Learning by confusion approach to identification of discontinuous phase transitions.

Recently, the learning by confusion (LbC) approach has been proposed as a machine learning tool to determine the critical temperature T_{c} of phase transitions without any prior knowledge of its even approximate value. The method has been proven effective, but it has been used only for continuous phase transitions, where the confusion results only from deliberate incorrect labeling of the data. However, in the case of a discontinuous phase transition, additional confusion can result from the coexistence of different phases.

Enhancing Superconductivity of the Nonmagnetic Quasiskutterudites by Atomic Disorder.

We investigated the effect of enhancement of superconducting transition temperature Tc by nonmagnetic atom disorder in the series of filled skutterudite-related compounds (La3M4Sn13, Ca3Rh4Sn13, Y5Rh6Sn18, Lu5Rh6Sn18; M= Co, Ru, Rh), where the atomic disorder is generated by various defects or doping. We have shown that the disorder on the coherence length scale ξ in these nonmagnetic quasiskutterudite superconductors additionally generates a non-homogeneous, superconducting phase with Tc⋆>Tc (dilute disorder scenario), while the strong fluctuations of stoichiometry due to increasing doping can rapidly increase the superconducting transition temperature of the sample even to the value of Tc⋆∼2Tc (dense disorder leading to strong inhomogeneity). This phenomenon seems to be characteristic of high-temperature superconductors and superconducting heavy fermions, and recently have received renewed attention.

Interplay between pairing and correlations in spin-polarized bound states.

We investigate single and multiple defects embedded in a superconducting host, studying the interplay between the proximity-induced pairing and interactions. We explore the influence of the spin-orbit coupling on energies, polarization and spatial patterns of the bound (Yu-Shiba-Rusinov) states of magnetic impurities in a two-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization that has been recently reported by S.

Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion.

Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction. As a test case, we first investigate a noninteracting Kitaev model and demonstrate that this approach perfectly reproduces the standard results.

Polarization of the Majorana quasiparticles in the Rashba chain.

We demonstrate that the selective equal-spin Andreev reflection (SESAR) spectroscopy can be used in STM experiments to distinguish the zero-energy Majorana quasiparticles from the ordinary fermionic states of the Rashba chain. Such technique, designed for probing the p-wave superconductivity, could be applied to the intersite pairing of equal-spin electrons in the chain of magnetic Fe atoms deposited on the superconducting Pb substrate. Our calculations of the effective pairing amplitude for individual spin components imply the magnetically polarized Andreev conductance, which can be used to 'filter' the Majorana quasiparticles from the ordinary in-gap states, although the pure spin current (i.

Dot-ring nanostructure: Rigorous analysis of many-electron effects.

We discuss the quantum dot-ring nanostructure (DRN) as canonical example of a nanosystem, for which the interelectronic interactions can be evaluated exactly. The system has been selected due to its tunability, i.e.

Charge transport through a semiconductor quantum dot-ring nanostructure.

Transport properties of a gated nanostructure depend crucially on the coupling of its states to the states of electrodes. In the case of a single quantum dot the coupling, for a given quantum state, is constant or can be slightly modified by additional gating. In this paper we consider a concentric dot-ring nanostructure (DRN) and show that its transport properties can be drastically modified due to the unique geometry.

Spin relaxation in semiconductor quantum rings and dots--a comparative study.

We calculate spin relaxation times due to spin-orbit-mediated electron-phonon interactions for experimentally accessible semiconductor quantum ring and dot architectures. We elucidate the differences between the two systems due to different confinement. The estimated relaxation times (at B = 1 T) are in the range between a few milliseconds to a few seconds.

The Fulde-Ferrell-Larkin-Ovchinnikov phase in the presence of pair hopping interaction.

The recent experimental support for the presence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in CeCoIn(5) directed attention towards the mechanisms responsible for this type of superconductivity. We investigate the FFLO state in a model where on-site/inter-site pairing coexists with the repulsive pair hopping interaction. The latter interaction is interesting in that it leads to pairing with non-zero momentum of the Cooper pairs even in the absence of the external magnetic field (the so-called η pairing).

Inhomogeneity-induced enhancement of the pairing interaction in cuprate superconductors.

Scanning tunneling spectroscopy has recently discovered a positive correlation between the magnitude of the superconducting gap and positions of dopant oxygen atoms in Bi-based cuprates. We propose a microscopic mechanism that could be responsible for this effect. In particular, we demonstrate that the dopant-induced spatial variation of the atomic levels always enhances the superexchange interaction.