Trapping massless Dirac particles in a rotating saddle

TL;DR

This paper demonstrates that rotating saddle-shaped potentials can localize massless Dirac particles, such as electrons in graphene, creating eigenstates with potential applications in quantum confinement.

Contribution

It introduces a novel method of trapping massless Dirac particles using rotating saddle potentials, extending previous work on particle confinement to relativistic-like particles.

Findings

Localized eigenstates near the saddle center at specific energies

Localized states have long life-times despite imperfections

Rotating saddle potentials enable confinement of massless Dirac particles

Abstract

We study particle motion in rotating saddle-shaped potentials. It is known that such rotating potentials can generate bounded motion for particles with a parabolic dispersion law through the combination of potential, centrifugal and Coriolis forces in the rotating frame. When applied to massless Dirac particles, for example electrons in graphene, such a potential is shown to lead to eigenstates that are spatially localized near the center of the saddle at certain energies. Although other states also exist at these energies, they have non-overlapping support in the oscillator basis, which tend to give the localized states a substantial life-time also when imperfections are present.