The Effect of a Magnetic Field on the Acoustoelectric current in a Narrow Channel

The effect of a perpendicular magnetic field on the quantized current induced by a surface acoustic wave in a quasi-1D channel is studied. The channel has been produced experimentally in a GaAs heterostructure by shallow etching techniques and by the application of a negative gate voltage to Schottky split gates. Commensurability oscillations of the quantized current in this constriction have been observed in the interval of current between quantized plateaus. The results can be understood in terms of a moving quantum dot with the electron in the dot tunneling into the adjacent two-dimensional region. The goal is to explain qualitatively the mechanism for the steplike nature of the acoustoelectric current as a function of gate voltage and the oscillations when a magnetic field is applied. A transfer Hamiltonian formalism is employed.Comment: 5 pages, 2 figure

Spin-dependent Scattering by a Potential Barrier on a Nanotube

The electron spin effects on the surface of a nanotube have been considered through the spin-orbit interaction (SOI), arising from the electron confinement on the surface of the nanotube. This is of the same nature as the Rashba-Bychkov SOI at a semiconductor heterojunction. We estimate the effect of disorder within a potential barrier on the transmission probability. Using a continuum model, we obtained analytic expressions for the spin-split energy bands for electrons on the surface of nanotubes in the presence of SOI. First we calculate analytically the scattering amplitudes from a potential barrier located around the axis of the nanotube into spin-dependent states. The effect of disorder on the scattering process is included phenomenologically and induces a reduction in the transition probability. We analyzed the relative role of SOI and disorder on the transmission probability which depends on the angular and linear momentum of the incoming particle, and its spin orientation. We demonstrated that in the presence of disorder perfect transmission may not be achieved for finite barrier heights.Comment: 16 pages, 15 figure

Disentangling surface and bulk transport in topological-insulator pp-nn junctions

By combining $n$-type $\mathrm{Bi_2Te_3}$ and $p$-type $\mathrm{Sb_2Te_3}$ topological insulators, vertically stacked $p$-$n$ junctions can be formed, allowing to position the Fermi level into the bulk band gap and also tune between $n$- and $p$-type surface carriers. Here we use low-temperature magnetotransport measurements to probe the surface and bulk transport modes in a range of vertical $\mathrm{Bi_2Te_3/Sb_2Te_3}$ heterostructures with varying relative thicknesses of the top and bottom layers. With increasing thickness of the $\mathrm{Sb_2Te_3}$ layer we observe a change from $n$- to $p$-type behavior via a specific thickness where the Hall signal is immeasurable. Assuming that the the bulk and surface states contribute in parallel, we can calculate and reproduce the dependence of the Hall and longitudinal components of resistivity on the film thickness. This highlights the role played by the bulk conduction channels which, importantly, cannot be probed using surface sensitive spectroscopic techniques. Our calculations are then buttressed by a semi-classical Boltzmann transport theory which rigorously shows the vanishing of the Hall signal. Our results provide crucial experimental and theoretical insights into the relative roles of the surface and bulk in the vertical topological $p$-$n$ junctions.Comment: 11 pages, 5 figure

Hidden dimers and the matrix maps: Fibonacci chains re-visited

The existence of cycles of the matrix maps in Fibonacci class of lattices is well established. We show that such cycles are intimately connected with the presence of interesting positional correlations among the constituent `atoms' in a one dimensional quasiperiodic lattice. We particularly address the transfer model of the classic golden mean Fibonacci chain where a six cycle of the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys. Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far been provided, to the best of our knowledge. In addition, we show that our prescription leads to a determination of other energy values for a mixed model of the Fibonacci chain, for which the full matrix map may have similar cyclic behaviour. Apart from the standard transfer-model of a golden mean Fibonacci chain, we address a variant of it and the silver mean lattice, where the existence of four cycles of the matrix map is already known to exist. The underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review

Dephasing time of disordered two-dimensional electron gas in modulated magnetic fields

The dephasing time of disordered two-dimensional electron gas in a modulated magnetic field is studied. It is shown that in the weak inhomogeneity limit, the dephasing rate is proportional to the field amplitude, while in strong inhomogeneity limit the dependence is quadratic. It is demonstrated that the origin of the dependence of dephasing time on field amplitude lies in the nature of corresponding single-particle motion. A semiclassical Monte Carlo algorithm is developed to study the dephasing time, which is of qualitative nature but efficient in uncovering the dependence of dephasing time on field amplitude for arbitrarily complicated magnetic-field modulation. Computer simulations support analytical results. The crossover from linear to quadratic dependence is then generalized to the situation with magnetic field modulated periodically in one direction with zero mean, and it is argued that this crossover can be expected for a large class of modulated magnetic fields.Comment: 8 pages, 2 figure

Acoustoelectric effect in a finite-length ballistic quantum channel

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients r_1 and r_2 at both channel ends are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging r_1 and r_2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r_1 and r_2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of qL. These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.Comment: 7 pages, 2 figure