All-electrostatic valley filtering by barrier rotation in tilted Dirac/Weyl semimetals

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, extend it 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, demonstrating that one valley is selectively transmitted, while the other is predominantly reflected by the angled barrier, without invoking real or pseudomagnetic fields.