Kondo-Anderson Transitions

Dilute magnetic impurities in a disordered Fermi liquid are considered close to the Anderson metal-insulator transition (AMIT). Critical Power law correlations between electron wave functions at different energies in the vicinity of the AMIT result in the formation of pseudogaps of the local density of states. Magnetic impurities can remain unscreened at such sites. We determine the density of the resulting free magnetic moments in the zero temperature limit. While it is finite on the insulating side of the AMIT, it vanishes at the AMIT, and decays with a power law as function of the distance to the AMIT. Since the fluctuating spins of these free magnetic moments break the time reversal symmetry of the conduction electrons, we find a shift of the AMIT, and the appearance of a semimetal phase. The distribution function of the Kondo temperature $T_{K}$ is derived at the AMIT, in the metallic phase and in the insulator phase. This allows us to find the quantum phase diagram in an external magnetic field $B$ and at finite temperature $T$. We calculate the resulting magnetic susceptibility, the specific heat, and the spin relaxation rate as function of temperature. We find a phase diagram with finite temperature transitions between insulator, critical semimetal, and metal phases. These new types of phase transitions are caused by the interplay between Kondo screening and Anderson localization, with the latter being shifted by the appearance of the temperature-dependent spin-flip scattering rate. Accordingly, we name them Kondo-Anderson transitions (KATs).Comment: 18 pages, 9 figure

Optimal Concentration of Information Content For Log-Concave Densities

An elementary proof is provided of sharp bounds for the varentropy of random vectors with log-concave densities, as well as for deviations of the information content from its mean. These bounds significantly improve on the bounds obtained by Bobkov and Madiman ({\it Ann. Probab.}, 39(4):1528--1543, 2011).Comment: 15 pages. Changes in v2: Remark 2.5 (due to C. Saroglou) added with more general sufficient conditions for equality in Theorem 2.3. Also some minor corrections and added reference

Strong suppression of weak (anti)localization in graphene

Low-field magnetoresistance is ubiquitous in low-dimensional metallic systems with high resistivity and well understood as arising due to quantum interference on self-intersecting diffusive trajectories. We have found that in graphene this weak-localization magnetoresistance is strongly suppressed and, in some cases, completely absent. This unexpected observation is attributed to mesoscopic corrugations of graphene sheets which cause a dephasing effect similar to that of a random magnetic field.Comment: improved presentation of the theory part after referees comments; important experimental info added (see "note added in proof"

Moscow Metropolis Labour Market Features: the Requirements of Employers and the Quality of Young Specialists

The subject-matter of the article is the study of the features of the youth labour market in such a specific region of Russia as the city of Moscow. The topic of the work is connected with the adaptation of training system for young specialists to the regional requirements of the employers of Moscow. The main hypothesis of the research suggests that the city of Moscow is an atypical region of Russia and it makes no sense to apply the standard criteria and methodological approaches, which are typical to our country, to its labour market. As the research method, the authors have used a sample survey of the key Moscow employers and the respondents aged from 14 to 30 years. On the basis of the data of the sociological survey conducted by the authors, it was succeeded to identify the following features of the region in question: a relatively low level of the youth unemployment for Russia; the employers’ focus on such target signs of personnel as good communication skills, learning ability, professional knowledge and competences. The Moscow employers pay insufficient attention to such characteristics of young specialists as foreign language and computer skills, and a diploma of a prestigious education institution. The principal barriers that cause dificulties to the employment of young specialists in Moscow are: their overestimated salary expectations, poor professional training level and disinclination for work in principle. As a result of the survey, some practical proposals were formulated. Their application area is differentiated in two ways: focused on the young people’s behavior at the learning stage and focused on the improvement of the practical component of the activity of the vocational education institutions. The authors have come to the conclusions on the expediency of a deep focus of education institutions on the applied nature of training specialists, a need for attracting practitioners to teaching special disciplines, a need for developing the future specialists’ ability to present themselves and their work results in the professional environment (self-presentation), and an objective assessment of their real employment opportunities.The authors of the article hereby express their gratitude to the Department of Labour and Social Protection of the Population of Moscow for its assistance in conducting the research of the problems of youth employment in the city of Moscow. The article is published with support of the RSF grant, Project “Fluctuating Unemployment in the Russian Federation: the Status and the Ways of Reduction” № 16–18–1014

Magnon influence on the superconducting DOS in FI/S bilayers

Heterostuctures superconductor/ferromagnetic insulator (FI/S) are paradigmic systems for studying mutual influence of superconductivity and magnetism via proximity effects. In particular, spin-split superconductivity is realized in such structures. Recent experiments and theories demonstrate a rich variety of transport phenomena occurring in devices based on such heterostructures that suggest direct applications in thermoelectricity, low-dissipative spintronics, radiation detection and sensing. In this work we investigate the influence of the electron-magnon interaction at the superconductor/ferromagnetic insulator interface on the spin-split superconductivity. It is predicted that due to the magnon-mediated electron spin-flip processes the spin-split quasiparticle branches are partially mixed and reconstructed, and the BCS-like spin-split shape of the superconducting DOS, which is typical for superconductors in the effective exchange field, is strongly modified. An odd-frequency superconducting order parameter admixture to the leading singlet order parameter is also found. These findings expand the physical picture of spin-split superconductivity beyond the mean-field description of the ferromagnet exchange field

Renormalization of antiferromagnetic magnons by superconducting condensate and quasiparticles

The ability to modify and tune the spin-wave dispersion is one of the most important requirements for engineering of magnonic networks. In this study we demonstrate the promise of synthetic thin-film hybrids composed of an antiferromagnetic insulator (AF) and a normal (N) or superconducting (S) metal for tuning and modifying the spin-wave dispersion in antiferromagnetic insulators. The key ingredient is the uncompensated magnetic moment at the AF/S(N) interface, which induces an effective exchange field in the adjacent metal via the interface exchange interaction. The exchange field spin polarizes quasiparticles in the metal and induces spinful triplet Cooper pairs screening the magnon. The quasiparticle and Cooper pair polarization renormalizes the magnon dispersion. The renormalization results in the splitting of the otherwise degenerate AF magnon modes with no need to apply a magnetic field. It is also proposed that measurements of the renormalized dispersion relations can provide the amplitude of the effective exchange field induced by the AF in the adjacent metal

Two remarks on generalized entropy power inequalities

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Disorder-quenched Kondo effect in mesosocopic electronic systems

Nonmagnetic disorder is shown to quench the screening of magnetic moments in metals, the Kondo effect. The probability that a magnetic moment remains free down to zero temperature is found to increase with disorder strength. Experimental consequences for disordered metals are studied. In particular, it is shown that the presence of magnetic impurities with a small Kondo temperature enhances the electron's dephasing rate at low temperatures in comparison to the clean metal case. It is furthermore proven that the width of the distribution of Kondo temperatures remains finite in the thermodynamic (infinite volume) limit due to wave function correlations within an energy interval of order $1/\tau$, where $\tau$ is the elastic scattering time. When time-reversal symmetry is broken either by applying a magnetic field or by increasing the concentration of magnetic impurities, the distribution of Kondo temperatures becomes narrower.Comment: 17 pages, 7 figures, new results on Kondo effect in quasi-1D wires added, 6 Refs. adde