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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

Top panels: domain shape with classical dynamics ranging from integrable (a = 0; left most panel) and mixed (a = 0.25 and 0.5; middle two panels) to chaotic (a = 1.0; right most panel). Middle panels: nonrelativistic AB oscillations (energy-flux dispersions). Bottom panels: relativistic AB oscillations.
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f2: Top panels: domain shape with classical dynamics ranging from integrable (a = 0; left most panel) and mixed (a = 0.25 and 0.5; middle two panels) to chaotic (a = 1.0; right most panel). Middle panels: nonrelativistic AB oscillations (energy-flux dispersions). Bottom panels: relativistic AB oscillations.

Mentions: To demonstrate our findings, we deform a circular ring domain ξ = 0.5 ≤ r ≤ 1, using the mapping w(z) = h[z + 0.05az2 + 0.18a exp(iω)z5], where ω = π/2, a ∈ [0, 1] is the deformation parameter that controls the classical dynamics. Specifically, when increasing a from zero to unity the deformed ring will undergo a transition from being regular to mixed and finally to being fully chaotic. The normalization coefficient guarantees that the domain area is invariant for arbitrary values of the deformation parameters {a, ω, ξ}. Four representative domains are shown in the top row in Fig. 2 where, classically, the left most domain is integrable, the right most domain is fully chaotic, and the two middle domains have mixed phase space. The middle and bottom rows of Fig. 2 show the lowest 10 energy levels as functions of the quantum flux parameter α, i.e., energy-flux dispersions, for Schrödinger and Dirac particles, respectively. We see that Ej(α) = Ej(−α) holds for the Schrödinger particle, but for the Dirac fermion, the symmetry is broken: Ej(α) ≠ E(−α). However, for both nonrelativistic and relativistic spectra, we have Ej(α) = Ej(α + 1). For the circular-symmetric ring (a = 0), AB oscillations in the energy levels have the period Φ0 (i.e., α = 1) and there are level crossings. Making the domain less symmetric by tuning up the value of the deformation parameter a leads to classical mixed phase space (regular and chaotic), and eventually to full chaos (a = 1). We see that, for the Schrödinger particle, emergence of a chaotic component in the classical space leads to opening of energy gaps, generating level repulsion and flattening the AB oscillations associated with the corresponding energy levels. Surprisingly, for the Dirac fermion, the AB oscillations are much more robust against asymmetric deformations. In particular, for the fully chaotic case, AB oscillations for the Schrödinger particle disappear almost entirely while those for the Dirac fermion persist with amplitudes of the same order of magnitudes as the integrable case.


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

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

Top panels: domain shape with classical dynamics ranging from integrable (a = 0; left most panel) and mixed (a = 0.25 and 0.5; middle two panels) to chaotic (a = 1.0; right most panel). Middle panels: nonrelativistic AB oscillations (energy-flux dispersions). Bottom panels: relativistic AB oscillations.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Top panels: domain shape with classical dynamics ranging from integrable (a = 0; left most panel) and mixed (a = 0.25 and 0.5; middle two panels) to chaotic (a = 1.0; right most panel). Middle panels: nonrelativistic AB oscillations (energy-flux dispersions). Bottom panels: relativistic AB oscillations.
Mentions: To demonstrate our findings, we deform a circular ring domain ξ = 0.5 ≤ r ≤ 1, using the mapping w(z) = h[z + 0.05az2 + 0.18a exp(iω)z5], where ω = π/2, a ∈ [0, 1] is the deformation parameter that controls the classical dynamics. Specifically, when increasing a from zero to unity the deformed ring will undergo a transition from being regular to mixed and finally to being fully chaotic. The normalization coefficient guarantees that the domain area is invariant for arbitrary values of the deformation parameters {a, ω, ξ}. Four representative domains are shown in the top row in Fig. 2 where, classically, the left most domain is integrable, the right most domain is fully chaotic, and the two middle domains have mixed phase space. The middle and bottom rows of Fig. 2 show the lowest 10 energy levels as functions of the quantum flux parameter α, i.e., energy-flux dispersions, for Schrödinger and Dirac particles, respectively. We see that Ej(α) = Ej(−α) holds for the Schrödinger particle, but for the Dirac fermion, the symmetry is broken: Ej(α) ≠ E(−α). However, for both nonrelativistic and relativistic spectra, we have Ej(α) = Ej(α + 1). For the circular-symmetric ring (a = 0), AB oscillations in the energy levels have the period Φ0 (i.e., α = 1) and there are level crossings. Making the domain less symmetric by tuning up the value of the deformation parameter a leads to classical mixed phase space (regular and chaotic), and eventually to full chaos (a = 1). We see that, for the Schrödinger particle, emergence of a chaotic component in the classical space leads to opening of energy gaps, generating level repulsion and flattening the AB oscillations associated with the corresponding energy levels. Surprisingly, for the Dirac fermion, the AB oscillations are much more robust against asymmetric deformations. In particular, for the fully chaotic case, AB oscillations for the Schrödinger particle disappear almost entirely while those for the Dirac fermion persist with amplitudes of the same order of magnitudes as the integrable 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