Nonlinear magnetotransport shaped by Fermi surface topology and convexity

The nature of Fermi surface defines the physical properties of conductors and many physical phenomena can be traced to its shape. Although the recent discovery of a current-dependent nonlinear magnetoresistance in spin-polarized non-magnetic materials has attracted considerable attention in spintronics, correlations between this phenomenon and the underlying fermiology remain unexplored. Here, we report the observation of nonlinear magnetoresistance at room temperature in a semimetal WTe2, with an interesting temperature-driven inversion. Theoretical calculations reproduce the nonlinear transport measurements and allow us to attribute the inversion to temperature-induced changes in Fermi surface convexity. We also report a large anisotropy of nonlinear magnetoresistance in WTe2, due to its low symmetry of Fermi surfaces. The good agreement between experiments and theoretical modeling reveals the critical role of Fermi surface topology and convexity on the nonlinear magneto-response. These results lay a new path to explore ramifications of distinct fermiology for nonlinear transport in condensed-matter.

vs. magnetic field H. Rω shows a quadratic dependence with the magnetic field, in consistent with previous reports in WTe2 1 . c,d, Temperature dependence of the linear MR measured at ∥ (c) and ∥ (d). The measurements were conducted at a 34 nm thick WTe2 flake with the current applied at 45° titled from the a axis of WTe2 crystal.   to the nominal a axis at room temperature. The peaks of P6 (~160 cm -1 ) and P7 (~210 cm -1 ) are marked, as defined in Ref. [2]. b, The peak intensity ratio of P6/P7 (red circle) as a function of ϕ. The a axis can be determined from the angle where the peak intensity of P6/P7 maximizes 3 , which shows a small difference (< 8°) from the nominal one. The angle ϕ between Ef and the nominal a axis is defined in the inset of b.
where vx,n(k) represents the velocity of the n-th band, and the contributions of each band are added independently. Since we are primarily interested in the variation of (2) bb J with the temperature and magnetic field, and not in accurately capturing its magnitude, we leave the relaxation time unspecified and present all the results in an arbitrary scale. We find that the sign of (2) bb J can be altered by changing either the temperature or Fermi 6 level μ. Though the sign inversion happens in (2) aa J as well, the sign change is more prominent and robust for (2) bb J , in agreement with the experimental results shown in Fig. 3c and 3d. By separating the contributions to (2) xx J arising from the hole and electron pockets, we find that the overall features of the nonlinear current are dominated by the electron pockets, especially the sign change for both current directions. This is shown in Supplementary Fig. 4b,c and Supplementary Fig. 5b,c.

Supplementary Note 2: Linear relation between J (2) and R2ω
As shown in Supplementary Note 1, under a magnetic field perpendicular to the electric field Ex in WTe2, the longitudinal current density Jx includes a nonlinear term, , in addition to the conventional linear one, (1) Starting from the longitudinal resistivity, the longitudinal resistance R can be expressed as

Supplementary Note 3: Temperature-induced Fermi level shift
The semimetal WTe2 is known to have a Fermi level (μ) whose position changes markedly with temperature 6,7 , which in turn leads to large variations in the electron and hole densities. To quantify these density variations from a theoretical perspective, we compute the electron (ne) and hole (nh) densities as a function of μ predicted from our DFTderived band structure.
The result, obtained with a 201×201×101 k-mesh, is shown in Supplementary Fig. 6.
The zero Fermi energy (μ = 0) is from DFT calculation, which is indicated by a dot-dashed line. It shows a similar trend as the experimentally extracted densities at the lowest measured temperature (2 K) in Fig. 2f, where the electron and hole carriers are nearly compensated. The experimental hole density drops by almost three orders of magnitude when the temperature increases from 2 to 300 K, and the magnitude of this reduction is captured by the calculated values in Supplementary Fig. 6 when μ varies between 0 and 120 meV. We note that this effective shift in μ (i.e. its rate of change with temperature) is in agreement with a previous APRES study 7 that find a temperature variation of 120 K induces a 50 meV variation in the Fermi level.
Supplementary Figure 6. Theoretically calculated electron (ne) and hole (nh) carrier densities versus the Fermi level μ for bulk WTe2.

Supplementary Note 4: Quasi-bulk tight-binding model
In order to elucidate the detailed microscopic aspects underlying the sign inversion of (2) xx J that we observed both experimentally (Fig. 2d) and theoretically ( Fig. 4a and 4d is the anisotropy term that changes the dispersion along , and in the last term is the inversion breaking strength. Once this low energy • model is established, we continue it on a rectangular lattice to have a Hamiltonian defined over the entire Brillouin zone. This extension defines what we designate by quasi-bulk tight-binding model. Its associated band structure is shown in Supplementary Fig. 7a and, for a direct comparison, the DFT band structure of bulk WTe2 at kz = 0 and π is displayed in Supplementary Fig.7b and 7c, respectively. This  In Supplementary Fig. 8a and 8b, we show this aspect in more detail by inspecting the k-resolved 2 ( , )