Transverse response from anisotropic Fermi surfaces

TL;DR

This paper shows that anisotropic, rotated Fermi surfaces can produce a finite transverse electron transport response without magnetic fields or Berry curvature, expanding possibilities for low-symmetry material applications.

Contribution

It introduces a symmetry-based mechanism for transverse responses in anisotropic materials, demonstrated through continuum and lattice models without relying on topological effects.

Findings

Finite transverse voltage arises from anisotropic Fermi surfaces.

Transverse response increases with anisotropy degree.

Response vanishes at mirror-symmetry restoring angles.

Abstract

We demonstrate that an anisotropic and rotated Fermi surface can generate a finite transverse response in electron transport, even in the absence of a magnetic field or Berry curvature. Using a two-dimensional continuum model, we show that broken $k_y \to -k_y$ symmetry inherent to anistropic bandstructures leads to a nonzero transverse conductivity. We construct a lattice model with direction-dependent nearest- and next-nearest-neighbor hoppings that faithfully reproduces the continuum dispersion and allows controlled rotation of the Fermi contour. Employing a multiterminal geometry and the B\"uttiker-probe method, we compute the resulting transverse voltage and establish its direct correspondence with the continuum transverse response. The effect increases with the degree of anisotropy and vanishes at rotation angles where mirror symmetry is restored. Unlike the quantum Hall effect, the transverse response predicted here is not quantized but varies continuously with the band-structure parameters. Our results provide a symmetry-based route to engineer transverse signals in low-symmetry materials without magnetic fields or topological effects.