Abstract:
A dynamic response to a magnetic field in a long disordered cylinder is considered. We show that, although at high frequencies conduction is classical in all directions, the low frequency behavior corresponds to localization in the longitudinal direction and to a diamagnetic dynamic persistent current in the transversal one. The current density does not vanish even in the limit of the infinitely long cylinder.

Abstract:
We study the effects of localization on the Hall transport in a granular system at large tunneling conductance $g_{T}\gg 1$ corresponding to the metallic regime. We show that the first-order in 1/g_T weak localization correction to Hall resistivity of a two- or three-dimensional granular array vanishes identically, $\de \rho_{xy}^{WL}=0$. This result is in agreement with the one for ordinary disordered metals. Being due to an exact cancellation, our result holds for arbitrary relevant values of temperature T and magnetic field H, both in the ``homogeneous'' regime of very low T and H corresponding to ordinary disordered metals and in the ``structure-dependent'' regime of higher values of T or H.

Abstract:
Mesoscopic conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance $<[\delta G]^2>$ is very sensitive to the elastic scattering breaking the valley symmetry. In the absence of such scattering (disorder potential smooth at atomic scales, trigonal warping negligible), the variance $<[\delta G]^2 > = 4 < [\delta G]^2 >_\text{metal}$ is four times greater than that in conventional metals, which is due to the two-fold valley degeneracy. In the absence of intervalley scattering, but for strong intravalley scattering and/or strong warping $<[\delta G]^2 > =2 < [\delta G]^2 >_\text{metal}$. Only in the limit of strong intervalley scattering $<[\delta G]^2 > = < [\delta G]^2 >_\text{metal}$. Our theory explains recent numerical results and can be used for comparison with existing experiments.

Abstract:
We theoretically investigate the possibility of excitonic condensation in a system of two graphene monolayers separated by an insulator, in which electrons and holes in the layers are induced by external gates. In contrast to the recent studies of this system, we take into account the screening of the interlayer Coulomb interaction by the carriers in the layers, and this drastically changes the result. Due to a large number of electron species in the system (two projections of spin, two valleys, and two layers) and to the suppression of backscattering in graphene, the maximum possible strength of the screened Coulomb interaction appears to be quite small making the weak-coupling treatment applicable. We calculate the mean-field transition temperature for a clean system and demonstrate that its highest possible value $T_c^\text{max}\sim 10^{-7}\epsilon_F\lesssim 1 \text{mK}$ is extremely small ($\epsilon_F$ is the Fermi energy). In addition, any sufficiently short-range disorder with the scattering time $\tau \lesssim \hbar /T_c^\text{max}$ would suppress the condensate completely. Our findings renders experimental observation of excitonic condensation in the above setup improbable even at very low temperatures.

Abstract:
The possibility of excitonic condensation in a recently proposed electrically biased double-layer graphene system is studied theoretically. The main emphasis is put on obtaining a reliable analytical estimate for the transition temperature into the excitonic state. As in a double-layer graphene system the total number of fermionic "flavors" is equal to N=8 due to two projections of spin, two valleys, and two layers, the large-$N$ approximation appears to be especially suitable for theoretical investigation of the system. On the other hand, the large number of flavors makes screening of the bare Coulomb interactions very efficient, which, together with the suppression of backscattering in graphene, leads to an extremely low energy of the excitonic condensation. It is shown that the effect of screening on the excitonic pairing is just as strong in the excitonic state as it is in the normal state. As a result, the value of the excitonic gap $\De$ is found to be in full agreement with the previously obtained estimate for the mean-field transition temperature $T_c$, the maximum possible value $\Delta^{\rm max},T_c^{\rm max}\sim 10^{-7} \epsilon_F$ ($\epsilon_F$ is the Fermi energy) of both being in $ 1{\rm mK}$ range for a perfectly clean system. This proves that the energy scale $\sim 10^{-7} \epsilon_F$ really sets the upper bound for the transition temperature and invalidates the recently expressed conjecture about the high-temperature first-order transition into the excitonic state. These findings suggest that, unfortunately, the excitonic condensation in graphene double-layers can hardly be realized experimentally.

Abstract:
We present a theory of Hall effect in granular systems at large tunneling conductance $g_{T}\gg 1$. Hall transport is essentially determined by the intragrain electron dynamics, which, as we find using the Kubo formula and diagrammatic technique, can be described by nonzero diffusion modes inside the grains. We show that in the absence of Coulomb interaction the Hall resistivity $\rho_{xy}$ depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains and type of granular lattice. Further, we study the effects of Coulomb interactions by calculating first-order in $1/g_T$ corrections and find that (i) in a wide range of temperatures $T \gtrsim \Ga$ exceeding the tunneling escape rate $\Ga$, the Hall resistivity $\rho_{xy}$ and conductivity $\sig_{xy}$ acquire logarithmic in $T$ corrections, which are of local origin and absent in homogeneously disordered metals; (ii) large-scale ``Altshuler-Aronov'' correction to $\sig_{xy}$, relevant at $T\ll\Ga$, vanishes in agreement with the theory of homogeneously disordered metals.

