Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

Khomitsky, D. V.; Malyshev, A. I.; Sherman, E. Ya.; Ventra, Massimiliano Di

doi:10.1103/physrevb.88.195407

Cited by 11 publications

(21 citation statements)

References 38 publications

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“…In these studies the non-Poissonian level statistics has been found which indicates the presence of quantum chaos. In our recent paper [21] we have found the development of strongly irregular dynamics in this system under the periodic driving by the electric field, which manifested itself in both charge and spin channels. Such nontrivial spin-dependent evolution of quantum states should also develop in the driving dynamics of electrons on the surface of 3D TIs and at the edge of 2D TIs, where the Dirac-Weyl Hamiltonian can be described as the limiting case of the electron Hamiltonian with extremely high linear-in-k SOC.…”

Section: Introductionmentioning

confidence: 77%

“…For our set of parameters (20), (21) one can easily check that for the driving frequency ω 0 = 0.58 · 10 12 s −1 considered below the amplitude of the driving field as low as E 0 ≈ 1 V/cm may put our system into an area of instability in the Ince-Strutt diagram. When this or higher electric field is driving the dynamics, one may expect the development of irregular regimes of spin and coordinate dynamics which are coupled through the system (14a)-(14e).…”

Section: Quasiclassical Dynamicsmentioning

confidence: 99%

“…We note that due to the confition k y (t) > 0 and the expression (15) our analysis is restricted to the area where k 0 > 1 which, according to (20), means that one must stay within in the quasiclassical region of moderate electric field. Taking into account (19), (20), (21), and by introducing the dimensionless time variable τ as…”

Section: Quasiclassical Dynamicsmentioning

confidence: 99%

“…The periodic driving allows us to apply some of the tools from the Floquet analysis [10,11,13,17,21] for understanding the system evolution. What is the most relevant for our system is the structure of the Floquet states where the (s)-th eigenstate is written as a vector A (s) n in the Hilbert space of the basis states Ψ n (y).…”

Section: Quantum Dynamics and Floquet Statesmentioning

confidence: 99%

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Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

Khomitsky¹,

Chubanov²,

Konakov³

2016

J. Exp. Theor. Phys.

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The dynamics of Dirac-Weyl spin-polarized wavepackets driven by periodic electric field is considered for the electrons in a mesoscopic quantum dot formed at the edge of two-dimensional HgTe/CdTe topological insulator with Dirac-Weyl massless energy spectra, where the motion of carriers is less sensitive to disorder and impurity potentials. It was observed that the interplay of strongly coupled spin and charge degrees of freedom creates the regimes of irregular dynamics both in coordinate and spin channels. The border between the regular and irregular regimes determined by the strength and frequency of the driving field is found analytically within the quasiclassical approach by means of the Ince-Strutt diagram for Mathieu equation, and is supported by full quantum mechanical simulations of the driven dynamics.The investigation of quasienergy spectrum by Floquet approach reveals the presence of non-Poissonian level statistics which indicates the possibility of chaotic quantum dynamics and corresponds to the areas of parameters for irregular regimes within the quasiclassical approach. We found that the influence of weak disorder leads to partial suppression of the dynamical chaos. Our findings are of interest both for progress in a fundamental field of quantum chaotic dynamics and for further experimental and technological applications of spin-dependent phenomena in nanostructures based on topological insulators.

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Section: Introductionmentioning

confidence: 77%

Section: Quasiclassical Dynamicsmentioning

confidence: 99%

Section: Quasiclassical Dynamicsmentioning

confidence: 99%

Section: Quantum Dynamics and Floquet Statesmentioning

confidence: 99%

See 2 more Smart Citations

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

Khomitsky¹,

Chubanov²,

Konakov³

2016

J. Exp. Theor. Phys.

Self Cite

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“…The analysis presented in that paper can be carried out for our system as well and we assume that the correspondence between classical and quantum chaotic behaviour holds in our case as well. A very interesting recent study of quantum billiard with spin-orbit coupling [54] provides further evidence that chaos will arise for spin-orbit coupled systems in …”

Section: B Nearest Neighbor Distributionsmentioning

confidence: 99%

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Marchukov¹,

Volosniev²,

Fedorov³

et al. 2014

J. Phys. B: At. Mol. Opt. Phys.

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We compute single-particle energy spectra for a one-body hamiltonian consisting of a twodimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding the Zeeman field we can reproduce a Brody distribution, which is known to describe a transition between the Poisson and linear Wigner distributions.

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Chaotic Cyclotron and Hall Trajectories Due to Spin‐Orbit Coupling

2020

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It is demonstrated that the synergistic effect of a gauge field, Rashba spin‐orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin‐dependent (so‐called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, the conditions of chaos emergence are studied and the dynamics both in the regular and chaotic regimes is reported. The critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions and problem parameters, that is the SOC and/or Zeeman constants, is observed. The transition to chaotic regime is further verified by the analysis of phase portraits as well as Lyapunov exponents spectrum. The considered chaotic behavior can occur in solid state systems, weakly relativistic plasmas, and cold atomic gases with synthetic gauge fields and spin‐related couplings.

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Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

Cited by 11 publications

References 38 publications

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

Regular and irregular dynamics of spin-polarized wavepackets in a mesoscopic quantum dot at the edge of topological insulator

Statistical properties of spectra in harmonically trapped spin–orbit coupled systems

Chaotic Cyclotron and Hall Trajectories Due to Spin‐Orbit Coupling

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