Spin--valley--resolved tunneling through magnetic barriers in WSe$_2$

TL;DR

This paper analyzes how magnetic fields influence spin and valley polarization, conductance, and tunneling in WSe$_2$, highlighting potential applications in valleytronics and fermion control.

Contribution

It provides an analytical and numerical study of magnetic field effects on tunneling, conductance, and polarization in WSe$_2$, emphasizing valley-specific behaviors and control mechanisms.

Findings

Transmission is more likely through the $K$ valley than $K'$.

Klein tunneling is observed in both valleys.

Magnetic fields modify energy levels and enable fermion confinement.

Abstract

We investigate the influence of a magnetic field on the electronic properties of WS$e_2$ with a focus on spin-orbit coupling, spin and valley polarization, and conductance. We solve the eigenvalue equation analytically and use the continuity equation to determine the transmission probability based on current densities. We calculate the conductance using B\"uttiker formula. Our numerical results indicate that transmission through the $K$ valley is more likely than through the $K'$ valley. For both valleys, the Klein tunneling effect is clearly observed. The conductance is affected by an increase in the magnetic field because it alters the energy levels of fermions via the Zeeman effect. These modifications enable the confinement of fermions within the barrier. Spin and valley polarization are also influenced by the magnetic field. As the field intensity increases, it steers the fermions and determines which channel can cross the barrier. This adds another tool of controlling fermions, paving the way for relevant applications in valleytronics and valley filtering for information storage.