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

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