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

The current in response to a bias in certain two-dimensional electron gas (2DEG), can have a nonzero transverse component under a finite magnetic field applied in the plane where electrons are confined. This phenomenon known as planar Hall effect (PHE) is accompanied by dependencies of both the longitudinal and the transverse components of the current on the angleϕbetween the bias direction and the magnetic field. This effect can be observed in a variety of systems, for example in topological insulators where spin-momentum locking of the topologically protected surface states is the root cause for the effect and in magnetic systems where anisotropic magnetic ordering induces it. In 2DEG with spin orbit coupling (SOC) such as oxide interfaces, this effect has been experimentally witnessed. Further, a fourfold oscillation in longitudinal resistance as a function ofϕhas also been observed. Motivated by these, we perform scattering theory calculations on a 2DEG with SOC in presence of an in-plane magnetic field connected to two-dimensional leads on either sides to obtain longitudinal and transverse conductances. We find that the longitudinal conductance isπ-periodic and the transverse conductance is 2π-periodic inϕ. The magnitude of oscillation in transverse conductance withϕis enhanced in certain patches in (α,b)-plane whereαis the strength of SOC andbis Zeeman energy due to magnetic field. The oscillation in transverse conductance withϕcan be highly multi-fold for large values ofαandb. The highly multi-fold oscillations of transverse conductance are due to Fabry-Pérot type interference between the modes in the central region as backed by its length dependent features. Our study establishes that SOC in a material is sufficient to observe PHE without the need for anisotropic magnetic ordering or nontrivial topology of the bandstructure.