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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

Probability distribution of the 10th eigenstate for (a–c) nonrelativistic and (d–f) relativistic AB chaotic billiard for α = −1/4, 0, 1/4, respectively.
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f3: Probability distribution of the 10th eigenstate for (a–c) nonrelativistic and (d–f) relativistic AB chaotic billiard for α = −1/4, 0, 1/4, respectively.

Mentions: We now present evidence of Dirac WGMs for the case of fully chaotic AB ring domain. By examining the eigenstates, we note that, for low energy levels, the Schrödinger particle is strongly localized throughout the domain, as shown in Figs. 3(a–c), leading to a flat energy-flux dispersion. However, the Dirac fermion typically travels around the ring's boundaries, forming relativistic WGMs that persist under irregular boundary scattering due to chaos and are magnetic-flux dependent, as shown in Fig. 3(d–f). Conventional wisdom for Schrödinger particle stipulates that asymmetry in the domain geometry can mix/couple well-defined angular momentum states, opening energy gaps and leading to localization of lower states in the entire domain region, so AB oscillations would vanish, as demonstrated both theoretically and experimentally2224. However, for Dirac fermion, this picture breaks down - there are robust AB oscillations even in the fully chaotic domain and the particle tends to execute motions corresponding to WGMs.


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

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

Probability distribution of the 10th eigenstate for (a–c) nonrelativistic and (d–f) relativistic AB chaotic billiard for α = −1/4, 0, 1/4, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Probability distribution of the 10th eigenstate for (a–c) nonrelativistic and (d–f) relativistic AB chaotic billiard for α = −1/4, 0, 1/4, respectively.
Mentions: We now present evidence of Dirac WGMs for the case of fully chaotic AB ring domain. By examining the eigenstates, we note that, for low energy levels, the Schrödinger particle is strongly localized throughout the domain, as shown in Figs. 3(a–c), leading to a flat energy-flux dispersion. However, the Dirac fermion typically travels around the ring's boundaries, forming relativistic WGMs that persist under irregular boundary scattering due to chaos and are magnetic-flux dependent, as shown in Fig. 3(d–f). Conventional wisdom for Schrödinger particle stipulates that asymmetry in the domain geometry can mix/couple well-defined angular momentum states, opening energy gaps and leading to localization of lower states in the entire domain region, so AB oscillations would vanish, as demonstrated both theoretically and experimentally2224. However, for Dirac fermion, this picture breaks down - there are robust AB oscillations even in the fully chaotic domain and the particle tends to execute motions corresponding to WGMs.

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