By numerically solving the Bogoliubov–de Gennes equations for the single vortex state in a two-band superconductor, we demonstrate that the disparity between the healing lengths of two contributing condensates is strongly affected by the band Fermi velocities, even in the presence of the magnetic field and far beyond the regime of nearly zero Josephson-like coupling between bands. Changing the ratio of the band Fermi velocities alters the temperature dependence of the condensate lengths and significantly shifts parameters of the “length-scales locking” regime at which the two characteristic lengths approach one another.

Exciton-photon beats known as polariton Rabi oscillations in semiconductor microcavities are usually excited by short pulses of light. We consider a different pumping scheme, assuming a cw pumping of the Rabi oscillator from an exciton reservoir. We account for the initial pulse of light setting the phase, exciton decay due to exciton-phonon and exciton-exciton scattering, photon leakage, and blueshift of the exciton resonance due to interactions. We find nontrivial stationary solutions reminiscent of the Kapitza pendulum, where polaritons are accumulated at the upper branch while the lower branch empties.

We have studied the proximity-induced superconducting triplet pairing in CoO_x/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni_{0.81}Fe_{0.19}). By optimizing the parameters of this structure we found a triplet channel assisted full switching between the normal and superconducting states. To observe an "isolated" triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect ΔTc in the dependence of the Py2-layer thickness dPy2. We determined the value of dPy2 at which ΔTc caused by the ordinary spin-valve effect (the difference in the superconducting transition temperature Tc between the antiparallel and parallel mutual orientation of magnetizations of the Py1 and Py2 layers) is suppressed. For such a sample a "pure" triplet spin-valve effect which causes the minimum in Tc at the orthogonal configuration of magnetizations has been observed.

We investigate the statistics of microcavity polariton Bose–Einstein condensation by measuring photoluminescence dynamics from a GaAs microcavity excited by single laser excitation pulses. We directly observe fluctuations (jitter) of the polariton condensation onset time and model them using a master equation for the occupancy probabilities. The jitter of the condensation onset time is an inherent property of the condensate formation and its magnitude is approximately equal to the rise time of the condensate density. We investigate temporal correlations between the emission of condensate in opposite circular or linear polarizations by measuring the second-order correlation function g(2)(t1,t2) . Polariton condensation is accompanied by spontaneous symmetry breaking revealed by the occurrence of random (i.e., varying from pulse to pulse) circular and linear polarizations of the condensate emission. The degree of circular polarization generally changes its sign in the course of condensate decay, in contrast to the degree of linear polarization.

We study the stationary Josephson current in a junction between a topological and an ordinary (topologically trivial) superconductor. Such an S-TS junction hosts a Majorana zero mode that significantly influences the current-phase relation. The presence of the Majorana state is intimately related with the breaking of the time-reversal symmetry in the system. We derive a general expression for the supercurrent for a class of short topological junctions in terms of the normal-state scattering matrix. The result is strongly asymmetric with respect to the superconducting gaps in the ordinary (Δ0) and topological (Δtop) leads. We apply the general result to a simple model of a nanowire setup with strong spin-orbit coupling in an external magnetic field and proximity-induced superconductivity. The system shows parametrically strong suppression of the critical current Ic∝Δtop/RN2 in the tunneling limit (RN is the normal-state resistance). This is in strong contrast with the Ambegaokar-Baratoff relation applicable to junctions with preserved time-reversal symmetry. We also consider the case of a generic junction with a random scattering matrix and obtain a more conventional scaling law Ic∝Δtop/RN.

We study theoretically the Josephson effect between two two-band superconductors respecting time-reversal symmetry, where we assume a spin-singlet s-wave pair potential in each conduction band. The superconducting phase at the first band ϕ1 and that at the second band ϕ2 characterize a two-band superconducting state. We consider a Josephson junction where an insulating barrier separates two such two-band superconductors. By applying the tunnel Hamiltonian description, the Josephson current is calculated in terms of the anomalous Green’s function on either side of the junction. We find that the Josephson current consists of three components which depend on three types of phase differences across the junction: the phase difference at the first band δϕ1, the phase difference at the second band δϕ2, and the difference at the center-of-mass phase (δϕ1 + δϕ2 )/2. A Cooper pair generated by the band hybridization carries the last current component. We discuss the relation between the Josephson current calculated in theories and that observed in experiments.

We study the Landau levels (LLs) of a Weyl semimetal with two adjacent Weyl nodes. We consider different orientations η = ∠(B,k0) of magnetic field B with respect to k0, the vector of Weyl node splitting. A magnetic field facilitates the tunneling between the nodes, giving rise to a gap in the transverse energy of the zeroth LL. We show how the spectrum is rearranged at different η and how this manifests itself in the change of behavior of the differential magnetoconductance dG(B)/dB of a ballistic p-n junction. Unlike the single-cone model where Klein tunneling reveals itself in positive dG(B)/dB, in the two-cone case, G(B) is nonmonotonic with a maximum at Bc ∝ 0k2 0 / ln(k0lE) for large k0lE, where lE = √hv/ ¯ |e|E, with E for the built-in electric field and 0 for the magnetic flux quantum.

