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# Axionic charge-density wave in the Weyl semimetal (TaSe4)2I

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An Author Correction to this article was published on 15 May 2020

## Abstract

An axion insulator is a correlated topological phase, which is predicted to arise from the formation of a charge-density wave in a Weyl semimetal1,2—that is, a material in which electrons behave as massless chiral fermions. The accompanying sliding mode in the charge-density-wave phase—the phason—is an axion3,4 and is expected to cause anomalous magnetoelectric transport effects. However, this axionic charge-density wave has not yet been experimentally detected. Here we report the observation of a large positive contribution to the magnetoconductance in the sliding mode of the charge-density-wave Weyl semimetal (TaSe4)2I for collinear electric and magnetic fields. The positive contribution to the magnetoconductance originates from the anomalous axionic contribution of the chiral anomaly to the phason current, and is locked to the parallel alignment of the electric and magnetic fields. By rotating the magnetic field, we show that the angular dependence of the magnetoconductance is consistent with the anomalous transport of an axionic charge-density wave. Our results show that it is possible to find experimental evidence for axions in strongly correlated topological condensed matter systems, which have so far been elusive in any other context.

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## Data availability

All data generated or analysed during this study are available within the paper and its Extended Data files. Reasonable requests for further source data should be addressed to the corresponding author.

## Change history

• ### 15 May 2020

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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## Acknowledgements

C.F. acknowledges the research grant DFG-RSF (NI616 22/1; ‘Contribution of topological states to the thermoelectric properties of Weyl semimetals’) and SFB 1143. First-principles calculations were funded by the US Department of Energy through grant number DE-SC0016239. B.A.B. acknowledges additional support from the US National Science Foundation EAGER through grant number NOA-AWD1004957, Simons Investigator grants ONR-N00014-14-1-0330 and NSF-MRSEC DMR-1420541, the Packard Foundation and the Schmidt Fund for Innovative Research. Z.W. acknowledges support from the National Thousand-Young-Talents Program, the CAS Pioneer Hundred Talents Program and the National Natural Science Foundation of China.

## Author information

Authors

### Contributions

B.A.B., C.F. and J.G. conceived the experiment. N.K., C. Shekhar and Y.Q. synthesized the single-crystal bulk samples. J.G., S.H. and C. Schindler fabricated the electrical-transport devices. J.G. carried out the transport measurements with the help of S.S.H. and C. Schindler. J.G. and C. Shekhar analysed the data. J.N., Z.W. and Y.S. calculated the band structure. B.B. and B.A.B. provided the theoretical background of the work. All authors contributed to the interpretation of the data and to the writing of the manuscript.

### Corresponding author

Correspondence to J. Gooth.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Jian Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 (TaSe4)2I crystal structure, growth, device and transport characterization.

a, Crystal structure of (TaSe4)2I. b, Sketch of the growth principle. A temperature gradient (temperatures T1 > T2) is imposed on an evacuated quartz ampule, which contains (TaSe4)2I powder at T1. The evaporated (TaSe4)2I diffuses towards the area with temperature T2 and condenses into single crystals. c, Optical micrograph of the as-grown (TaSe4)2I crystals. d, Distribution of Weyl points in momentum (k) space of chirality ±χ. e, Scanning electron microscope image of a crystal. f, Typical device used for electrical-transport measurements. g, h, Single-particle resistance of samples B, C, D and E. The electrical resistance R, normalized by R0 = R(300 K) (g) and its logarithmic derivative (h) as a function of T−1, where T is the temperature. i, Single-particle gaps of all (TaSe4)2I samples investigated. The error denotes the fitting error of 1σ. The dotted line displays the mean value of all samples.

### Extended Data Fig. 2 Hall measurements and Fermi level position of sample D.

a, Device used for the Hall measurements in a magnetic field B. b, Single-particle longitudinal resistivity ρ versus temperature T. ci, Single-particle Hall resistance RH at 125 K (c), 155 K (d), 185 K (e), 215 K (f), 245 K (g) and 300 K (h). The measured data (black) are fitted linearly (red) to extract the carrier concentration n (i). The error bars denote the error of the linear fits to 1σ. j, Estimated Fermi level position below Tc. ΔE is the single-particle gap, obtained from Extended Data Fig. 1.

