Abstract
Tunneling transport across electrical potential barriers in Weyl semimetals with tilted energy dispersion is investigated. We report that the electrons around different valleys experience opposite direction refractions at the barrier interface when the energy dispersion is tilted along one of the transverse directions. Chirality dependent refractions at the barrier interface polarize the Weyl fermions in angle-space according to their valley index. A real magnetic barrier configuration is used to select allowed transmission angles, which results in electrically controllable and switchable valley polarization. Our findings may pave the way for experimental investigation of valley polarization, as well as valleytronic and electron optic applications in Weyl semimetals.
Highlights
Charge carriers in crystal lattices may carry a valley isospin degree of freedom, in addition to their real spin
We focus on the simplest Weyl semimetal case where the time reversal symmetry is broken, which allows the presence of a single pair of Weyl nodes related by the inversion symmetry
Since the number of Weyl nodes, their respective chirality and tilt direction can vary according to the host materials, we have focused on the simplest Weyl semimetal case where there exists only one pair of Weyl nodes related by inversion symmetry
Summary
The valley polarization highly depends on the tilt strength that generates the valley-dependent transverse shift at the barrier interface Note that this anomalous momentum shift is caused by the combined effect of the electrical potential and tilted band structure. In such case, there would still be non-zero valley polarization as the presence of valley dependent refractions does not depend on the specific B-field profile. Having a small finite thickness may be a crucial factor if one requires the use of gated potential barriers due to the short range screening effect In this part, we consider the case where the system has a finite thickness along one of the directions and calculate the valley dependent conductance. The finite thickness dx along the x-direction leads to sub-band obtain t dependent mass he eigenspectr due to um, t the he quantization of kx such that 〈kx2〉n Schrodinger equation can b
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