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). Similar instability may also be observable in clean superconducting films.

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. It is feasible to experimentally verify these predictions by tuning the interaction strength with the use of Feshbach or confinement-induced resonances, for example, in (7)Li or (39)K.

Three-particle complexes in two-dimensional semiconductors.

We evaluate binding energies of trions X±, excitons bound by a donor or acceptor charge X^{D(A)}, and overcharged acceptors or donors in two-dimensional atomic crystals by mapping the three-body problem in two dimensions onto one particle in a three-dimensional potential treatable by a purposely developed boundary-matching-matrix method. We find that in monolayers of transition metal dichalcogenides the dissociation energy of X^{±} is typically much larger than that of localized exciton complexes, so that trions are more resilient to heating, despite the fact that their recombination line in optics is less redshifted from the exciton line than the line of X^{D(A)}.

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. We use experimental R(T) and assume phonon mechanism of the cooling taking into account its strong suppression by disorder. Our description of the details of the I-V characteristics does not involve adjustable parameters and turns out to be in quantitative agreement with the experiments. We propose experiments for more direct checks of this physical picture.

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.