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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

Incident, reflected and transmitted local plane waves at a potential jump.
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f5: Incident, reflected and transmitted local plane waves at a potential jump.

Mentions: The origin of the “exceptional” magnetic response of the chaotic Dirac fermion can be understood through the behavior of the current carried by the particle at the boundary interface. We have developed an analytic understanding to predict the occurrence of Dirac WGMs and, consequently, SPCs. In particular, we consider the following problem: a plane wave incident obliquely on a straight potential jump M(x, y) given byas shown in Fig. 5. Without loss of generality, we let the incident wave ψi be described by the wave vector k0 = (k cos θ0, k sin θ0), the reflected wave ψr by k1 = (k cos θ1, k sin θ1, and the transmitted wave ψt by u = (iq, K), where θ1 = π − θ0 and K ≡ k sin θ0. We focus on the situation where the energy of the incident wave satisfies E < V0, which corresponds to the total reflection case.


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

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

Incident, reflected and transmitted local plane waves at a potential jump.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Incident, reflected and transmitted local plane waves at a potential jump.
Mentions: The origin of the “exceptional” magnetic response of the chaotic Dirac fermion can be understood through the behavior of the current carried by the particle at the boundary interface. We have developed an analytic understanding to predict the occurrence of Dirac WGMs and, consequently, SPCs. In particular, we consider the following problem: a plane wave incident obliquely on a straight potential jump M(x, y) given byas shown in Fig. 5. Without loss of generality, we let the incident wave ψi be described by the wave vector k0 = (k cos θ0, k sin θ0), the reflected wave ψr by k1 = (k cos θ1, k sin θ1, and the transmitted wave ψt by u = (iq, K), where θ1 = π − θ0 and K ≡ k sin θ0. We focus on the situation where the energy of the incident wave satisfies E < V0, which corresponds to the total reflection case.

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