Center Of Cyclotron Orbit Research Articles

Electron dynamics in solid state via time varying wavevectors

In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors k(t). In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schröedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics differ from classical Lorentz force equations. We show that in a periodic potential, on application of electric field, the electron wave function adiabatically follows the wavefunction of a time varying Bloch wavevector k(t), with its energies suitably shifted with time. We derive the effective mass equation and discuss conduction in conductors and insulators.

The effect of electric potential on Landau levels for topological insulator surface states

We study the effect of an electric potential well on the Landau level (LL) spectrum for surface states of a three-dimensional (3D) topological insulator (TI) by using a method of numerical diagonalization for the Hamiltonian in a truncated Hilbert space. It is found that the dispersivity of energy is dependent on the position of electron cyclotron orbit center (COC). A dispersionless energy spectrum like flat LLs appeared as if without the confining potential when the electron COC is far away from the well boundaries (corners). When the electron COC is near the boundaries, however, there exist some interesting interface states propagating along the well due to the presence of electric confinement which causes quantized subband mixing. Moreover, the probability density and the spin polarization of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside. These findings here may provide a further understanding of 3D TI surface states.

General approach to the quantum kicked particle in a magnetic field: Quantum-antiresonance transition

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for general values of the conserved coordinate x(c) of the cyclotron orbit center. The system exhibits spectral structures ["Hofstadter butterflies" (HBs)] and quantum diffusion depending sensitively on x(c). Most significant changes take place when x(c) approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially "doubles" and the quantum-diffusion coefficient D(x(c)) is strongly reduced. An explanation of these phenomena, including an approximate formula for D(x(c)) in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all x(c) is briefly considered.

Uniform stochastic web in low-dimensional Hamiltonian systems

When an unperturbed Hamiltonian is degenerate and some resonance conditions are satisfied a stochastic web is formed. A classical example of this phenomena is the wave-particle interaction in a constant uniform magnetic field. Recently, Dana has observed that for wide wave packets, the initial position of the cyclotron orbit center, x c, may influence dramatically the diffusion of particles in phase space. A consistent method for finding the bare-web and the rigorous bounds on the separatrix splitting are derived for arbitrary position of the cyclotronic orbit center. The dramatic, sensitive dependence of the width of the stochastic layer on x c is thus revealed. It is then argued that x c = 0 corresponds to a nongeneric case, resolving contradictory results found for estimating the width of the stochastic layer in the commonly studied x c = 0 case.

Interband Transition Strength and Magneto‐Absorption Spectrum in Type‐I Superlattices in In‐Plane Magnetic Fields

AbstractUsing a simplified parabolic band model approach within the framework of the envelope function approximation, the influence of in‐plane magnetic fields on the electronic and optical properties of type‐I superlattices is studied. The results are in qualitative agreement with experimental facts previously reported, as well as with previous theoretical results obtained using more elaborated and toilsome methods. Furthermore, this approach allows to advance, in a great extent, in the analytical treatment of interband transitions, leading straightforwardly to some general conclusions. The not well understood case of high magnetic field effects (magnetic length comparable with the superlattice period) is studied in detail. There strong variations of the interband transition strengths as function of the cyclotron orbit center position are found, a fact which is directly connected with the broadening and final saturation of the magneto‐absorption spectrum with increasing fields. A consistent explanation of such strong variations is given in terms of magnetic subband mixing.

On the resonant tunneling through double-barrier structures in a tilted magnetic field

The influence of a tilted magnetic field on the resonant structure of current-voltage ( I-V) characteristics of layered semiconductor systems is analyzed both for the cases of weak and strong magnetic field. The Hall current and a current caused by tunneling assisted shift of cyclotron orbit center are also discussed.

Hydrodynamic theory of magnetoplasmons in a modulated two-dimensional electron gas

The dielectric response properties and the collective charge-density oscillations of a two-dimensional electron gas subject to both a perpendicular magnetic field and an in-plane superlattice potential are studied with use of a hydrodynamic theory of linear response. It is demonstrated that in addition to the usual principal magnetoplasmon, an additional branch in the collective spectrum develops as a result of the resonance drift of the cyclotron-orbit center in the crossed-field configuration, which leads to regular oscillations in 1/B of this mode frequency. Both one-dimensional and two-dimensional superlattice potentials are considered, and the respective dielectric tensors and magnetoplasma spectra are examined.

On transverse magnetoconductivity in strict born approximation

Various assumptions and approximations used in the quantum theory of magnetotransport in the strict Born approximation are critically discussed. It is concluded that the motion about the center of cyclotron orbit with proper damping of the Breit-Wigner type gives correct form of magnetoconducctivity which explains the observed behaviour of magnetoresistance.