Maxim Vavilov

Magnetotransport in a two-dimensional electron gas at large filling factors

We derive the quantum Boltzmann equation for the two-dimensional electron gas in a magnetic field such that the filling factor v»1. This equation describes all of the effects of the external fields on the impurity collision integral including Shubnikov-de Haas oscillations, the smooth part of the magnetoresistance, and nonlinear transport. Furthermore, we obtain quantitative results for the effect of the external microwave radiation on the linear and nonlinear de transport in the system. Our findings are relevant for the description of the oscillating resistivity discovered by Zudov et al., the zero-resistance state discovered by Mani et al. and Zudov et al., and for the microscopic justification of the model of Andreev et al. We also present a semiclassical picture for the qualitative consideration of the effects of the applied field on the collision integral.

Charge pumping and photovoltaic effect in open quantum dots

We propose a random matrix theory to describe the influence of a time-dependent external field on electron transport through open quantum dots. We describe the generation of the current by an oscillating field for the dot, connected to two leads with equal chemical potentials. For low-frequency fields, our results correspond to adiabatic charge pumping. Finite current can be produced if the system goes along a closed loop in parameter space, which covers a finite area. At high frequency, a finite current is produced even if the loop is a line in parameter space. This result can be explained in the same way as adiabatic pumping, but considering the evolution of the system in phase space rather than in parametric space.

Momentum dependence and nodes of the superconducting gap in the iron pnictides

Received 31 March 2009; revised manuscript received 1 October 2009; published 29 October 2009 Using general symmetry arguments and model calculations we analyze the superconducting gap in materials with multiple Fermi-surface pockets, with applications to iron pnictides. We show that the gap in the pnictides has an extended s-wave symmetry but is either nodeless or has nodes, depending on the interplay between intraband and interband interactions. We argue that the nodes in the gap emerge without a phase transition as the tendency toward a spin-density-wave order gets weaker. These findings provide a way to reconcile seemingly conflicting results of numerical and experimental studies of the pnictides.

Superconductivity and spin-density waves in multiband metals

We present a detailed description of two-band quasi-2D metals with s-wave superconducting (SC) and antiferromagnetic spin-density wave (SDW) correlations. We present a general approach and use it to investigate the influence of the difference between the shapes and the areas of the two Fermi surfaces on the phase diagram. In particular, we determine the conditions for the co-existence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order co-exists with SDW order only at very low T and in a very tiny range of parameters. An extended s-wave superconductivity, for which SC gap changes sign between the two bands, co-exists with antiferromagnetic SDW over a much wider range of parameters and temperatures, but even for this SC order the regions of SDW and SC can still be separated by a first order transition. We show that the co-existence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which co-existence of SDW and SC orders has been detected.

Non-linear Resistivity of a Two-Dimensional Electron Gas in a Magnetic Field

We develop a theory of nonlinear response to an electric field of a two-dimensional electron gas (2DEG) placed in a classically strong magnetic field. The latter leads to a nonlinear current-voltage characteristic at a relatively weak electric field. The origin of the nonlinearity is twofold: the formation of a nonequilibrium electron distribution function and the geometrical resonance in the inter-Landau-level transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG.

Superfluid density and penetration depth in the iron pnictides

tended s-wave symmetry (s + ) in the presence of non-magnetic impurities and apply the results to Fe-pnictides. We show that the behavior of the superfluid density is essentially the same as in an ordinary s-wave superconductor with magnetic impurities. We show that, for moderate to strong inter-band impurity scattering, �s(T) behaves as a power-law T n with n � 1.6 ÷ 2 over a wide range of T. We argue that the power-law behavior is consistent with recent experiments on the penetration depth �(T) in doped BaFe2As2, but disagree quantitatively with the data on LaFePO.

Mechanisms of the microwave photoconductivity in two-dimensional electron systems with mixed disorder

We present a systematic study of the microwave-induced oscillations in the magnetoresistance of a twodimensional electron gas for mixed disorder including both short-range and long-range components. The obtained photoconductivity tensor contains contributions of four distinct transport mechanisms. We show that the photoresponse depends crucially on the relative weight of the short-range component of disorder. Depending on the properties of disorder, the theory allows one to identify the temperature range within which the photoresponse is dominated by one of the mechanisms analyzed in the paper.

Noise through quantum pumps

We study the current noise through an unbiased quantum electron pump and its mesoscopic fluctuations for arbitrary temperatures and beyond the bilinear response. In the bilinear regime, we find the full distributions of the noise power and the current-to-noise ratio for chaotic quantum dots with single-channel and many-channel ballistic point contacts. For a dot with many-channel point contacts we also calculate the ensemble-averaged noise at arbitrary temperature and pumping strength. In the limit of strong pumping, a new temperature scale appears that corresponds to the broadening of the electron distribution function in the dot as a result of the time-dependent perturbations.

Universal gap fluctuations in the superconductor proximity effect.

Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal function in rescaled units. Our analytical prediction for the gap distribution agrees well with exact diagonalization of a model Hamiltonian.

Failure of the Wiedemann-Franz law in mesoscopic conductors

We study the effect of mesoscopic fluctuations on the validity of the Wiedemannn-Franz WF law for quasi-one-dimensional metal wires and open quantum dots. At temperatures much less than the generalized Thouless energy, Ec, the WF law is satisfied for each specific sample, but as the temperature is raised through Ec, a sample-specific correction to the WF law of order 1/g appears g is the dimensionless conductance and then tends to zero again at kBTEc. The mesoscopic violation of the Weidemann-Franz law is even more pronounced in a ring geometry for which the Lorenz number exhibits h/e flux-periodic Aharonov-Bohm oscillations.