, with a resistance peak appearing around 50 K. We note that similar RT curves were also observed in recent studies of Dirac semimetals, where chiral anomaly induced transport features were reported40,41. One of the important properties of Dirac semimetals is the giant non-saturating linear magnetoresistance (linear MR) in high magnetic elds2833. Indeed, our Cd3As2 ribbons do exhibit such an intriguing linear MR. Figure 2e shows the MR measured at T 2 K with varying angle between magnetic and electric eld

applied (see inset). When the magnetic eld (B) is applied perpendicular to the ribbon in the z direction, that is, the B-eld tilting angle y 90o, a linear MR up to 1670% at 14 T is observed.

This linear MR decreases at smaller titling angles when we rotate the B-eld in the xz plane. For yr10o, a negative MR begins to emerge in low magnetic elds, as shown in the Fig. 2f. For y 0o,

that is, the B-eld is parallel to the electric eld direction, the negative MR is the most prominent. We also rotate the B-eld in the xy plane and study the in-plane angle dependence of this negative MR (see Supplementary Note 1 and Supplementary Fig. 1 for details). The emergence of such a negative MR when B||E is recently ascribed to the chiral anomaly of topological semimetals8,9.

Linear MR in perpendicular elds. To gain more physical insights into the observed linear MR and negative MR, we further study the temperature dependence of these two phenomena. Figure 3a shows the RB curves measured at y 90o and different

temperatures indicated. As temperature increases from 2 to 50 K, the linear MR in high magnetic elds (48 T) is almost unchanged but it starts to weaken gradually as T further increases. At low temperatures, some wiggles are superimposed on the linear MR but quickly disappear as temperature increases. In addition, we note that the RB curves show a quadratic B-eld dependence in low magnetic elds (o1 T) distinct from the linear

MR in high magnetic elds. As shown in the inset of Fig. 3b, the RB curves at T 2 to 300 K can be well tted by parabolas

within a small B-eld range. Such a parabolic MR is believed to arise from the Lorentz deection of carriers and the B2 tting allows us to deduce the carrier mobility, m, by42

R B

R0 1 mB

2

: 1

a b

Energy

kz ky

kx

kII

kz

Figure 1 | Nontrivial band structure and Berry curvature of a topological semimetal. (a) A schematic of the energy spectrum of a topological semimetal. (kx, ky, kz) is the wave vector. k2j j k2x k2y . (b) The vector plot of the Berry curvature in momentum space. The conduction and valence bands of a topological semimetal touch at the Weyl nodes, at which a pair of monopoles is hosted. The arrows show that the ux of the Berry curvature ows from one monopole (red) to the other (blue), dening the nontrivial topological properties of a topological semimetal.

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Figure 2 | Topological semimetal Cd3As2 microribbon device and magnetotransport characteristics. (a) The scanning electron microscopy and(b) atomic force microscopy images of the device. Scale bars, 1 mm (a); 200 nm (b). (c) The height prole of the Cd3As2 microribbon in b. (d)The measured resistance (R) as a function of temperature (T) at zero magnetic eld. (e) The magnetoresistance (MR) measured at 2 K with applied magnetic eld (B)

direction changing from perpendicular (y 90) to parallel (y 0) to the electric eld (E) direction in the zx plane. (f) The replot of MR with yo10

showing the negative MR at low magnetic elds.

The obtained mobility of our Cd3As2 ribbon at different temperatures is shown in Fig. 3b. It increases monotonically with decreasing temperature. At T 2 K, the mobility reaches

104 cm2V 1 s 1, which is comparable to those reported in previous studies of Cd3As2 (refs 29,30,32,33). It has to be pointed out that equation (1) is valid when Boo1/m. Considering the high mobility, we restrict the tting range of the magnetic eld below0.15 T throughout the work. On the basis of Drude model of electric conduction, the carrier density n of our ribbon can be derived by

n 1= rem

l= Rwtem

; 2 where e is the elementary charge, r is the resistivity of the ribbon and the resistance R at different temperatures is shown in Fig. 2c. Figure 3c shows the obtained carrier density as a function of temperature. Below 50 K, the carrier density is almost a constant. From 50 to 300 K, it increases with temperature by about one order of magnitude from 2.2 1016 to 3.0 1017 cm 3,

following Arrheniuss law (solid curve in Fig. 3c):

n T

/ exp D=kBT

; 3 where kB is the Boltzmann constant and the thermal activation energy D is about 51 meV. Such a thermally activated process of

carriers accounts for the insulator-like RT behaviour above 50 K shown in Fig. 2d, while the metallic behaviour below 50 K is mainly due to the increase of the carrier mobility with decreasing temperature. Since the intrinsic carriers will not follow Arrheniuss law for Dirac fermions43, we tentatively ascribe the thermal activation of carriers to some traps present in our Cd3As2 ribbons. It is worth pointing out that both the observed linear MR and the carrier density are almost temperature independent when To50 K and become temperature dependent when T450 K. This coincidence implies that the observed strength of the linear MR is related to the change of carrier density. We can thus examine the temperature dependence of the linear MR in the temperature range from 50 to 300 K in terms of the carrier density. The slope k of the linear MR is extracted by linearly tting the RB curves between 8 and 14 T, as shown in Fig. 3a. The obtained k as a function of n is shown in Fig. 3d.

