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.