Anisotropic conductivity tensor on a half-filled high Landau level

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. As it is known, the unidirectional charge density wave state can exist near a half-filled high Landau level at low temperatures if disorder is weak enough. We show that the existence of the unidirectional charge density wave state at temperature $T<T_c$ where $T_c$ is the transition temperature leads to the anisotropic conductivity tensor. We find that the anisotropic part of conductivity tensor is proportional to $(T_c-T)/T_c$ below the transition in accordance with the experimental findings. The order parameter fluctuations wash out the mean-field cusp at $T=T_c$ and the conductivity tensor becomes anisotropic even above the mean-field transition temperature $T_c$.Comment: RevTeX, 13 pages, 6 figure

Two-instanton approximation to the Coulomb blockade problem

We develop the two-instanton approximation to the current-voltage characteristic of a single electron transistor within the Ambegaokar-Eckern-Sch\"on model. We determine the temperature and gate voltage dependence of the Coulomb blockade oscillations of the conductance and the effective charge. We find that a small (in comparison with the charging energy) bias voltage leads to significant suppression of the Coulomb blockade oscillations and to appearance of the bias-dependent phase shift

Comment on "Super-universality in Anderson localization"

Comment on recent paper by I. Horv\'ath and P. Marko\v{s}, "Super-universality in Anderson localization", Phys. Rev. Lett. 129, 106601 (2022) [arXiv:2110.11266]