All-Electrostatic Valley Filtering by Barrier Rotation in Tilted Dirac/Weyl Semimetals

TL;DR

This paper demonstrates a purely electrostatic method for valley filtering in tilted Dirac/Weyl semimetals using angled barriers, enabling selective valley transmission without magnetic effects.

Contribution

It introduces a generalized transfer-matrix formalism for tilted, anisotropic Dirac Hamiltonians and shows how angled barriers can achieve valley filtering.

Findings

Valley-dependent refraction and reflection occur at electrostatic barriers.

Angled barriers produce finite valley-polarized conductance.

Simulation results show selective transmission of one valley.

Abstract

Charge carriers in Dirac/Weyl semimetals with tilted anisotropic energy dispersion exhibit valley-dependent refraction and reflection at electrostatic barrier interfaces. Here, we show that an angled barrier interface provides a purely electrostatic route to valley filtering, producing finite valley-polarized conductance. We develop a generalized transfer-matrix formalism for the tilted, anisotropic Dirac Hamiltonian, extended to treat electrostatic barriers at arbitrary angles, and calculate the transmission in the rotated-barrier frame. We also present simulated valley-resolved trajectories in a finite device geometry, which clearly show that one valley is selectively transmitted, whereas the other is predominantly reflected by the angled barrier, without secondary effects such as real or pseudo-magnetic fields.