Dynamics of a charged particle in a magnetic-flux lattice

Abstract

The dynamics of a charged particle in a two-dimensional space under the influence of a nonuniform, periodic magnetic field, similar to the magnetic induction inside an extremely type-II superconductor in the vortex state, is studied. The Hamiltonian for this model is found to be classically nonintegrable. A study of classical trajectories shows a global transition from a confined chaotic motion on tori for small amplitude of the periodic modulation, to an extended chaotic system that fills phase space uniformly, for strong modulations. The classical dynamics is confronted with a semiclassical Gaussian wave-packet approach and a time-dependent quantum-mechanical ͑QM͒ propagation scheme, for the same Hamiltonian. When the magnetic field modulation is small the envelopes of both the semiclassical and the exact QM autocorrelation functions are found to be Gaussian at short times. For a strong magnetic field modulation the envelope of the semiclassical autocorrelation function crosses over to a decaying exponential, determined by the characteristic Lyapunov exponent of the chaotic motion. It deviates significantly from the exact QM autocorrelation function, which retains the Gaussian envelope. The relatively strong recursion peaks of the latter may indicate a quantum localization effect.

Chiral two-dimensional electron gas in a periodic magnetic field

“…Previous investigations of the 2D electronic system in periodic magnetic fields concentrated mostly on the onedimensional periodic modulation 8,9 and, in some cases, on a mutual effect of the uniform and periodic magnetic fields. 10,11,12,13,14 The main difference of our work is that we assume that the uniform magnetic field is exactly zero, whereas the periodic field forms a real two-dimensional nanolattice. For definiteness, here we focus on the case of triangular lattice, which corresponds to the nanocylinder structure of Ref.…”

Quasiparticles Density of States and the Scattering Rate in Ideal Type II Superconductor by a Time-Dependent Approach

“…(12) function found by Heller [24] and by Rom et al [25]. The shortest time scale, 1 , determined by the half-width halfmaximum of a recursion peak, is related to the broadest The Gaussian envelope obtained in the time domain subbands with a mirror symmetry around E ϭ 0 due to indicates a Gaussian broadening envelop of the DOS in the symmetry of the BdG equations [23].…”