Decay of semiclassical massless Dirac fermions from integrable and chaotic cavities

TL;DR

This paper investigates the decay properties of massless Dirac fermions in cavities with integrable and chaotic dynamics, revealing conditions under which their confinement can be comparable to electromagnetic waves, with implications for Dirac electron optics.

Contribution

It uncovers an interval of refractive index where massless Dirac fermions exhibit long confinement times similar to electromagnetic waves, regardless of cavity dynamics, supported by numerical verification.

Findings

Existence of a refractive index interval with high confinement lifetime

Scaling laws for escape time ratios between electromagnetic and Dirac waves

Numerical verification of confinement behavior in integrable and chaotic cavities

Abstract

Conventional microlasing of electromagnetic waves requires (1) a high $Q$ cavity and (2) a mechanism for directional emission. Previous theoretical and experimental work demonstrated that the two requirements can be met with deformed dielectric cavities that generate chaotic ray dynamics. Is it possible for a massless Dirac spinor wave in graphene or its photonic counterpart to exhibit a similar behavior? Intuitively, because of the absence of backscattering of associated massless spin-1/2 particles and Klein tunneling, confining the wave in a cavity for a long time seems not feasible. Deforming the cavity to generate classical chaos would make confinement even more difficult. Investigating the decay of a spin-1/2 wave from a scalar potential barrier defined cavity characterized by an effective refractive index $n$ that depends on the applied potential and the particle energy, we uncover the striking existence of an interval of the refractive index in which the average lifetime of the massless spin-1/2 wave in the cavity can be as high as that of the electromagnetic wave, for both integrable and chaotic cavities. We also find scaling laws for the ratio between the mean escape time associated with electromagnetic waves and that with massless spin-1/2 particles versus the index outside of this interval. The scaling laws hold regardless of the nature of the classical dynamics. All the results are verified numerically. The findings provide insights into the emergent field of Dirac electron optics and have potential applications in developing unconventional electronics using 2D Dirac materials.