Abstract:
We study particle-hole instabilities in the framework of the spin-fermion (SF) model. In contrast to previous study, we assume that adjacent hot spots can overlap due to a shallow dispersion of the electron spectrum in the antinodal region. In addition, we take into account effects of a remnant low energy and momentum Coulomb interaction. We demonstrate that at sufficiently small values $|\varepsilon (\pi ,0)-E_{F}|\lesssim \Gamma $, where $E_{F}$ is the Fermi energy, $\varepsilon \left( \pi ,0\right) $ is the energy in the middle of the Brillouin zone edge, and $\Gamma $ is a characteristic energy of the fermion-fermion interaction due to the antiferromagnetic fluctuations, the leading particle-hole instability is a d-form factor Fermi surface deformation (Pomeranchuk instability) rather than the charge modulation along the Brillouin zone diagonals predicted within the standard SF model previously. At lower temperatures, we find that the deformed Fermi surface is further unstable to formation of a d-form factor charge density wave (CDW) with a wave vector along the Cu-O-Cu bonds (axes of the Brillouin zone). We show that the remnant Coulomb interaction enhances the d-form factor symmetry of the CDW. These findings can explain the robustness of this order in the cuprates. The approximations made in the paper are justified by a small parameter that allows one an Eliashberg-like treatment. Comparison with experiments suggests that in many cuprate compounds the prerequisites for the proposed scenario are indeed fulfilled and the results obtained may explain important features of the charge modulations observed recently.

Abstract:
We theoretically investigate the anomalous Hall effect in a system of dense-packed ferromagnetic grains in the metallic regime. Using the formalism recently developed for the conventional Hall effect in granular metals, we calculate the residual anomalous Hall conductivity $\sigma_{xy}$ and resistivity $\rho_{xy}$ and weak localization corrections to them for both skew-scattering and side-jump mechanisms. We find that, unlike for homogeneously disordered metals, the scaling relation between $\rho_{xy}$ and the longitudinal resistivity $\rho_{xx}$ does not hold. The weak localization corrections, however, are found to be in agreement with those for homogeneous metals. We discuss recent experimental data on the anomalous Hall effect in polycrystalline iron films in view of the obtained results.

Abstract:
Using a simple two-band model for Fe-based pnictides and the generalized Eilenberger equation, we present a microscopic derivation of a time-dependent equation for the amplitude of the spin density wave near the quantum critical point where it turns to zero. This equation describes the dynamics of the magnetic---$m$, as well as the superconducting order parameter---$\Delta$. It is valid at low temperatures $T$ and small $m$ (${T, m \ll \Delta}$) in a region of coexistence of both order parameters, $m$ and $\Delta$. The boundary of this region is found in the space of the nesting parameter $\{\mu_{0},\mu_{\phi}\}$ where $\mu_{0}$ describes the relative position of the electron and the hole pockets on the energy scale, and $\mu_{\phi}$ accounts for the ellipticity of the electron pocket. At low $T$ the number of quasiparticles is small due to the presence of the energy gap $\Delta$, and therefore the quasiparticles do not play a role in the relaxation of $m$. This circumstance allows one to derive the time-dependent equation for $m$ in contrast to the case of conventional superconductors for which the time-dependent Ginzburg--Landau equation can be derived near $T_{\text{c}}$ only in some special cases (high concentration of paramagnetic impurities. In the stationary case the derived equation is valid at arbitrary temperatures. We find a solution of the stationary equation which describes a domain wall in the magnetic structure. In the center of the domain wall the superconducting order parameter has a maximum, which means a local enhancement of superconductivity. Using the derived time-dependent equation for $m$, we investgate also the stability of a uniform commensurate SDW and obtain the values of $\{\mu_{0}, \mu_{\phi}\}$ at which the first order transition into the state with ${m = 0}$ takes place or the transition to the state with an inhomogeneous SDW occurs.

Abstract:
Interfacial superconductivity is observed in a variety of heterostructures composed of different materials including superconducting and nonsuperconducting (at appropriate doping and temperatures) cuprates and iron-based pnictides. The origin of this superconductivity remains in many cases unclear. Here, we propose a general mechanism of interfacial superconductivity for systems with competing order parameters. We assume that parameters characterizing the material allow formation of another order like charge- or spin-density wave competing and prevailing superconductivity in the bulk (hidden superconductivity). Diffusive electron scattering on the interface results in a suppression of this order and releasing the superconductivity. Our theory is based on the use of Ginzburg--Landau equations applicable to a broad class of systems. We demonstrate that the local superconductivity appears in the vicinity of the interface and the spatial dependence of the superconducting order parameter~$\Delta(x)$ is described by the Gross--Pitaevskii equation. Solving this equation we obtain quantized values of temperature and doping levels at which~$\Delta(x)$ appears. Remarkably, the local superconductivity shows up even in the case when the rival order is only slightly suppressed and may arise also on the surface of the sample (surface superconductivity).