Decay of semiclassical massless Dirac fermions from 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.

Electron wave and quantum optics in graphene

“…In [226], the decay features of integrable disk-and chaotic stadium-type cavities were studied based on classical ray tracing. Schrepfer et al [103] explores charge carrier trapping and (directed) emission for deformed leaky graphene micro-disks by considering the complete ray-wave correspondence through classical and quantum simulations.…”

Electrical confinement in a spectrum of two-dimensional Dirac materials with classically integrable, mixed, and chaotic dynamics

“…In the quantum-dot regime k 0 R 1 V R, we have |k 0 | |q|. In the language of Dirac electron optics, waves inside the cavity will have a large relative refractive index, rendering existent a critical angle for total internal reflection [15,27,42], which makes confinement possible.…”

“…Similar to optics [24], such a structure can be exploited for storage and energy transfer in spintronics and valleytronics [25,26]. However, even in a perfectly circular cavity generated by, e.g., an electrostatic potential, confinement of pseudospin-1/2 particles in graphene is already a nontrivial issue [27], due to the phenomenon of Klein tunneling [28][29][30][31][32][33][34]. To confine pseudospin-1 particles is also difficult, due to super-Klein tunneling [33], in which particles can penetrate through a high and wide potential barrier at any angle.…”

“…In order to confine an electron inside the cavity, its energy should be far away from the Klein tunneling regime that occurs for E ≈ U/2 for graphene [28][29][30][31][32][33][34] and pseudospin-1 materials [33]. For the confinement problem to have physical and applied significance, we focus on the quantum-dot regime where the effect of Klein tunneling is weak [15,27,42]. First, we choose the incident energy E such that it is much smaller than the electric potential: |E | |U |, as shown by the energy band structure in Fig.…”

Dirac fermion optics and directed emission from single- and bilayer graphene cavities

“…In Ref. [40] the decay features of integrable disk-and chaotic stadium-type cavities were studied based on classical ray tracing.…”