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The current in response to a bias in certain two-dimensional electron gas(2DEG), can have a nonzero transverse component under a finite magnetic fieldapplied in the plane where electrons are confined. This phenomenon known asplanar Hall effect is accompanied by dependencies of both the longitudinal andthe transverse components of the current on the angle $\phi$ between the biasdirection and the magnetic field. In 2DEG with spin orbit coupling (SOC) suchas oxide interfaces, this effect has been experimentally witnessed. Further, afourfold oscillation in longitudinal resistance as a function of $\phi$ hasalso been observed. Motivated by these, we perform scattering theorycalculations on a 2DEG with SOC in presence of an in-plane magnetic fieldconnected to two dimensional leads on either sides to obtain longitudinal andtransverse conductances. We find that the longitudinal conductance is$\pi$-periodic and the transverse conductance is $2\pi$-periodic in $\phi$. Themagnitude of oscillation in transverse conductance with $\phi$ is enhanced incertain patches in $(\alpha,b)$-plane where $\alpha$ is the strength of SOC and$b$ is Zeeman energy due to magnetic field. The oscillation in transverseconductance with $\phi$ can be highly multi-fold for large values of $\alpha$and $b$. The highly multi-fold oscillations of transverse conductance are dueto Fabry-P\'erot type interference between the modes in the central region asbacked by its length dependent features. Our study establishes that SOC in amaterial is sufficient to observe planar Hall effect without the need foranisotropic magnetic ordering or nontrivial topology of the bandstructure.

journal of physics. condensed matter

Finite transverse conductance and anisotropic magnetoconductance under  an applied in-plane magnetic field in two-dimensional electron gases with  strong spin-orbit coupling