Subgap states in dirty superconductors and their effect on dephasing in Josephson qubits

We present a theory of the subgap tails of the density of states in a diffusive superconductor containing magnetic impurities. We show that the subgap tails have two contributions: one arising from mesoscopic gap fluctuations, previously discussed by Lamacraft and Simons, and the other associated to the long-wave fluctuations of the concentration of magnetic impurities. We study the latter both in small superconducting grains and in bulk systems [$d=1,2,3$], and establish the dimensionless parameter that controls which of the two contributions dominates the subgap tails. We observe that these contributions are related to each other by dimensional reduction. We apply the theory to estimate the effects of a weak concentration of magnetic impurities [$\approx 1 {\rm p.p.m}$] on the phase coherence of Josephson qubits. We find that at these typical concentrations, magnetic impurities are relevant for the dephasing in large qubits, designed around a $10 {\rm \mu m}$ scale, where they limit the quality factor to be $Q<10^4-10^5$.Comment: 13 pages, 1 figur

Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+\epsilon$ dimensions, we calculate the localization length $\xi(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $\xi(B)$ by a numerical factor when the magnetic field is in the range \ell\ll{\ell_{\!{_H}}}\alt\xi(0), $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $\xi(B)$ and $\xi(0)$. The effect of spin-orbit interaction is briefly considered as well.Comment: 4 pages, revtex, no figures; to be published in Europhysics Letter

Theory of quantum metal to superconductor transitions in highly conducting systems

We derive the theory of the quantum (zero temperature) superconductor to metal transition in disordered materials when the resistance of the normal metal near criticality is small compared to the quantum of resistivity. This can occur most readily in situations in which ``Anderson's theorem'' does not apply. We explicitly study the transition in superconductor-metal composites, in an s-wave superconducting film in the presence of a magnetic field, and in a low temperature disordered d-wave superconductor. Near the point of the transition, the distribution of the superconducting order parameter is highly inhomogeneous. To describe this situation we employ a procedure which is similar to that introduced by Mott for description of the temperature dependence of the variable range hopping conduction. As the system approaches the point of the transition from the metal to the superconductor, the conductivity of the system diverges, and the Wiedemann-Franz law is violated. In the case of d-wave (or other exotic) superconductors we predict the existence of (at least) two sequential transitions as a function of increasing disorder: a d-wave to s-wave, and then an s-wave to metal transition

Levitation of the quantum Hall extended states in the B→B\to 0 limit

We investigate the fate of the quantum Hall extended states within a continuum model with spatially correlated disorder potentials. The model can be projected onto a couple of the lowest Landau bands. Levitation of the $n=0$ critical states is observed if at least the two lowest Landau bands are considered. The dependence on the magnetic length $l_B=(\hbar/(eB))^{1/2}$ and on the correlation length of the disorder potential $\eta$ is combined into a single dimensionless parameter $\hat\eta=\eta/l_B$. This enables us to study the behavior of the critical states for vanishing magnetic field. In the two Landau band limit, we find a disorder dependent saturation of the critical states' levitation which is in contrast to earlier propositions, but in accord with some experiments.Comment: 7 pages, 9 figures. Replaced with published versio

Squeezing superfluid from a stone: Coupling superfluidity and elasticity in a supersolid

In this work we start from the assumption that normal solid to supersolid (NS-SS) phase transition is continuous, and develop a phenomenological Landau theory of the transition in which superfluidity is coupled to the elasticity of the crystalline $^4$He lattice. We find that the elasticity does not affect the universal properties of the superfluid transition, so that in an unstressed crystal the well-known $\lambda$-anomaly in the heat capacity of the superfluid transition should also appear at the NS-SS transition. We also find that the onset of supersolidity leads to anomalies in the elastic constants near the transition; conversely, inhomogeneous strains in the lattice can induce local variations of the superfluid transition temperature, leading to a broadened transition.Comment: 4 page

Weak levitation of 2D delocalized states in a magnetic field.

The deviation of the energy position of a delocalized state from the center of Landau level is studied in the framework of the Chalker-Coddington model. It is demonstrated that introducing a weak Landau level mixing results in a shift of the delocalized state up in energy. The mechanism of a levitation is a neighboring - Landau level - assisted resonant tunneling which ``shunts'' the saddle-points. The magnitude of levitation is shown to be independent of the Landau level number.Comment: Latex file (12 pages) + 3 Postscript figures

Magneto-optical evidence of the percolation nature of the metal-insulator transition in the 2D electron system

We compare the results of the transport and time-resolved magneto-luminescence measurements in disordered 2D electron systems in GaAs-AlGaAs heterostructures in the extreme quantum limit, in particular, in the vicinity of the metal-insulator transition (MIT). At filling factors $\nu <1$, the optical signal has two components: the single-rate exponentially decaying part attributed to a uniform liquid and a power-law long-living tail specific to a microscopically inhomogeneous state of electrons. We interprete this result as a separation of the 2D electron system into a liquid and localized phases, especially because the MIT occurs strikingly close to those filling factors where the liquid occupies ${1\over 2}$ of the sample area (the percollation threshold condition in two-component media).Comment: 5 pages RevTex + 4 fig., to appear in PRB, Rapid Com

Topological Phase Diagram of a Two-Subband Electron System

We present a phase diagram for a two-dimensional electron system with two populated subbands. Using a gated GaAs/AlGaAs single quantum well, we have mapped out the phases of various quantum Hall states in the density-magnetic filed plane. The experimental phase diagram shows a very different topology from the conventional Landau fan diagram. We find regions of negative differential Hall resistance which are interpreted as preliminary evidence of the long sought reentrant quantum Hall transitions. We discuss the origins of the anomalous topology and the negative differential Hall resistance in terms of the Landau level and subband mixing.Comment: 4 pages, 4 figure

The stability of a cubic fixed point in three dimensions from the renormalization group

The global structure of the renormalization-group flows of a model with isotropic and cubic interactions is studied using the massive field theory directly in three dimensions. The four-loop expansions of the \bt-functions are calculated for arbitrary $N$. The critical dimensionality $N_c=2.89 \pm 0.02$ and the stability matrix eigenvalues estimates obtained on the basis of the generalized Pad$\acute{\rm e}$-Borel-Leroy resummation technique are shown to be in a good agreement with those found recently by exploiting the five-loop \ve-expansions.Comment: 18 pages, LaTeX, 5 PostScript figure

Universal relation between longitudinal and transverse conductivities in quantum Hall effect

We show that any critical transition region between two adjacent Hall plateaus in either integer or fractional quantum Hall effect is characterized by a universal semi-circle relationship between the longitudinal and transverse conductivities, provided the sample is homogeneous and isotropic on a large scale. This conclusion is demonstrated both for the phase-coherent quantum transport as well as for the incoherent transport.Comment: REVTEX 3.0, 1 figure, 4 pages. SISSA-08179