Inelastic electron scattering off a quantum dot in the cotunneling regime: the signature of mesoscopic Stoner instability

We explore the inelastic electron scattering cross section off a quantum dot close to the Stoner instability. We focus on the regime of strong Coulomb blockade in which the scattering cross section is dominated by the cotunneling processes. For large enough exchange interaction the quantum dot acquires a finite total spin in the ground state. In this, so-called mesoscopic Stoner instability, regime we find that at low enough temperatures the inelastic scattering cross section (including the contribution due to an elastic electron spin-flip) for an electron with a low energy with respect to the chemical potential is different from the case of a magnetic impurity with the same spin. This difference stems from (i) presence of a low-lying many-body states of a quantum dot and (ii) the correlations of the tunneling amplitudes. Our results provide a possible explanation for absence of the dephasing rate saturation at low temperatures in recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012)] in which existence of local spin droplets in disordered electron liquid has been unraveled.Comment: 14 pages, 3 figure

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

Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells

We study indirect exchange interaction between magnetic impurities in the (001) CdTe/HgTe/CdTe symmetric quantum well. We consider low temperatures and the case of the chemical potential placed in the energy gap of the 2D quasiparticle spectrum. We find that the indirect exchange interaction is suppressed exponentially with the distance between magnetic impurities. The presence of inversion asymmetry results in oscillations of the indirect exchange interaction with the distance and generates additional terms which are non-invariant under rotations in the (001) plane. The indirect exchange interaction matrix has complicated structure with some terms proportional to the sign of the energy gap.Comment: 13 pages, 6 figure

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

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

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

Instability of a crystal 4He facet in the field of gravity

We analyze the analog of the Rayleigh instability in the field of gravity for the superfluid-crystal 4He interface provided that the heavier 4He crystal phase occupies the half-space over the lighter superfluid phase. The conditions and the onset of the gravitational instability are different in kind above and below the roughening transition temperature when the crystal 4He surface is in the rough or in the smooth faceted state, respectively. In the rough state of the surface the gravitational instability is similar to the classical case of the fluid-fluid interface. In contrast, in the case of the crystal faceted surface the onset of the gravitational instability is associated with surmounting some potential barrier. The potential barrier results from nonzero magnitude of the linear facet step energy. The size and the tilting angle of the crystal facet are also important parameters for developing the instability. The initial stage of the instability can be described as a generation of crystallization waves at the superfluid-crystal interface. The experiments which may concern the gravitational instability of the superfluid-crystal 4He interface are discussed.Comment: 6 pages, 4 figures. The J.Low Temp.Phys.(2011) version plus supplementary figures herewit

Helical edge transport in the presence of a magnetic impurity

We consider the effects of electron scattering off a quantum magnetic impurity on the current-voltage characteristics of the helical edge of a two-dimensional topological insulator. We compute the backscattering contribution to the current along the edge for a general form of the exchange interaction matrix and arbitrary value of the magnetic impurity spin. We find that the differential conductance is a non-monotonous function of the voltage with several extrema.Comment: 7 pages, 1 figure, to appear in JETP Letter

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