A giant non-saturating linear MR has been observed in various Dirac semimetals2833, but its physical origin is still under debate. One possible mechanism is the quantum linear MR model proposed by Abrikosov44, where a non-saturating linear MR would appear in three-dimensional gapless semiconductors with linear energy dispersion when all the carriers are condensed into the lowest bands of Landau levels, that is, in the quantum limit.

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Figure 3 | Linear MR in B perpendicular to E. (a) The MR measured at different T indicated. (b) The T dependence of the carrier mobility, which is calculated using Kohlers rule or equation (1). Inset: the MR at small magnetic elds and the parabola ttings (solid lines) at different T indicated.(c) The carrier density as a function of T. The solid red curve is the tting using Arrheniuss law. (d) The slope k of the linear MR at high B (from 8 to 14 T, obtained in a, see solid curves) as a function of carrier density, n. The solid red and blue curves are the ttings using n 1 and n 2, respectively.

The corresponding temperature for each data point is also indicated.

According to this model, the linear MR is temperature independent but should follow the 1/n2 dependence, that is, r B?

/ B?=n2, where n2 arises because the longitudinal

resistance r s=s2H in the limit that the longitudinal

conductivity s is much smaller than the Hall conductivity sH and the Hall conductivity is proportional to n. Abrikosovs model with linear dispersion leads to a longitudinal s independent on the carrier density, which may be violated in real materials. If s is also proportional to n, as in most cases, the carrier density dependence should be corrected to r B?

/ B?n 1. As a result,

the slope of the quantum linear MR is inversely proportional to the carrier density. For comparison we plot kpn 1 (red solid line) and kpn 2 (blue solid line) curves in Fig. 3d. As it can be seen, the measured k follows n 1 dependence. In addition, our system is believed to enter the quantum limit in the tting magnetic eld range from 8 to 14 T, as will be discussed later in this work. All these seem to suggest the quantum model as the underlying physical origin of the observed linear MR in high elds shown in Fig. 3a. Besides this quantum model, there is another classical model proposed by Parish and Littlewood45 to account for the linear MR observed in polycrystalline silver chalcogenides. It is the disorder-induced admixture of the Hall signal that gives rise to the linear MR. Considering the low carrier density and quite high mobility of our Cd3As2 ribbons, this classical model is unlikely applicable to the observed linear MR. Also, there is explanation in the presence of balanced electron and hole carriers46, which is apparently not our case. The linear transverse MR observed in different systems may have various origins, and is still a challenging theoretical question47,48.

Negative MR in parallel elds. In Fig. 4a, the RB curves obtained at y 0o are shown at different temperatures. There

exists a critical B-eld for each curve, below which a pronounced negative MR is observed even with temperature up to 300 K. At T 50 K and B 8 T, the highest negative MR of 66% can be

obtained. It is also noted in Fig. 4a that some MR ripples are superimposed on the negative MR especially as low temperatures. Besides the apparent negative MR, a small resistance dip appears in low elds with To20 K, as shown in Fig. 4b. Such a dip is believed to arise from the weak anti-localization effect in Dirac semimetals34,49. In Fig. 4c, the low-eld-negative MR is shown at different temperatures. Note that the measured resistance has been converted to the conductivity s and Ds s s0, where s0

is the conductivity at zero magnetic eld. Remarkably, all the data in Fig. 4c show a quadratic dependence on the magnetic eld, as indicated by the tting curves with Ds CaB2. This is

consistent with the prediction in previous theoretical studies8,9. When an external electric eld is applied in parallel with the magnetic eld, chiral charges will be pumped from one Weyl node to the other, as a result of the nontrivial Berry curvature (see Fig. 1b). The chiral charge is therefore not conserved at each Weyl node. Such a chiral anomaly is expected to give rise to a prominent positive conductivity proportional to B2 based on a semiclassical transport calculation8,9. It should be noted that such a quadratic eld dependence of the conductivity is only valid in weak magnetic elds or high temperatures such that the Landau quantization can be ignored. Indeed, the quadratic eld dependence of Ds in Fig. 4c occurs in low magnetic elds (o0.8 T).

