Crossover from weak localization to Shubnikov-de Haas oscillations in a high mobility 2D electron gas

We study the magnetoresistance, \delta\rho_{xx}(B)/\rho_0, of a high-mobility 2D electron gas in the domain of magnetic fields, B, intermediate between the weak localization and the Shubnikov-de Haas oscillations, where \delta\rho_{xx}(B)/\rho_0 is governed by the interaction effects. Assuming short-range impurity scattering, we demonstrate that in the {\em second order} in the interaction parameter, $\lambda$, a {\em linear} B-dependence, \delta\rho_{xx}(B)/\rho_0\sim \lambda^2\omega_c/E_F with {\em temperature-independent} slope emerges in this domain of B (here \omega_c and E_F are the cyclotron frequency and the Fermi energy, respectively). Unlike previous mechanisms, the linear magnetoresistance is {\em unrelated} to the electron executing the full Larmour circle, but rather originates from the impurity scattering via the B-dependence of the {\em phase} of the impurity-induced Friedel oscillations.Comment: 4+ pages, 3 figure

Zero-bias tunneling anomaly in a clean 2D electron gas caused by smooth density variations

We show that smooth variations, \delta n({\bf r}), of the local electron concentration in a clean 2D electron gas give rise to a zero-bias anomaly in the tunnel density of states, \nu(\omega), even in the absence of scatterers, and thus, without the Friedel oscillations. The energy width, \omega_0, of the anomaly scales with the magnitude, \delta n, and characteristic spatial extent, D, of the fluctuations as (\delta n/D)^{2/3}, while the relative magnitude \delta\nu/\nu scales as (\delta n/D). With increasing \omega, the averaged \delta\nu oscillates with \omega. We demonstrate that the origin of the anomaly is a weak curving of the classical electron trajectories due to the smooth inhomogeneity of the gas. This curving suppresses the corrections to the electron self-energy which come from the virtual processes involving two electron-hole pairsComment: 4+ pages, 3 figure

Hofstadter Problem on the Honeycomb and Triangular Lattices: Bethe Ansatz Solution

We consider Bloch electrons on the honeycomb lattice under a uniform magnetic field with $2 \pi p/q$ flux per cell. It is shown that the problem factorizes to two triangular lattices. Treating magnetic translations as Heisenberg-Weyl group and by the use of its irreducible representation on the space of theta functions, we find a nested set of Bethe equations, which determine the eigenstates and energy spectrum. The Bethe equations have simple form which allows to consider them further in the limit $p, q \to \infty$ by the technique of Thermodynamic Bethe Ansatz and analyze Hofstadter problem for the irrational flux.Comment: 7 pages, 2 figures, Revte

Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.Comment: 4 pages, 4 figure

Integrable XYZ Model with Staggered Anisotropy Parameter

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.Comment: 8 pages ; epic packag

Smearing of the 2D Kohn anomaly in a nonquantizing magnetic field: Implications for the interaction effects

Thermodynamic and transport characteristics of a clean two-dimensional interacting electron gas are shown to be sensitive to the weak perpendicular magnetic field even at temperatures much higher than the cyclotron energy, when the quantum oscillations are completely washed out. We demonstrate this sensitivity for two interaction-related characteristics: electron lifetime and the tunnel density of states. The origin of the sensitivity is traced to the field-induced smearing of the Kohn anomaly; this smearing is the result of curving of the semiclassical electron trajectories in magnetic field.Comment: 4.5 pages, 3 figures, published versio