Multifractality at Anderson transitions with Coulomb interaction

We explore mesoscopic fluctuations and correlations of the local density of states (LDOS) near localization transition in a disordered interacting electronic system. It is shown that the LDOS multifractality survives in the presence of Coulomb interaction. We calculate the spectrum of multifractal dimensions in $2+\epsilon$ spatial dimensions and show that it differs from that in the absence of interaction. The multifractal character of fluctuations and correlations of the LDOS can be studied experimentally by scanning tunneling microscopy of two-dimensional and three-dimensional disordered structures.Comment: 16 pages, 2 figure

Mesoscopic fluctuations of the local density of states in interacting electron systems

We review our recent theoretical results for mesoscopic fluctuations of the local density of states in the presence of electron-electron interaction. We focus on the two specific cases: (i) a vicinity of interacting critical point corresponding to Anderson-Mott transition, and (ii) a vicinity of non-interacting critical point in the presence of a weak electron-electron attraction. In both cases strong mesoscopic fluctuations of the local density of states exist.Comment: A brief review based on arXiv:1305.2888, arXiv:1307.5811, arXiv:1412.3306, arXiv:1603.0301

Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the non-linear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore 2D systems that would be Anderson insulators in the absence of interaction and 2D or 3D systems that undergo Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature $T_c$) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions -- especially, in the regime when $T_c$ is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approaches the SIT

Superconductor-insulator transitions: Phase diagram and magnetoresistance

Influence of disorder-induced Anderson localization and of electron-electron interaction on superconductivity in two-dimensional systems is explored. We determine the superconducting transition temperature $T_c$, the temperature dependence of the resistivity, the phase diagram, as well as the magnetoresistance. The analysis is based on the renormalization group (RG) for a nonlinear sigma model. Derived RG equations are valid to the lowest order in disorder but for arbitrary electron-electron interaction strength in particle-hole and Cooper channels. Systems with preserved and broken spin-rotational symmetry are considered, both with short-range and with long-range (Coulomb) interaction. In the cases of short-range interaction, we identify parameter regions where the superconductivity is enhanced by localization effects. Our RG analysis indicates that the superconductor-insulator transition is controlled by a fixed point with a resistivity $R_c$ of the order of the quantum resistance $R_q = h/ 4e^2$. When a transverse magnetic field is applied, we find a strong nonmonotonous magnetoresistance for temperatures below $T_c$.Comment: 34 pages, 20 figure

Strongly correlated two-dimensional plasma explored from entropy measurements

Charged plasma and Fermi liquid are two distinct states of electronic matter intrinsic to dilute two-dimensional electron systems at elevated and low temperatures, respectively. Probing their thermodynamics represents challenge because of lacking an adequate technique. Here we report thermodynamic method to measure the entropy per electron in gated structures. Our technique appears to be three orders of magnitude superior in sensitivity to the ac calorimetry, allowing entropy measurements with only $10^8$ electrons. This enables us to investigate the correlated plasma regime, previously inaccessible experimentally in two-dimensional electron systems in semiconductors. In experiments with clean two-dimensional electron system in Si-based structures we traced entropy evolution from the plasma to Fermi-liquid regime by varying electron density. We reveal that the correlated plasma regime can be mapped onto the ordinary non-degenerate Fermi gas with an interaction-enhanced temperature dependent effective mass. Our method opens up new horizons in studies of low-dimensional electron systems.Comment: 5 pages 3 figures + Supplementary Informatio

Temperature derivative of the chemical potential and its magnetooscillations in two-dimensional system

We report first thermodynamic measurements of the temperature derivative of chemical potential (d{\mu}/dT) in two-dimensional (2D) electron systems. In order to test the technique we have chosen Schottky gated GaAs/AlGaAs heterojunctions and detected experimentally in this 2D system quantum magnetooscillations of d{\mu}/dT. We also present a Lifshits-Kosevitch type theory for the d{\mu}/dT magnetooscillations in 2D systems and compare the theory with experimental data. The magnetic field dependence of the d{\mu}/dT value appears to be sensitive to the density of states shape of Landau levels. The data in low magnetic field domain demonstrate brilliant agreement with theory for non-interacting Fermi gas with Lorentzian Landau level shape.Comment: 4 pages, 3 figure

Critical behavior of transport and magnetotransport in 2D electron system in Si in the vicinity of the metal-insulator transition

We report on studies of the magnetoresistance in strongly correlated 2D electron system in Si in the critical regime, in the close vicinity of the 2D metal-insulator transition. We performed self-consistent comparison of our data with solutions of two equations of the cross-over renormalization group (CRG) theory which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the \rho(T,B) data and the RG theory in a wide range of the in-plane fields, 0-2.1 T. This agreement supports the interpretation of the observed 2D MIT as the true quantum phase transition.Comment: 5 pages, 4 figures, uses jetpl.cl

Residual bulk viscosity of a disordered 2D electron gas

The nonzero bulk viscosity signals breaking of the scale invariance. We demonstrate that a disorder in two-dimensional noninteracting electron gas in a perpendicular magnetic field results in the nonzero disorder-averaged bulk viscosity. We derive analytic expression for the bulk viscosity within the self-consistent Born approximation. This residual bulk viscosity provides the lower bound for the bulk viscosity of 2D interacting electrons at low enough temperatures.Comment: 10 pages, 2 figure

Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films

We develop a theory for the vortex unbinding transition in homogeneously disordered superconducting films. This theory incorporates the effects of quantum, mesoscopic and thermal fluctuations stemming from length scales ranging from the superconducting coherence length down to the Fermi wavelength. In particular, we extend the renormalization group treatment of the diffusive nonlinear sigma model to the superconducting side of the transition. Furthermore, we explore the mesoscopic fluctuations of parameters in the Ginzburg-Landau functional. Using the developed theory, we determine the dependence of essential observables (including the vortex unbinding temperature, the superconducting density, as well as the temperature-dependent resistivity and thermal conductivity) on microscopic characteristics such as the disorder-induced scattering rate and bare interaction couplings

Probing spin susceptibility of a correlated two-dimensional electron system by transport and magnetization measurements

We report temperature and density dependences of the spin susceptibility of strongly interacting electrons in Si inversion layers. We measured (i) the itinerant electron susceptibility $\chi^*$ from the Shubnikov-de Haas oscillations in crossed magnetic fields and (ii) thermodynamic susceptibility $\chi_{\rm T}$ sensitive to all the electrons in the layer. Both $\chi^*$ and $\chi_{\rm T}$ are strongly enhanced with lowering the electron density in the metallic phase. However, there is no sign of divergency of either quantity at the density of the metal-insulator transition $n_c$. Moreover, the value of $\chi_{\rm T}$, which can be measured across the transition down to very low densities deep in the insulating phase, increases with density at $n<n_c$, as expected. In the absence of magnetic field, we found the temperature dependence of $\chi^*$ to be consistent with Fermi-liquid-based predictions, and to be much weaker than the power-law, predicted by non-Fermi-liquid models. We attribute a much stronger temperature dependence of $\chi_{\rm T}$ to localized spin droplets. In strong enough in-plane magnetic field, we found the temperature dependence of $\chi^*$ to be stronger than that expected for the Fermi liquid interaction corrections.Comment: 16 pages, 13 figure