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Figure 4 | Negative MR in B parallel to E. (a) The MR measured at different T indicated. (b) The weak anti-localization effect at low temperatures and very small magnetic elds. (c) The positive conductivity Ds ss0, where s0 is the conductivity at B 0, converted from measured negative

MR at different T indicated. The solid red curves are the ttings using Ds CaB2. (d) Ca as a function of the carrier density, n. The solid red curve is a

tting using n 2/3. The corresponding temperature for each data point is also indicated.

Furthermore, because the chiral anomaly arises from the nontrivial Berry curvature, which diverges at the Weyl nodes, the positive conductivity will increase with decreasing Fermi energy and carrier density. More specically, the theory predicts Ca /

E 2F / n 2=3 if the Fermi level EF is close to the Weyl nodes8,9.

As a result, we plot the obtained tting parameter Ca as a function of the carrier density in Fig. 4d together with a Ca / n 2=3 curve

(solid red line). One can see that Ca does obey the n 2/3 relationship reasonably well. All these experimental evidences, that is, measured Ds CaB2 and Ca / n 2=3, lead us to believe

that it is the chiral anomaly that gives rise to the observed negative MR shown in Fig. 4a. In the above discussion, we only consider the inuence of n on Ca. But Ca is also proportional to the internode scattering time ta (refs 8,9). Since the momentum transfer assisted by phonons is suppressed at low temperatures, ta will increase with decreasing temperature. As shown in Fig. 3c, the carrier density of our sample follows Arrheniuss law. ta is

thus expected to increase with decreasing n. At higher carrier density, the deviation from perfect linear dispersion can also lead to a correction to the power law of n. Therefore, the n 2/3 tting of Ca in Fig. 4d, which assumes a constant ta for different n, would over- and underestimate the value of Ca at high and low carrier densities, respectively. This accounts for the deviation of Ca from the tting at 300 K and below 50 K shown in Fig. 4d.

The observation of chiral anomaly induced negative MR also requires tact, where t is the momentum relaxation time.

In Supplementary Note 2 and Supplementary Fig. 2, the ratio of ta/t has been estimated. ta is at least one order of magnitude larger than t, in consistent with the theories8,9.

It is well known that, in solids, negative MR may have other physical origins. It can arise from the weak localization effect due to the quantum interference of time-reversed scattering loops. Since the phase coherence length decreases rapidly with increasing temperature, the weak localization can only be observed at low temperatures. The negative MR observed in Cd3As2 ribbons persists up to 300 K; therefore, cannot be attributed to the weak localization effect. Magnetic scattering might be another mechanism for negative MR, as reported in some magnetic systems50, but our Cd3As2 ribbons are non-magnetic.

MR in the quantum limit. As mentioned above, a critical magnetic eld BC exists for each MR curve to characterize the change of MR from negative to positive in Fig. 4a, as illustrated by the arrows. We believe that this sign change in MR is an indication of the system to enter the quantum limit at BC, that is, the Fermi energy crosses only the lowest Landau bands with the band index v 0 and lies right below the bottom of the v 1

Landau bands, as shown in the inset of Fig. 5a. The energy spacing between the v 1 and v 0 bands is roughly related to

the cyclotron frequency as o eB=m , with m* as the

effective mass of carriers in Cd3As2. On the other hand, o 2k2F= 2m

, where the Fermi wave vector in the

v 0 bands is related to the carrier density according to

kF 2p2 n= eB

. Note that there is no spin degeneracy for the

lowest Landau band of Dirac semimetal (Supplementary Note 3; Supplementary Fig. 3). Combing them, we can deduce a

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Figure 5 | MR in the quantum limit. (a) BC as a function of n2/3, n is the carrier density. The corresponding temperature for each data point is also indicated. The solid red line is a linear tting. BC is dened as the critical eld at which the MR in B parallel to E is minimum. At BC, the system enters the quantum limit with a structure of the Landau bands illustrated as in the inset. v is the index of the Landau bands and o is the cyclotron frequency.

(b) The high-B-eld magnetoconductivity in B parallel to E as a function of 1/B. The magnetoconductivity is found to follow a k0/B dependence while approaching 14 T (see solid red lines). (c) The slope k0 as a function of the carrier density. The solid red line is a linear tting.

relationship between the critical eld and the carrier density as BC 2p4

1=3 n2=3=e 3:8 10 11n2=3: To justify this

scenario, we extract BC from the MR curves at different temperatures (except 300 K curve) in Fig. 4a, and plot them in terms of the carrier density n2/3 as it is shown in Fig. 5a. As the carrier density only changes within the temperature range of 50200 K, a straight line tting of the data in this range with BC bn2/3 yields

b 3.0 10 11, which is close to the above theoretical value.

