### Theoretical studies on the nanoscale

We developed a theory of the upper critical field in a BCS superconductor with a nonlocal interaction between electrons. We have shown that the nonlocal interaction is characterized by the universal dimensionless parameter *k _{F}ρ_{0}*, where

*k*is the Fermi momentum and

_{F}*ρ*is the radius of electron-electron interaction. The presence of the external magnetic field leads to the generation of additional components of the order parameter with different angular momenta. This effect leads to the enhancement of the upper critical field above the orbital limiting field. In addition the upward curvature in the temperature dependence of the upper critical field in the clean limit is predicted.

_{0}We have developed a theoretical model in order to describe the polaron ordering on triangular lattice. The model takes into account the short range attraction between polarons due to lattice deformation and long range Coulomb repulsion. In addition to that we introduce the modulation due to charge density wave ordering. Monte Carlo simulations show that the resulting patterns are similar to that observed in the STM experiments on TaS_{2}.

We derive the kinetic equations for polaron hopping in organics that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages the equations can be reduced to effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in ordered system with zero Hubbard energy, the magnetoresistance vanishes.

We have developed a theoretical model in order to describe the polaron ordering on triangular lattice. The model describes the commensurate ordering of polarons with doping level n=1/3,1/4,1/7,1/9.1/12,1/13,…It is shown that at intermediate doping the polarons form amorphous hyper-uniform state. In Monte Carlo simulations show that the resulting patterns are similar to that observed in the STM experiments on TaS2.

**Ultrafast Switching to a Stable Hidden Quantum State in an Electronic Crystal
Science **11 April 2014, Vol. 344, Issue 6180, pp. 177-180

**DOI: 10.1126/science.1241591**

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