Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems

Hongya Xu, Liang Huang, Ying-Cheng Lai*, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)
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Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schro "dinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

Original languageEnglish
Article number8963
Number of pages8
JournalScientific Reports
Early online date11 Mar 2015
Publication statusPublished - 11 Mar 2015

Bibliographical note

This work was supported by AFOSR under Grant No. FA9550-12-1-0095 and by ONR under Grant No. N00014-08-1-0627. LH was supported by the NSF of China under Grant No. 11422541


  • topological dirac semimetal
  • time-reversal symmetry
  • persistent currents
  • mesoscopic rings
  • directional emission
  • graphene
  • billiards
  • single
  • oscillations
  • potentials


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