We experimentally study lateral electron transport between two 5−μm-spaced superconducting indium leads on a top of magnetic Weyl semimetal Co3Sn2S2. For the disordered magnetic state of Co3Sn2S2 crystal, we observe only the Andreev reflection in the proximity of each of the leads, which is indicative of highly transparent In-Co3Sn2S2 interfaces. If the sample is homogeneously magnetized, it demonstrates a well-developed anomalous Hall effect state. In this regime we find the Josephson current that takes place even for 5−μm-long junctions and show the unusual magnetic field and temperature dependencies. As a possible reason for the results obtained, we discuss the contribution to the proximity-induced spin-triplet Josephson current from the topologically protected Fermi-arc states on the surface of Co3Sn2S2.

Copper borate Cu3(BO3)2 is a complex compound with a layered crystallographic structure in which the Jahn-Teller active and magnetic copper Cu2+ ions occupy 16 nonequivalent positions in the unit cell displaying controversial magnetic behavior. In this paper, we report on the infrared and Raman spectroscopic studies of the lattice dynamics and the electronic structure of 3d9 copper states below the fundamental absorption band. The lattice dynamics is characterized by a large number of phonons due to a low P1 space-group symmetry and a large unit cell with Z = 10. An unusually rich set of phonons was found in the low-energy part of the infrared and Raman spectra below 100 cm−1, which we tentatively assign to interlayer vibrations activated by a crystal superstructure and/or to weak force constants for modes related to some structural groups. Several phonons show anomalous behavior in the vicinity of the magnetic phase transition at TN = 10 K, thus evidencing magnetoelastic interaction. No new phonons were found below TN, which excludes the spin-Peierls type of the magnetic transition. In the region of electronic transitions, a strong broad absorption band centered at ∼1.8 eVis observed, which we assign to overlapping of transitions between the 3d9 states of Cu2+ ions split by the crystal field in nonequivalent positions. The fundamental charge-transfer absorption band edge has a complex structure and is positioned around ∼2.8−3.0 eV.

Microscopic description of Raman spectra in nanopowders of nonpolar crystals is accomplished by developing the theory of disorder-induced broadening of optical vibrational eigenmodes. Analytical treatment of this problem is performed, and line shape and width are determined as functions of phonon quantum numbers, nanoparticle shape, size, and the strength of disorder. The results are found to be strongly dependent on whether the broadened line is separated from or overlaps other lines of the spectrum. Three models of disorder, i.e., weak pointlike impurities, weak smooth random potential, and strong rare impurities, are investigated in detail. The possibility of forming the phonon-impurity bound state is also studied.

Disorder-induced broadening of optical vibrational eigenmodes in nanoparticles of nonpolar crystals is studied numerically. The methods previously used to treat the phonons in defectless particles are adjusted for numerical evaluation of the disordered problem. Imperfections in the forms of Gaussian and binary disorders as well as surface irregularities are investigated thoroughly in a wide range of impurity concentrations and disorder strengths. For dilute and weak pointlike impurities the regimes of separated and overlapped phonon levels are obtained and the behavior of the linewidth predicted analytically is confirmed; the crossover scale falls into the actual range of several nanometers. These notions survive for strong dilute impurities, as well. Regimes and crossovers predicted by the analytical approach are checked and identified, and the minor discrepancies are discussed. We mention a few of them: slower than in analytics increasing of the linewidth with the phonon quantum number for weak disorder and only a qualitative agreement between analytics and numerics for the resonant broadening in strong dilute disorder. The novel phenomena discovered numerically are the “mesoscopic smearing” of the distribution function in the ensemble of identical disordered particles, an inflection of the linewidth dependence on the impurity concentration for light “dense” binary impurities, and a position-dependent capability of a strong impurity to catch the phonon. It is shown that surface irregularities contribute to the phonon linewidth less than the volume disorder, and their rates reveal faster decay with increasing of the particle size. It is argued that the results of the present research are applicable also for quantum dots and short quantum wires.

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the nonlinear 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 two-dimensional systems that would be Anderson insulators in the absence of interaction and two- or three-dimensional systems that undergo an 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) 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 transition temperature 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 approach the SIT.

T

) 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 approach the SIT.

