Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

TL;DR

This paper develops a method to map known solutions of 2D Dirac equations in graphene onto tilted Dirac materials like borophene, enabling precise modeling of quantum confinement and valley polarization control.

Contribution

It introduces a transformation technique that extends solutions from graphene to tilted Dirac materials, facilitating the design of valleytronic devices.

Findings

Exact solutions for tilted Dirac materials derived from graphene solutions

Waveguides can manipulate valley polarization in borophene

Hyperbolic secant potential models realistic top-gated valleytronic structures

Abstract

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given 1D potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a tilted anisotropic 2D Dirac material. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.