The influence of disorder on the temperature of superconducting transition (T{c}) is studied within the σ-model renormalization-group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes Anderson localization leads to strong enhancement of T{c} related to the multifractality of wave functions. Screening of the long-range Coulomb interaction thus opens a promising direction for searching novel materials for high-T{c} superconductivity.

The influence of the disorder-induced Anderson localization and electron-electron interaction on the superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature T c , the temperature dependence of the resistivity, the phase diagram, and the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. The derived RG equations are valid to the lowest order in disorder but for an arbitrary electron-electron interaction strength in a particle-hole and the Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, with both short-range and long-range (Coulomb) interactions. In the case of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity R c of the order of the quantum resistance R q = h/4e 2 . When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below T c .

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of the Coulomb interaction. We calculate the spectrum of multifractal dimensions in 2+ϵ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.

We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema. PACS:Introduction. -Two-dimensional topological insulators (2D TIs) are in the focus of recent interest due to existence of two helical edge states inside the band gap [1,2]. Because of spin-momentum locking caused by strong spin-orbit coupling, electrical current transfers helicity along the edge [3,4]. This "spin" current is a hallmark of the quantum spin Hall effect, and it has been detected experimentally in HgTe/CdTe quantum wells [5][6][7][8][9]. If only elastic scattering is allowed, and in the absence of time-reversal symmetry breaking, the helical state is a realization of the ideal transport channel with conductance of G 0 = e 2 /h. This prediction was questioned by the experiments in HgTe/CdTe [5,[10][11][12] and InAs/GaSb [13,14] quantum wells. Therefore, studies of mechanisms which can lead to the destruction of the ideal helical transport are important.A local perturbation breaking the time-reversal symmetry, e.g., a classical magnetic impurity, leads to backscattering of helical edge states and reduction of the edge conductance [15,16]. Electron-electron interactions along the edge can promote edge reconstruction and, consequently, spontaneous time-reversal symmetry breaking at the edge [17]. Furthermore, even in the absence of time-reversal symmetry breaking, electronelectron interactions may induce backscattering [18], resulting in the suppression of the helical edge conductance at finite temperatures (see [19] and references therein). A combination of electron-electron interactions and magnetic impurities can significantly modify the picture of ideal helical edge transport [20][21][22][23][24].In the absence of electron-electron interactions along the edge, the ideal transport along the helical edge may