Magnetic impurities in a strongly coupled superconductor.

We revisit certain aspects of a problem concerning the influence of carrier scattering induced by magnetic impurities in metals on their superconducting properties. Superconductivity is assumed to be driven by strong electron-phonon interaction. We use the self-consistent solution of the Nagaoka equations for the scattering matrix together with the Migdal-Eliashberg theory of superconductivity to compute the energy of the in-gap bound states, superconducting critical temperature and tunneling density of states for a wide range of values of the Kondo temperature and impurity concentrations.

Collective modes in terahertz field response of disordered superconductors.

We consider a problem of nonlinear response to an external electromagnetic radiation in conventional disordered superconductors which contain a small amount of weak magnetic impurities. We focus on the diffusive limit and use Usadel equation to analyze the excitation energy and dispersion relation of the collective modes. We determine the resonant frequency and dispersion of both amplitude (Schmidt-Higgs) and phase (Carlson-Goldman) modes for moderate strength of magnetic scattering.

Migdal-Eliashberg superconductivity in a Kondo lattice.

We apply the Migdal-Eliashberg theory of superconductivity to heavy-fermion and mixed valence materials. Specifically, we extend the Anderson lattice model to a case when there exists a strong coupling between itinerant electrons and lattice vibrations. Using the saddle-point approximation, we derive a set of coupled nonlinear equations which describe competition between the crossover to a heavy-fermion or mixed-valence regimes and conventional superconductivity.

Superconductivity in Ce-based cage compounds.

Cerium-based ternary compounds CeNiCdand CePdCddo not exhibit long-range order down to millikelvin temperature range. Given the large separation between Ce ions which significantly reduces the super-exchange interactions and vanishingly small Ruderman-Kittel-Kasuya-Yosida interaction, here we show that nodal superconductivity mediated by the valence fluctuations must be a ground state in these materials. We propose that the critical temperature for the superconducting transition can be significantly increased by applying hydrostatic pressure.

Interacting fermions in narrow-gap semiconductors with band inversion.

Highly unconventional behavior of the thermodynamic response functions has been experimentally observed in a narrow gap semiconductor samarium hexaboride. Motivated by these observations, we use renormalization group technique to investigate many-body instabilities in the-orbital narrow gap semiconductors with band inversion in the limit of weak coupling. By projecting out the double occupancy of the-states we formulate a low-energy theory describing the interacting particles in two hybridized electron- and hole-like bands.

Exploring itinerant states in divalent hexaborides using rare-earth L edge resonant inelastic x-ray scattering.

We present a study of resonant inelastic x-ray scattering (RIXS) spectra collected at the rare-earth L edges of divalent hexaborides YbB and EuB. In both systems, RIXS-active features are observed at two distinct resonances separated by [Formula: see text] eV in incident energy, with angle-dependence suggestive of distinct photon scattering processes. RIXS spectra collected at the divalent absorption peak resemble the unoccupied 5d density of states calculated using density functional theory.

Quench-induced Floquet topological p-wave superfluids.

Ultracold atomic gases in two dimensions tuned close to a p-wave Feshbach resonance were expected to exhibit topological superfluidity, but these were found to be experimentally unstable. We show that one can induce a topological Floquet superfluid if weakly interacting atoms are brought suddenly close ("quenched") to such a resonance, in the time before the instability kicks in. The resulting superfluid possesses Majorana edge modes, yet differs from a conventional Floquet system as it is not driven externally.

Cubic topological Kondo insulators.

Current theories of Kondo insulators employ the interaction of conduction electrons with localized Kramers doublets originating from a tetragonal crystalline environment, yet all Kondo insulators are cubic. Here we develop a theory of cubic topological Kondo insulators involving the interaction of Γ(8) spin quartets with a conduction sea. The spin quartets greatly increase the potential for strong topological insulators, entirely eliminating the weak topological phases from the diagram.

Non-Fermi liquid regimes with and without quantum criticality in Ce(1-x)Yb(x)CoIn5.

One of the greatest challenges to Landau's Fermi liquid theory--the standard theory of metals--is presented by complex materials with strong electronic correlations. In these materials, non-Fermi liquid transport and thermodynamic properties are often explained by the presence of a continuous quantum phase transition that happens at a quantum critical point (QCP). A QCP can be revealed by applying pressure, magnetic field, or changing the chemical composition.

Correlated disorder in a Kondo lattice.

Motivated by recent experiments on Yb-doped CeCoIn5, we study the effect of correlated disorder in a Kondo lattice. Correlations between the impurities are considered at the two-particle level. We use a mean-field theory approximation for the Anderson lattice model to calculate how the emergence of coherence in the Kondo lattice is impacted by correlations between impurities.

Topological Kondo insulators.

Kondo insulators are a particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological classification of emergent band structures for Kondo insulators and show that these materials may host three-dimensional topological insulating phases. We propose a general and practical prescription of calculating the Z(2) topological indices for various lattice structures.

Dynamical vanishing of the order parameter in a fermionic condensate.

We analyze the dynamics of a condensate of ultracold atomic fermions following an abrupt change of the pairing strength. At long times, the system goes to a nonstationary steady state, which we determine exactly. The superfluid order parameter asymptotes to a constant value.

Superconductivity in charge Kondo systems.

We present a theory for superconductivity and charge Kondo fluctuations, i.e., resonant quantum valence fluctuations by two charge units, for Tl-doped PbTe.