  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 of this phenomenon. We investigate
this phenomenon based on scattering theory on a normal metal-TI-normal metal
hybrid structure and calculate the conductances in longitudinal and transverse
directions to the applied bias. The transverse conductance depends on the
spatial location between the two NM-TI junctions where it is calculated. It is
zero in the drain electrode when the chemical potentials of the top and the
bottom TI surfaces ($\mu_t$ and $\mu_b$ respectively) 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 $\mu_t=\mu_b$ whereas it is
$2\pi$-periodic in $\phi$ when $\mu_t\neq\mu_b$. As a function of the magnetic
field, the magnitude of transverse conductance increases initially and peaks.
At higher magnetic fields, it decays for angles $\phi$ closer to $0,\pi$
whereas oscillates for angles $\phi$ close to $\pi/2$. The conductances
oscillate with the length of the TI region. A finite width of the system makes
the transport separate into finitely many channels. The features of the
conductances are similar to those in the limit of infinitely wide system except
when the width is so small that only one channel participates in the transport.
When only one channel participates in transport, the transverse conductance in
the region $0<x<L$ is zero for $\mu_t=\mu_b$ and the transverse conductance in
the region $x>L$ is zero even for the case $\mu_t\neq\mu_b$. We understand the
features in the obtained results.