### Extended Data Fig. 3 V–I characteristics of sample A at zero magnetic field and selected temperatures.

aj, VI characteristics at 80 K (a), 105 K (b), 130 K (c), 155 K (d), 180 K (e), 205 K (f), 230 K (g), 255 K (h), 280 K (i) and 305 K (j). These data were used to calculate the differential resistance dV/dI curves in Fig. 2d. At temperatures below 180 K, we start to observe nonlinearity. This nonlinearity becomes even more apparent in the dV/dI curves shown in Fig. 2d, where a deviation from the linear behaviour is already seen at 230 K.

### Extended Data Fig. 4 Fitting the nonlinear V–I characteristics of sample A at zero magnetic field.

ag, VI characteristics (black line), a linear fit Isp(V) = mV (green line) and a fit with the Bardeen model6 I(V) = Isp(V) + ICDW(V) (red line), where ICDW(V) = I0(V − VT)exp(−V0/V) at 80 K (a), 105 K (b), 130 K (c), 155 K (d), 180 K (e), 205 K (f) and 230 K (g). h, i, m (h) and the threshold voltage Vth extracted from Fig. 2 were employed to extract the fit parameters. j, I0. k, V0. The error bars in hk denote the error of the fits to 1σ.

### Extended Data Fig. 5 Dependence of the switching voltage of sample A on the contact separation.

a, b, VI characteristics (a) and differential resistance dV/dI (b) at 80 K and zero magnetic field B for various contact lengths L on sample A. ce, Second derivatives d2V/dI2 used to estimate the threshold voltages Vth shown in Fig. 2g. We define Vth as the voltage at which the last data point of d2V/dI2 (marked by the vertical line) touches the zero baseline before the global minimum upon enhancing V.

### Extended Data Fig. 6 Testing the origin of the nonlinear V–I curves of sample A.

a, The increasing Joule heating power Pth = Vth2/[dV/dI(Vth)] at the threshold, as a function of increasing T. b, The linear dependence of Vth on L shown at 80 K (the line denotes a linear fit) demonstrate that the observed effects are intrinsic to the (TaSe4)2I crystals.

### Extended Data Fig. 7 Symmetry and temperature dependence of the V–I characteristics in the magnetic field of sample A.

a, b, VI characteristics (a) and differential resistance dV/dI (b) at 80 K for sample A in magnetic fields perpendicular to the applied current, but opposite to the magnetic field in Fig. 3. c, d, Corresponding VI characteristics (c) and dV/dI (d) in magnetic fields parallel to the applied current. eg, VI characteristics at 80 K (e), 105 K (f) and 130 K (g).

### Extended Data Fig. 8 Bias-dependent data of samples A and B at 105 K.

The two samples have similar contact separation. a, b, VI characteristics (a) and differential resistance dV/dI (b) at various magnetic fields B applied perpendicular to the current direction (IB) for sample A. c, Magnetic field dependence of the magnetoconductance Δ(dI/dV)B = (dI/dV)B − (dI/dV)0 T at 105 K and at various voltages V for sample A. d, e, Corresponding VI characteristics (d) and dV/dI (e) at various magnetic fields B applied perpendicular to the current direction (IB). f, Magnetic field dependence of the magnetoconductance Δ(dI/dV)B for sample B.

a, d1. b, d2.

### Extended Data Fig. 10 Homogeneity test of the current distribution on sample E.

a, First configuration. I is injected from contacts 1 and 6 and V is measured between contacts 2 and 3. be, VI characteristics (b, d) and dV/dI (c, e) at 80 K and at various magnetic fields B for IB (b, c) and for IB (d, e). f, g, Δ(dI/dV)B = (dI/dV)B − (dI/dV)0 T for IB (f) and for IB (g). h, Second configuration. V is measured between contacts 4 and 5. in, Corresponding characteristics (i, k) and dV/dI (j, l) for IB (i, j) and for IB (k, l). m, n, Δ(dI/dV)B = (dI/dV)B − (dI/dV)0 T for IB (m) and for IB (n).

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Gooth, J., Bradlyn, B., Honnali, S. et al. Axionic charge-density wave in the Weyl semimetal (TaSe4)2I. Nature 575, 315–319 (2019). https://doi.org/10.1038/s41586-019-1630-4

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• DOI: https://doi.org/10.1038/s41586-019-1630-4

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