Confining massless Dirac particles in two-dimensional curved space

Abstract

Dirac particles have been notoriously difficult to confine. Implementing a curved-space Dirac equation solver based on the quantum lattice Boltzmann method, we show that curvature in a two-dimensional space can confine a portion of a charged, massless Dirac fermion wave packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved-space region. We propose a general power-law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.