Transverse response from anisotropic Fermi surfaces

TL;DR

This work addresses how a finite transverse transport can arise without a magnetic field or Berry curvature by exploiting an anisotropic and rotated Fermi surface. It develops a continuum two-dimensional electron gas with an elliptical Fermi contour rotated by angle $\phi$ and a lattice model with direction-dependent hoppings that reproduces the same dispersion, enabling a controlled rotation of the Fermi contour. Using a multiterminal Büttiker-probe setup, it demonstrates that the transverse conductivity $G_{yx}$ is nonzero for generic $\phi$ and grows with the anisotropy parameter $\delta$, while vanishing at symmetry points where $k_y \to -k_y$ is restored; the lattice results qualitatively agree with the continuum predictions through a measurable transverse voltage $V_H$. Notably, the effect is continuous and not quantized, offering a symmetry-based route to engineer transverse signals in low-symmetry materials (e.g., strained metals, anisotropic 2D materials, artificial lattices, and potentially altermagnets) without magnetic fields or topological Berry-curvature effects.

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 Büttiker-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.

Figures (4)

• Figure 1: A two-dimensional electron gas with an anisotropic bandstructure, translationally invariant along both directions, is subjected to a bias applied along $\hat{x}$. The elliptical Fermi contour is rotated such that its major axis is misaligned with both $\hat{x}$ and $\hat{y}$. The red arrows denote the direction of the quasiparticle velocity on the contour. As a consequence of this misalignment, a longitudinal bias along $\hat{x}$ generates a net transverse current along $\hat{y}$.
• Figure 2: Transverse conductivity as a function of the angle between the major axis of the elliptical Fermi contour and the longitudinal bias direction ($\hat{x}$) for $E=0.1t$. Different curves correspond to different values of the anisotropy ratio $\delta/t$ (shown in the legend).
• Figure 3: Schematic of the lattice-based setup used to probe the transverse response arising from an anisotropic Fermi contour. The central region is a square lattice with direction-dependent nearest- and next-nearest-neighbor hopping amplitudes, connected to source and drain terminals on either side. Two voltage probe terminals are attached symmetrically along the transverse direction. A bias voltage $V$ applied between the source and drain drives a longitudinal current, while the transverse voltage difference $V_H$ that develops between the probe terminals quantifies the transverse response. See the Hamiltonian in Eq. \ref{['eq:ham-lattice-setup']} for details.
• Figure 4: (a) Transverse voltage as a function of $\phi$, the angle of rotation of the system. Parameters: $L_x=L_y=11$, $n_{x0}=6$, $\mu_n = -2t$, $\mu_M = -4t$, $t' = t$, $t_P = 0.05t$, and $eV=0.05t$. Different curves correspond to different values of $\delta$. (b) Fermi contour of the central lattice for various choices of $\delta$ at energy $0.1t$. The legends indicate the values of $\delta/t$.