Instability of the Abrikosov Lattice due to Nonanalytic Core Reconstruction of Vortices in Bosonic Superfluids.

We study the impact of the nonanalytic reconstruction of vortex cores on static vortex structures in weakly coupled superfluids. We show that, in rotating two-dimensional systems, the Abrikosov vortex lattice is unstable to vortex core deformation: Each zero of the wave function becomes a cut of finite length. The directors characterizing the orientations of the cuts are themselves ordered in superstructures due either to surface effects or to interaction with shear deformations of the lattice (spiral structure).

Finite-temperature fluid-insulator transition of strongly interacting 1D disordered bosons.

We consider the many-body localization-delocalization transition for strongly interacting one-dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions, an increase in the interaction strength leads to insulator [Formula: see text] fluid transition, and, for large interactions, there is a reentrance to the insulator regime.

Jumps in current-voltage characteristics in disordered films.

We argue that giant jumps of current at finite voltages observed in disordered films of InO, TiN, and YSi manifest a bistability caused by the overheating of electrons. One of the stable states is overheated and thus low resistive, while the other, high-resistive state is heated much less by the same voltage. The bistability occurs provided that cooling of electrons is inefficient and the temperature dependence of the equilibrium resistance R(T) is steep enough.

Random resistor network model of minimal conductivity in graphene.

Transport in undoped graphene is related to percolating current patterns in the networks of n- and p-type regions reflecting the strong bipolar charge density fluctuations. Finite transparency of the p-n junctions is vital in establishing the macroscopic conductivity. We propose a random resistor network model to analyze scaling dependencies of the conductance on the doping and disorder, the quantum magnetoresistance and the corresponding dephasing rate.