I. S. Burmistrov

Enhancement of the critical temperature of superconductors by Anderson localization.

I.S. Burmistrov, I.V. Gornyi, 3, 4 and A.D. Mirlin 4, 5, 6 1 L.D. Landau Institute for Theoretical Physics, Kosygina street 2, 117940 Moscow, Russia 2 Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany 3 A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia. 4 DFG Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany 5 Inst. für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany 6 Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia.

Metal-insulator transition in two dimensions: experimental test of the two-parameter scaling.

We report a detailed scaling analysis of resistivity rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two-parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the rho(T,n) data.

Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the finkelstein action describing a system of spin polarized or spinless electrons near two dimensions, in the presence of disorder as well as the Coulomb interactions.We extend the renormalization group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an (d-2) expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature and/or electron density.

Multifractality at Anderson Transitions with Coulomb Interaction

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.

θ renormalization, electron-electron interactions and super universality in the quantum Hall regime

Abstract The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of θ renormalization by instantons. Within the generalized non-linear σ model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive—for the first time—explicit expressions for the non-perturbative (instanton) contributions to the renormalization group β and γ functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.

Non-fermi liquid criticality and superuniversality in the quantum hall regime

The results of a microscopic theory, based on the topological concept of a θ vacuum, which show that the Coulomb potential, unlike any finite-ranged interaction potential, renders the long-standing problem of the plateau transitions in the quantum Hall regime like a non-Fermi liquid are reported. These results, which are important for quantum-phase transitions in general and composite fermion ideas in particular, provide a novel understanding of the critical exponent values that have recently been (re-)taken from a series of state-of-the-art quantum Hall samples.

Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. We discuss possible experimental measurements of the half-integer Hall conductance g x y of topological insulator surface states and explain how to reconcile Laughlins flux insertion argument with half-integer g x y . Using a vortex state representation of Landau level wave functions, we calculate current density beyond linear response, which is in particular relevant to the topological image monopole effect. As a major result, the field theory describing the localization physics of the quantum Hall effect of a single species of Dirac fermions is derived. In this connection, the issue of (absent) parity anomaly is revisited. The renormalization group (RG) flow and the resulting phase diagram are extensively discussed. Starting values of the RG flow are given by the semiclassical conductivity tensor which is obtained from the Boltzmann transport theory of the anomalous Hall effect.

Coulomb blockade and superuniversality of the theta angle.

Based on the Ambegaokar-Eckern-Schön approach to the Coulomb blockade, we develop a complete quantum theory of the single electron transistor. We identify a previously unrecognized physical observable in the problem that, unlike the usual average charge on the island, is robustly quantized for any finite value of the tunneling conductance as the temperature goes to absolute zero. This novel quantity is fundamentally related to the nonsymmetrized current noise of the system. Our results display all of the superuniversal topological features of the theta angle concept that previously arose in the theory of the quantum Hall effect.

Electronic properties in a two-dimensional disordered electron liquid: Spin-valley interplay

We report the detailed study of the influence of the spin and valley splittings on such physical observables of the two-dimensional disordered electron liquid as resistivity, spin and valley susceptibilities. We explain qualitatively the nonmonotonic dependence of the resistivity with temperature in the presence of a parallel magnetic field. In the presence of either the spin splitting or the valley splitting we predict novel, with two maximum points, temperature dependence of the resistivity.

Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the non-linear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore 2D systems that would be Anderson insulators in the absence of interaction and 2D or 3D systems that undergo Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature