Finite transverse conductance in topological insulators under an applied in-plane magnetic field

Abhiram Soori, Dhavala Suri

Published 2021-01-19Version 1

Recently, in topological insulators~(TIs) the phenomenon of planar Hall effect~(PHE) wherein a current driven in presence an in-plane magnetic field generates a transverse voltage has been experimentally witnessed. There have been a couple of theoretical explanations that explain the origin of this phenomenon. We suggest an origin of this effect based on scattering theory on a normal metal-TI-normal metal junction and calculate the conductances in longitudinal and transverse directions to the applied bias. The transverse conductance depends on the location and is zero in the drain electrode when the chemical potentials on the top and the bottom surfaces of the TI are equal. The longitudinal conductance is $\pi$-periodic in $\phi$-the angle between the bias direction and the direction of the in-plane magnetic field. The transverse conductance is $\pi$-periodic in $\phi$ when the chemical potentials of the top and the bottom TI surfaces are the same whereas it is $2\pi$-periodic in $\phi$ when the chemical potentials of the top and the bottom surfaces are different. As a function of the magnetic field, the magnitude of transverse conductance increases initially, peaks. At higher magnetic fields, it decays for angles $\phi$ closer to $0,\pi$ whereas oscillates for angles $\phi$ close to $\pi/2$. We understand the features in the obtained results, which agree with the existing experimental results.