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arXiv:2512.05014

Hall-like response from anisotropic Fermi surfaces

Abhiram Soori

cond-mat.mes-hallquant-phSubmitted Dec 4, 2025• Announced Dec 5, 2025
v1 · Dec 4, 2025v2 · Dec 13, 2025v3 · Apr 11, 2026v4 · Apr 26, 2026
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Abstract

We demonstrate that an anisotropic and rotated Fermi surface can generate a finite Hall-like 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 band structures 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 Hall 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 Hall response predicted here is not quantized but varies continuously with the band-structure parameters. Our results provide a symmetry-based route to engineer Hall-like signals in low-symmetry materials without magnetic fields or topological effects.

Journal reference
J. Phys.: Condens. Matter 38, 175301 (2026)
DOI
10.1088/1361-648X/ae6387
Comments
6 pages, 4 captioned figures. Comments are welcome

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We demonstrate that an anisotropic and rotated Fermi surface can generate a finite Hall-like 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 ky→−kyk_y \to -k_yky​→−ky​ symmetry inherent to anistropic band structures 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 Hall 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 Hall response predicted here is not quantized but varies continuously with the band-structure parameters. Our results provide a symmetry-based route to engineer Hall-like signals in low-symmetry materials without magnetic fields or topological effects.
We study the Hall response of two-dimensional lattice systems of charged fermions in a transverse magnetic field, in the ballistic coherent limit. We identify a setup in which this response vanishes over wide regions of parameter space: the "Landauer-Büttiker" setup commonly studied for coherent quantum transport, consisting of a strip contacted to biased ideal reservoirs of charges. We show that this effect does not rely on particle-hole symmetry, and is robust to a variety of perturbations including variations of the transverse magnetic field, chemical potential, and temperature. We trace this robustness back to a topological property of the Fermi surface: the number of Fermi points with positive velocity of the system. We argue that the mechanism leading to a vanishing Hall response applies to noninteracting and interacting systems alike, which we verify in concrete examples using density-matrix renormalization group simulations.
Valley-layer coupling (VLC) two-dimensional (2D) materials define a distinct class of quantum systems in which valleys are related by crystal, rather than time-reversal (T\mathcal{T}T) symmetry, enabling gate-controlled valley-contrasted layer polarization. Here we extend this concept to excitons. Using TiSiCo as a prototype VLC material, we show that a perpendicular electric field E⊥E_{\perp}E⊥​ controls exciton- dispersion anisotropy and thereby generates unconventional linear transverse exciton transport in both monolayer and twisted bilayer structures. In the monolayer, this response is characterized by anisotropy-induced transverse conductivities, arising from the antisymmetric combination of diagonal elements in the conductivity tensor and strongly tunable by E⊥E_{\perp}E⊥​. In the twisted bilayer, symmetry additionally permits transverse responses from the symmetric part of the conductivity tensor. Since intralayer excitons in different layers are connected by the Förster coupling, these symmetric and antisymmetric responses coexist and compete with the recently proposed T\mathcal{T}T-even layer Hall and Nernst exciton counterflow. This interplay is highly tunable by twisted angle, temperature, and the direction of the in-plane driving force, providing a route to disentangle distinct transverse exciton transport signals experimentally. Our results establish E⊥E_{\perp}E⊥​ as a powerful knob for controlling exciton transport via VLC and identify VLC 2D materials as a promising platform for engineered excitonic phenomena.
The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}{\ensuremath{\sigma}}_{yx}$. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, ${\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}$, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces ${\ensuremath{\alpha}}_{xy}=\ensuremath{-}{\ensuremath{\alpha}}_{yx}$. This suggests that quasiparticle-free ground states (so-called non-Fermi liquids) may be detected by examining the relationship between ${\ensuremath{\alpha}}_{xy}$ and ${\ensuremath{\alpha}}_{yx}$ in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results. (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles. (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid, the latter lead to deviations that vanish as T3{T}^{3}T3. (iii) We calculate the thermoelectric response in a model of weakly coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\alpha}}$. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.
We introduce a mechanism that produces a Hall-like transverse response in time-reversal-invariant materials, driven entirely by geometric effects. Specifically, we demonstrate that a tilted potential interface causes electron wave packets to undergo a refractionlike deflection upon transmission through the barrier, leading to a finite transverse current and a corresponding Hall-like conductance. Our analytical framework captures the essential features of this refraction-driven charge transport, and the resulting transverse conductance profile is corrob- orated by numerical simulations across different lattice models and device geometries. We further visualize our predicted effect through real-time wave packet dynamics, which reveals its purely geometric origin and the robustness of the transverse response. These findings establish a fundamentally distinct class of Hall-like transport phenomena in mesoscopic systems that preserve time-reversal symmetry.
We study the effects of anisotropic interactions in the quantum Hall effect in the presence of a fourfold discrete rotational (C4)({C}_{4})(C4​) symmetry. Employing the density matrix renormalization group technique on an infinite cylinder geometry (iDMRG), we calculate the anisotropy response of the Laughlin state at $\ensuremath{\nu}=1/3$ and the composite-Fermi liquid (CFL) state at $\ensuremath{\nu}=1/2$. We find that the anisotropy transferred from the interaction potential to the $\ensuremath{\nu}=1/3$ state is stronger when compared with the complementary case of an anisotropic band. Further, the strength of anisotropy reduces as the interaction is made shorter ranged. Quite surprisingly, at $\ensuremath{\nu}=1/2$, the deformation in the CF Fermi surface changes sign as the interaction range is reduced. Our results imply that the short-distance and long-distance parts of the interaction potential have opposite effects on the CFL state in the presence of C4{C}_{4}C4​-symmetric anisotropy.
Low-dimensional Dirac systems offer a versatile platform for quantum-geometric non-linear transport. Hexagonal warping in topological insulator (TI) surface states generates rich momentum-space geometric textures. However, mirror and time-reversal symmetries strictly constrain both the Berry curvature and quantum metric dipoles to zero. Here, we show that proximity-coupling a hexagonally warped TI to a d-wave altermagnet lifts spatial mirror symmetry via the interplay of C_{3v} warping and d-wave spin-splitting. This symmetry breaking enables finite Berry curvature dipole components, which, however, remain heavily suppressed near charge neutrality, establishing the intrinsic quantum metric dipole as the sole driver of the non-linear Hall response. This scattering-independent response vanishes at μ= 0 and exhibits odd parity under chemical potential inversion. Importantly, rotating the altermagnetic orientation angle φcontinuously tunes quantum metric dipole and induces a sign reversal, peaking near φ=0 and vanishing at φ= π/4. Our findings highlight TI-altermagnet interfaces as ideal candidates for gate- and orientation-tunable quantum metric spintronics.