We develop a self-consistent approach for calculating the local impedance at a rough surface of a chiral p-wave superconductor. Using the quasiclassical Eilenberger-Larkin-Ovchinnikov formalism, we numerically find the pair potential, pairing functions, and the surface density of states taking into account diffusive electronic scattering at the surface. The obtained solutions are then employed for studying the local complex conductivity and surface impedance in the broad range of microwave frequencies (ranging from subgap to above-gap values). We identify anomalous features of the surface impedance caused by generation of odd-frequency superconductivity at the surface. The results are compared with experimental data for Sr2RuO4 and provide a microscopic explanation of the phenomenological two-fluid model suggested earlier to explain anomalous features of the microwave response in this material.

It is shown that the spin-orbit and Zeeman interactions result in phase shifts of Andreev-reflected holes propagating at the surface of a topological insulator, or in Rashba spin-orbit-coupled two dimensional normal metals, which are in a contact with an s-wave superconductor. Due to interference of holes reflected through different paths of Andreev interferometer the electric current through external contacts varies depending on the strength and direction of the Zeeman field. It also depends on mutual orientations of Zeeman fields in different shoulders of the interferometer. Such a nonlocal effect is a result of the long-range coherency caused by the superconducting proximity effect. This current has been calculated within the semiclassical theory for Green functions in the diffusive regime, by assuming a strong disorder due to elastic scattering of electrons.

Infinite-temperature long-time dynamics of Heisenberg model *H*^=-1/2tsumi,jJijS^i⋅S^j is investigated. It is shown that the quantum-spin pair correlator is equal to the correlator of a classically evaluated vector field averaged over the initial conditions with respect to the Gaussian measure. In the continuous-limit case, the scaling estimations allow one to find the one-point correlator that turns out to be *C*(r=0;*t*)∝const×t−6/7. All results are obtained by straightforward procedures without any assumptions of the phenomenological character.

Time evolution of long-range spatial coherence in a freely decaying cavity-polariton condensate excited resonantly in a high-Q GaAs microcavity is found to be qualitatively different from that in nonresonantly excited condensates. The first-order spatial correlation function g(1)(r1,r2) in response to resonant 1.5 ps pump pulses at normal incidence leaving the exciton reservoir empty is found to be nearly independent of the excitation density. g(1) exceeds 0.7 within the excited spot and decreases very slowly in the decaying and expanding condensate. It remains above 0.5 until the polariton blue shift α|ψ2∣∣ gets comparable to the characteristic amplitude of the disorder potential δELP. The disorder is found to reveal itself at α|ψ2|≲δELP in fast and short-range phase fluctuations as well as vortex formation. They lead to oscillations in g(1)(t), but have little effect on the overall coherence, which is well reproduced in the framework of the Gross-Pitaevskii equations.

The low-frequency dynamical response of an Anderson insulator is dominated by so-called Mott resonances: hybridization of pairs of states close in energy but separated spatially. We study the effect of interaction on Mott resonances in the model of spinful fermions (electrons) with local attraction. This model is known to exhibit a so-called pseudogap: a suppression of the low-energy, single-particle excitations. Correspondingly, the low-energy dynamical response is also reduced. However, this reduction has mostly quantitative character. In particular, the Mott formula for frequency-dependent conductivity preserves its functional asymptotic behavior at low frequencies, but with a small numerical prefactor. This result can be explained in terms of Mott resonances for electron pairs instead of single electrons.

Using two experimental techniques, we studied single crystals of the 122-FeAs family with almost the same critical temperature, Tc. We investigated the temperature dependence of the lower critical field Hc1(T ) of a Ca0.32Na0.68Fe2As2 (Tc ≈ 34 K) single crystal under static magnetic fields H parallel to the c axis. The temperature dependence of the London penetration depth can be described equally well either by a single anisotropic s-wave-like gap or by a two-gap model, while a d-wave approach cannot be used to fit the London penetration depth data. Intrinsic multiple Andreev reflection effect spectroscopy was used to detect bulk gap values in single crystals of the intimate compound Ba0.65K0.35Fe2As2, with the same Tc. We estimated the range of the large gap value L = 6–8 meV (depending on small variation of Tc) and its a k space anisotropy of about 30%, and the small gap S ≈ 1.7 ± 0.3 meV. This clearly indicates that the gap structure of our investigated systems more likely corresponds to a nodeless s-wave two gaps.

Bismuth chalcogenides are the most studied 3D topological insulators. As a rule, at low temperatures, thin films of these materials demonstrate positive magnetoresistance due to weak antilocalization. Weak antilocalization should lead to resistivity decrease at low temperatures; in experiments, however, resistivity grows as temperature decreases. From transport measurements for several thin films ( with various carrier density, thickness, and carrier mobility), and by using a purely phenomenological approach, with no microscopic theory, we show that the low-temperature growth of the resistivity is accompanied by growth of the Hall coefficient, in agreement with the diffusive electron-electron interaction correction mechanism. Our data reasonably explain the low-temperature resistivity upturn.