Observation of Many-Body Quantum Phase Transitions beyond the Kibble-Zurek Mechanism.

Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both the dynamical steady-state-relaxation region and the phase-oscillation region. Based on various observables, two different values for the same quantum critical parameter are observed.

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems.

Strongly correlated electron systems are generally described by tight-binding lattice Hamiltonians with strong local (onsite) interactions, the most popular being the Hubbard model. Although the half-filled Hubbard model can be simulated by Monte Carlo (MC), physically more interesting cases beyond half-filling are plagued by the sign problem. One therefore should resort to other methods.

Dynamical instability of the electric transport in superconductors.

We develop a nonlinear theory of the electronic transport in superconductors in the framework of the time-dependent Ginzburg-Landau (TDGL) equation. We utilize self-consistent Gaussian approximation and reveal the conditions under which the current-voltage V(I) dependence (I-V characteristics) acquires an S-shape form leading to switching instabilities. We demonstrate that in two-dimensions the emergence of such an instability is a hallmark of the Berezinskii-Kosterlitz-Thouless (BKT) transition that we have detected by transport measurements of titanium nitride (TiN) films.

Type I superconductivity in Dirac materials.

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals while in the PdTe, superconductivity is clearly of the first kind. This is very rare in Dirac semi-metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic.

Semiclassical magnetotransport in strongly spin-orbit coupled Rashba two-dimensional electron systems.

Semiclassical magnetoelectric and magnetothermoelectric transport in strongly spin-orbit coupled Rashba two-dimensional electron systems is investigated. In the presence of a perpendicular classically weak magnetic field and short-range impurity scattering, we solve the linearized Boltzmann equation self-consistently. Using the solution, it is found that when Fermi energy E F locates below the band crossing point (BCP), the Hall coefficient is a nonmonotonic function of electron density n e and not inversely proportional to n e.

Triplet superconductivity in 3D Dirac semi-metal due to exchange interaction.

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi-metal. Investigation of the order parameters and energies of these states at zero temperature in a wide range of values of chemical potential μ, the effective electron-electron coupling constant λ and Debye energy TD demonstrates that when the exchange interaction is neglected the singlet always prevails, however, in significant portions of the (μ, λ, TD) parameter space the energy difference is very small. This means that interactions that are small, but discriminate between the spin singlet and the spin triplet, are important in order to determine the nature of the superconducting order there.

Theory of the vortex matter transformations in high-Tc superconductor YBCO.

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges.