# Vanishing Hall Response of Charged Fermions in a Transverse Magnetic Field

## TL;DR

This paper demonstrates that in a specific quantum transport setup, the Hall response of charged fermions can vanish over a wide parameter range due to a topological property of the Fermi surface, applicable to both noninteracting and interacting systems.

## Contribution

The study reveals a topologically protected vanishing Hall response in a Landauer-Büttiker setup, independent of particle-hole symmetry and robust against various perturbations.

## Key findings

- Hall response vanishes over a wide parameter range
- Robustness to magnetic field, chemical potential, and temperature variations
- Applicable to both noninteracting and interacting fermionic systems

## Abstract

We study the Hall response of quasi-two-dimensional lattice systems of charged fermions under a weak transverse magnetic field, in the ballistic coherent limit. We identify a setup in which this response vanishes over a wide range of parameters: the paradigmatic "Landauer-B\"uttiker" setup commonly studied for coherent quantum transport, consisting of a strip contacted to biased ideal reservoirs of charges. We show that the 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 (central charge) of the system. We argue that the mechanism responsible for the vanishing Hall response can operate both in noninteracting and interacting systems, which we verify in concrete examples using density-matrix renormalization group (DMRG) simulations.