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Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.

Xu H, Huang L, Lai YC, Grebogi C - Sci Rep (2015)

Bottom Line: Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos.Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials.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.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.

ABSTRACT
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger 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.

No MeSH data available.


Related in: MedlinePlus

Persistent current (PC) as a function of the quantum flux parameter α from five lowest states (including spin) for nonrelativistic (a,b) and relativistic (c,d) cases.The domain is integrable for (a,c) and chaotic for (b,d).
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f4: Persistent current (PC) as a function of the quantum flux parameter α from five lowest states (including spin) for nonrelativistic (a,b) and relativistic (c,d) cases.The domain is integrable for (a,c) and chaotic for (b,d).

Mentions: The robust AB oscillations in chaotic Dirac rings lead to SPCs. The total persistent current can be calculated at zero temperature through166, where the sum runs over all occupied states with Ej > 0. Due to periodicity in the energy: Ej(α) = Ej(α + 1), the current is also periodic in α with the fundamental period α = 1. Figure 4 shows, for the nonrelativistic (top panels) and relativistic (bottom panels) cases, PCs resulted from the lowest three states (including spin) in regular (left column) and chaotic (right column) rings. We see that, for classical integrable dynamics, PC oscillations display a common sawtooth form. However, at zero flux, PC is zero for the nonrelativistic case [Fig. 4 (a)], while it has a finite value for the relativistic case due to breaking of the time-reversal symmetry. In the chaotic case, the oscillations become smooth due to level repulsion in the corresponding energy-flux dispersion pattern. As a result, PCs carried by the Schrödinger particle practically vanish as compared with the integrable case but, strikingly, the Dirac fermion still carries a persistent current with amplitude of the same order of magnitude as that for the integrable case - SPCs. Intuitively, SPCs carried by the Dirac fermion as an “exceptional” magnetic response are associated with the chaotic Dirac WGMs exemplified in Fig. 3.


Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.

Xu H, Huang L, Lai YC, Grebogi C - Sci Rep (2015)

Persistent current (PC) as a function of the quantum flux parameter α from five lowest states (including spin) for nonrelativistic (a,b) and relativistic (c,d) cases.The domain is integrable for (a,c) and chaotic for (b,d).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4355680&req=5

f4: Persistent current (PC) as a function of the quantum flux parameter α from five lowest states (including spin) for nonrelativistic (a,b) and relativistic (c,d) cases.The domain is integrable for (a,c) and chaotic for (b,d).
Mentions: The robust AB oscillations in chaotic Dirac rings lead to SPCs. The total persistent current can be calculated at zero temperature through166, where the sum runs over all occupied states with Ej > 0. Due to periodicity in the energy: Ej(α) = Ej(α + 1), the current is also periodic in α with the fundamental period α = 1. Figure 4 shows, for the nonrelativistic (top panels) and relativistic (bottom panels) cases, PCs resulted from the lowest three states (including spin) in regular (left column) and chaotic (right column) rings. We see that, for classical integrable dynamics, PC oscillations display a common sawtooth form. However, at zero flux, PC is zero for the nonrelativistic case [Fig. 4 (a)], while it has a finite value for the relativistic case due to breaking of the time-reversal symmetry. In the chaotic case, the oscillations become smooth due to level repulsion in the corresponding energy-flux dispersion pattern. As a result, PCs carried by the Schrödinger particle practically vanish as compared with the integrable case but, strikingly, the Dirac fermion still carries a persistent current with amplitude of the same order of magnitude as that for the integrable case - SPCs. Intuitively, SPCs carried by the Dirac fermion as an “exceptional” magnetic response are associated with the chaotic Dirac WGMs exemplified in Fig. 3.

Bottom Line: Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos.Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials.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.

View Article: PubMed Central - PubMed

Affiliation: 1] School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA [2] School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China.

ABSTRACT
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger 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.

No MeSH data available.


Related in: MedlinePlus