Robustness of persistent currents in two-dimensional Dirac systems with disorder

Abstract

We consider two-dimensional (2D) Dirac quantum ring systems formed by the infinite mass constraint. When an Aharonov-Bohm magnetic flux is present, e.g., through the center of the ring domain, persistent currents, i.e., permanent currents without dissipation, can arise. In real materials, impurities and defects are inevitable, raising the issue of robustness of the persistent currents. Using localized random potential to simulate the disorders, we investigate how the ensemble averaged current magnitude varies with the disorder density. For comparison, we study the nonrelativistic quantum counterpart by analyzing the solutions of the Schrödinger equation under the same geometrical and disorder settings. We find that, for the Dirac ring system, as the disorder density is systematically increased, the average current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents. The physical mechanism responsible for the robustness is the emergence of a class of boundary states -whispering gallery modes. In contrast, in the Schrödinger ring system, such boundary states cannot form and the currents diminish rapidly to zero with increase in the disorder density. We develop a physical theory based on a quasi one-dimensional approximation to understand the striking contrast in the behaviors of the persistent currents in the Dirac and Schrödinger rings. Our 2D Dirac ring systems with disorders can be experimentally realized, e.g., on the surface of a topological insulator with natural or deliberately added impurities from the fabrication process.

Relativistic quantum chaos

“…The underlying physical mechanism was identified to be Dirac whispering gallery modes (WGMs) along the domain boundary, which carry large angular momenta. It was also found that in Dirac fermion systems, persistent currents are robust against random disorders [139]. The focus of our discussion will then be on the robustness of persistent currents in relativistic quantum systems with classical chaos or random disorders.…”

“…In RQC, topics that have been studied so far include energy level-spacing statistics in graphene systems [115][116][117][118][119][120], relativistic quantum scarring [121][122][123][124], relativistic quantum chaotic scattering and transport [125][126][127][128][129][130][131][132][133], quantum resonant tunneling in Dirac fermion and graphene systems [134][135][136], effects of chaos and random disorder on persistent currents in Dirac fermion sys-tems [137][138][139], the role of classical dynamics in confinement of massless Dirac fermions [140][141][142][143], chaos and spin transport in graphene quantum dot systems [144], and the interplay among chaos, relativistic quantum mechanics, and many body interaction in graphene billiards [136,145].…”

Relativistic quantum chaos—An emergent interdisciplinary field

“…Further support for the robustness of the persistent currents in 2D relativistic quantum systems was obtained recently through a systematic study of the effects of random disorders. 236 In the study, the same geometric setting of an infinite mass confined Dirac ring domain with a vertical magnetic flux through the center was used. Uncorrelated disorders were assumed to exist throughout the domain, which were simulated using localized, uniformly distributed random electric potentials.…”

“…The total number of disorders in the whole domain was chosen as a control parameter, and the Dirac equation was solved numerically to obtain the magnitudes of the persistent currents as a function of the control parameter. It was found 236 that, as the number of the disorders is systematically increased, the average current decreases slowly initially and then plateaus at a finite nonzero value, indicating that the persistent currents are robust. Whispering gallery modes along the domain edges were again identified to be the physical mechanism responsible for the robust currents.…”

Charge currents and induced magnetic fields in a bounded two-dimensional hydrogen atom

“…The effect of static high magnetic fields on the optical spectra of excitons confined in semiconductor quantum rings along with the magnetization associated with the persistent current in these excitons has been studied by Govorov et al [33]. For a 2D Dirac quantum ring system, the disorder due to impurities and defects has been simulated by using localized random potential thus establishing the robustness of the per- sistent currents in comparison with the non-relativistic case [34]. Confinement effects on persistent currents in hydrogenic atoms under the effect of Hulthén plus a ring-shaped potential have been studied in our earlier work [35].…”