Dirac materials in parallel non-uniform electromagnetic fields generated by SUSY: A new class of chiral Planar Hall Effect?

TL;DR

This paper uses SUSY-QM to solve the Dirac equation in non-uniform parallel electromagnetic fields, revealing a chiral Planar Hall Effect driven by chiral symmetry and specific potential profiles.

Contribution

It introduces a SUSY-QM approach to analyze Dirac materials under non-uniform fields, uncovering conditions for a chiral Planar Hall Effect with analytic zero-mode solutions.

Findings

Non-zero current density perpendicular to electric and magnetic fields.

Chiral symmetry leads to net current from combined chiralities.

Analytic solutions for specific potential profiles support the effect.

Abstract

Within a Supersymmetric Quantum Mechanics (SUSY-QM) framework, the (3+1) Dirac equation describing a Dirac material in the presence of external parallel electric and magnetic fields is solved. Considering static but non-uniform electric and magnetic profiles with translational symmetry along the y-direction, the Dirac equation is transformed into two decoupled pairs of Schr\"odinger equations, one for each chirality of the fermion fields. Taking trigonometric and hyperbolic profiles for the vector and scalar potentials, respectively, we arrive at SUSY partner P\"oschl-Teller-like quantum potentials. Restricting to the conditions of the potentials that support an analytic zero-mode solution, we obtain a nontrivial current density in the same plane where the electric and magnetic fields lie, but perpendicular to both of them, indicating the possibility of realizing the Planar Hall Effect. Furthermore, this non-vanishing current density is the sum of current densities for the left- and right-chiralities, suggesting that the net current is a consequence of chiral symmetry.