Persistent current of relativistic electrons on a Dirac ring in presence of impurities

Ghosh, Sumit; Saha, Arijit

doi:10.1140/epjb/e2014-50223-1

Cited by 8 publications

(3 citation statements)

References 42 publications

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“…In 1D systems with random impurities, Klein tunneling has a strong manifestation in the behavior of the persistent currents 62 . This is because, in one dimension, the incident "angle" of a wave on an impurity is zero so that the condition for Klein tunneling is always met.…”

Section: Results and Qualitative Understandingmentioning

confidence: 99%

“…In nonrelativistic quantum systems the disorders have a devastating effect on the persistent currents, so they can only be observed in systems of sufficiently small size (e.g., size the phase coherence length of the material). For relativistic quantum systems, there is a recent work on the effects of random disorders on persistent currents in one dimension 62 . It is of interest to understand the effect in experimentally more feasible 2D systems.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…In relativistic quantum systems, Klein tunnel- ing is referred to as the phenomenon where an incoming electron can penetrate a potential barrier whose height is larger than the electron energy with probability one 61 . In 1D systems with random impurities, Klein tunneling has a strong manifestation in the behavior of the persistent currents 62 . This is because, in one dimension, the incident "angle" of a wave on an impurity is zero so that the condition for Klein tunneling is always met.…”

Section: Model Hamiltonian and Simulation Settingmentioning

confidence: 99%

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

Ying

Lai

2017

Phys. Rev. B

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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.

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Section: Results and Qualitative Understandingmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%