Giant Berry curvature dipole density in a ferroelectric Weyl semimetal

Abstract

The nonlinear Hall effect (NLHE) reflects Berry-curvature-related properties in non-centrosymmetric but time-reversal-symmetric materials. So far, the NLHE of the investigated systems remains a tiny effect due to the lack of Weyl point as magnetic monopoles in 2D systems or to the high carrier concentration in 3D systems. Here, we report large NLHE due to gigantic Berry curvature dipole density as generated by tilted Weyl cones near the Fermi level in a model ferroelectric Weyl semimetal In-doped Pb1−xSnxTe. By systematically lowering the carrier concentration down to ~1016 cm−3, the Berry curvature dipole density reaches values around 10−21 m3, 102–107 times higher than the previously reported ones. Furthermore, NLHE exhibits a power law of carrier concentration and follows the k−2 relation of the Berry curvature expression derived from the monopole. The present study establishes giant NLHE in a ferroelectric Weyl semimetal, promising for future applications such as current rectification.

How to identify and characterize strongly correlated topological semimetals

“…For the purpose of comparison, we adopt the NLHE terminology in what follows. NLHE studies have been carried out in various (non-or weakly interacting) materials [72][73][74][75][76][77][78][79][80][81], but the identification of intrinsic Berry curvature contributions has been challenging. It involves the separation from extrinsic contributions due to effects such as side jump and skew scattering [82].…”

“…In general, the situation is considerably more complex. Here we focus on investigations of (Pb 1−x Sn x ) 1−y In y Te [80], MoTe 2 [78], WTe 2 [72], and TaIrTe 4 [73], where-via stoichiometry optimization in (Pb 1−x Sn x ) 1−y In y Te to reach a ferroelectric state with extremely low carrier concentration and via exfoliation in the other three noninteracting/weakly interacting reference compounds-a Berry curvature dipole contribution to the NLHE became sufficiently large to be identified with some confidence. (Pb 1−x Sn x ) 1−y In y Te is an In-doped alloy of two rock salt-type compounds: the normal insulator (NI) PbTe and the topological crystalline insulator SnTe.…”

“…225), thereby enabling the formation of a Weyl semimetal [84]. An 'optimally doped' sample shows an electrical conductivity that decreases with decreasing temperature [80]. Using this and the temperature dependent /(E ω x ) 2 , of (candidate) Weyl semimetals as function of (A) the inverse scaled Weyl velocity (v/v0) −1 as a measure of correlation strength.…”

“…T d -TaIrTe4, T d -MoTe2, and Ce3Bi4Pd3, which have similar charge carrier concentrations (of order 10 20 cm −3 ), lie on a universal curve ∼ (v/v0) −2 , as seen from the dashed guide-to-the-eyes curve. For the two shaded lines at higher and lower n, we used the same slope; (B) the inverse charge carrier concentration n −1 (of hole-like charge carriers for consistency with [80]). The charge carrier concentrations of the quasi-2D material T d -WTe2 were calculated using n = n2D/d, where d is the interlayer distance of (2.7-2.8) Å [87].…”

“…Ce3Bi4Pd3: from the slope Γ of ∆C/T vs T 2 , with the phonon contribution subtracted [38]. (Pb 1−x Snx) 1−y InyTe: from a linear fit of the optical conductivity vs photon energy, yielding v = 1.7 × 10 5 m s −1 [84], and from a linear-in-T fit of the electrical conductivity, leading to v = 1.2 × 10 5 m s −1 [80]. MoTe2: from 1/v = m/[h(3π 2 n) 1/3 ], using the charge carrier concentrations n = 0.70 × 10 20 and 0.93 × 10 20 cm −3 of two orbits in Shubnikov-de Haas (SdH) oscillations, and effective masses of m = (1.0 − 1.2)m0 extracted in a Liftshitz-Kosevich analysis [89].…”