Magnetic field induced Fabry-P\'erot resonances in helical edge states

Abstract

We study electronic transport across a helical edge state exposed to a uniform magnetic ({$\vec B$}) field over a finite length. We show that this system exhibits Fabry-P\'erot type resonances in electronic transport. The intrinsic spin anisotropy of the helical edge states allows us to tune these resonances by changing the direction of the {$\vec B$} field while keeping its magnitude constant. This is in sharp contrast to the case of non-helical one dimensional electron gases with a parabolic dispersion, where similar resonances do appear in individual spin channels ($\uparrow$ and $\downarrow$) separately which, however, cannot be tuned by merely changing the direction of the {$\vec B$} field. These resonances provide a unique way to probe the helical nature of the theory.