We develop a theory of magnetooscillations in the photoconductivity of a two-dimensional electron gas observed in recent experiments. The effect is governed by a change of the electron distribution function induced by the microwave radiation. We analyze a nonlinearity with respect to both the dc field and the microwave power, as well as the temperature dependence determined by the inelastic relaxation rate.

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

We consider the superfluid density ρs(T ) in a two-band superconductor with sign-changing extended 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, ρs(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 λ(T ) in doped BaFe2As2, but disagree quantitatively with the data on LaFePO.

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.

We present a detailed description of two-band quasi-two-dimensional metals with s-wave superconducting ͑SC͒ and antiferromagnetic spin-density-wave ͑SDW͒ 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 coexistence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order coexists 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, coexists 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 coexistence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which coexistence of SDW and SC orders has been detected.

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 non-linear current-voltage characteristic at a relatively weak electric field. The origin of the non-linearity is two-fold: the formation of a non-equilibrium electron distribution function, and the geometrical resonance in the inter-Landau-levels transitions rates. We find the dependence of the current-voltage characteristics on the electron relaxation rates in the 2DEG.

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.

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. 74.50.+r, 74.80.Fp A normal metal in the proximity of a superconductor acquires characteristics that are typical of the superconducting state [1]. One of those characteristics is that the quasiparticle density of states vanishes at the Fermi energy. This superconductor proximity effect is most pronounced in a confined geometry, such as a thin metal film or metal grain, or a semiconductor quantum dot. In that case, provided the scattering in the normal metal is chaotic, no excitations exist within an energy gap E g ∼h/τ , where τ is the typical time between collisions with the superconductor [2][3][4][5][6][7].If the coupling to the superconductor is weak (as for the point contact coupling of Fig. 1), the functional form of the density of states becomes independent of microscopic properties of the normal metal, such as the shape, dimensionality, or mean free path. Weak coupling means that τ is much bigger than the time τ erg needed for ergodic exploration of the phase space in the normal region. For a point contact with N ≫ 1 propagating modes at the Fermi level ε = 0, the density of states has a square root singularity at the excitation gap [4],For a ballistic point contact and in the absence of a magnetic field, E g = cN δ and ∆ g = c ′ N 1/3 δ, where c = 0.048 and c ′ = 0.068 are numerical constants and δ is the mean level spacing in the normal metal when it is decoupled from the superconductor. Equation (1) was obtained in a self-consistent diagrammatic perturbation theory that uses τ δ/h ∼ N −1 as a small parameter. Such a mean-field theory provides a smoothed density of states for which energies can only be resolved on the scale ofh/τ ∼ N δ, not on smaller energy scales, and is unable to deal with mesoscopic sampleto-sample fluctuations of the excitation gap. Mesoscopic fluctuations arise, e.g., upon varying the shape of a quantum dot or the impurity configuration in a metal grain. The lowest excited state ε 1 fluctuates from sample to sample around the mean field value E g , with a probability distribution P (ε 1 ). It is the purpose of this paper to go beyond mean field theory and to study the mesoscopic fluctuations of the excitation spectrum close to E g . Our main result is that the gap distribution P (ε 1 ) is a universal function of the rescaled energy x = (ε 1 − E g )/∆ g , in a broad range |x| ≪ N 2/3 . The Fermi level itself (ε = 0) falls outside this range, which is why the universal gap distribution was not found in a recent related study [9]. Our main findings are illustrated in Fig. 2.We first consider the gap distribution in the absence of a magnetic field, and then include a time-reversal symmetry breaking magnetic ...