Such a good agreement strongly supports our assumption that our system is indeed in the quantum limit above BC. The

deviation of data below 50 K, where the carrier density is almost constant, is probably caused by the superimposed ripples on the MR that prevent an accurate extraction of BC. As it is shown in

Fig. 4a, after the system is in the quantum limit, the measured magnetoresistance becomes positive, or the magnetoconductivity becomes negative. We nd at high elds approaching 14 T, the magnetoconductivity follows a good B 1 dependence, as indicated by the linear ttings in Fig. 5b (red solid curves). We also nd that the obtained slope k0 of these linear ttings is inversely proportional to the carrier density n (see Fig. 5c). This observed negative linear magnetoconductivity at high elds is contrary to the theoretical expectation, in which a positive linear magnetoconductivity is predicted as an additional signature of the chiral anomaly8,51,52. However, in reality, the relaxation time and Fermi velocity can bring extra magnetic eld dependences, leading to either positive or negative magnetoconductivity in Dirac semimetals53.

DiscussionIn conclusion, we have performed a systematic magnetotransport study of Cd3As2 microribbons. Due to the low carrier density in

our samples, we can observe both the non-saturating linear MR in a high perpendicular magnetic eld and the quadratic negative MR when a weak magnetic eld is in parallel with the measurement electric eld. Furthermore, the thermally activated behaviour of carriers in our Cd3As2 ribbons allows us to study the carrier density dependence of these two phenomena. Although the mechanism for the linear MR is still not well understood, the quadratic negative MR can be safely ascribed to the chiral anomaly intrinsic to the Dirac semimetal Cd3As2. Our work provides new physical insights into the intriguing transport properties of Dirac semimetals, revealing the importance of carrier density in mediating the linear MR in perpendicular elds and the quadratic negative MR in parallel elds. It also calls for the thin-lm growth of Dirac semimetals. By applying an external gate to effectively tune the Fermi level of the lm towards the Weyl nodes, much larger linear MR and prominent negative MR would be expected.

Methods

Growth. The Cd3As2 microribbon was grown by a chemical vapour deposition method. Cd3As2 powders and Si (001) covered with 2-nm Au layer were used as the precursor and substrates, respectively, and argon were used as a carrier gas. Before each growth, the furnace was pumped and ushed for several times to remove water and oxygen using dry argon. The precursor powder boat was placed in the hot centre of the furnace, while the Si (100) substrates were placed downstream about 32 cm away from the precursor powders. The furnace was gradually heated up to 750 C in 40 min, and the Ar ow was kept as 100 s.c.c.m. during the growth process. The typical growth time is 60 min, and after then the furnace was cooled down to room temperature naturally.

Characterization. Structural investigations have been performed on scanning electron microscopy (JEOL-6300) and atomic force microscopy (Dimension 3100) at room temperature. The growth direction of the Cd3As2 microribbon has been

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conrmed by the transmission electron microscopy (JEM 2010, JEOL) measurements. The high-resolution transmission electron microscopy identied [110] as the growth or axial direction of the ribbon (Supplementary Note 4 and Supplementary Fig. 4).

Devices fabrication and magnetoresistance measurements. To study the magnetotransport properties, a four-terminal device was fabricated with standard electron-beam lithography and lift-off processes. Au/Cr electrodes with the thickness of 275/25 nm were deposited using thermal evaporation methods. The transport properties of the device were then investigated in a Quantum Design PPMS system with the highest magnetic eld up to 14 T.

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Acknowledgements

This work was supported in part by the Research Grants Council of the Hong Kong SAR under Grant Nos. 16305514, 17303714 and AoE/P-04/08, and in part by the National Natural Science Foundation of China under Grant Nos. 11204183 and 11374135. The electron-beam lithography facility is supported by the Raith-HKUST Nanotechnology Laboratory at MCPF (SEG HKUST08).

Author contributions

J.W. and S.-Q.S. conceived the project; H.L. grew the samples and fabricated devices with support from Z.F., H.Z., H.C.L. and R.M.; H.H. and H.L. performed transport experiments;H.-Z.L. and S.-Q.S. provided theoretical support; H.H., H.-Z.L., H.L., J.W. and S.-Q.S. analysed experimental data and wrote the manuscript with contribution from others.

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How to cite this article: Li, H. et al. Negative magnetoresistance in Dirac semimetal Cd3As2. Nat. Commun. 7:10301 doi: 10.1038/ncomms10301 (2016).

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