Electrostatic control of valley-dependent phase in tilted Dirac/Weyl channels

Abstract

Valley degrees of freedom are a promising resource for solid-state quantum information. However, traditional architectures rely on engineered valley energy splitting in semiconductors to utilize the valley degree of freedom as an information carrier, an approach not naturally available in the gapless, energetically degenerate valleys of Dirac and Weyl materials. In this work, we demonstrate electrostatic control of valley-dependent phase in tilted Dirac/Weyl semimetals. The presented scheme utilizes the tilted energy dispersion of Dirac/Weyl cones separated in momentum space. By routing wave-packets through a shaped electrostatic barrier, the valley-dependent tilt induces differential spatial drift and dwell times, accumulating a continuously tunable relative dynamical phase. Because the two valleys' propagation diverges transversely due to the tilt velocity in the absence of the potential barrier, the gate is defined relative to the corresponding zero-barrier evolution, so the barrier acts as a valley-diagonal phase element within the transported reference basis. Time-dependent transport simulations demonstrate electrically tunable relative phases (including $\pi/4$, $\pi/2$, and $\pi$ targets) operating on equal-energy valleys, with good mode preservation, and high transmission probability ($T_{K,K'} \approx 1$). Furthermore, we identify coherent deviation from the transported reference modes as the primary mechanism that limits ideal behavior at higher barrier heights. This work isolates a transport-based route to coherent $Z$-type valley phase control driven purely by relativistic transport dynamics.