This series consists of talks in the area of Condensed Matter.
We report on our recent progress to investigate materials classes exhibiting d+id superconductivity, where topologically nontrivial pairing phases can emerge. Specifically, motivated by recent experimental progress, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity.
It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) will emerge when electrons move in Landau levels. In this talk, I will show FQHE can emergy even in the absence of Landau levels in interacting fermion models and boson models. The non-interacting part of our Hamiltonian contains topologically nontrivial flat band.
Recently, we developed a user friendly scheme based on the quantum kinetic equation for studying thermal transport phenomena in the presence of interactions and disorder . This scheme is suitable for both a systematic perturbative calculation as well as a general analysis. We believe that this method presents an adequate alternative to the Kubo formula, which for thermal transport is rather cumbersome. We have applied this approach in the study of the Nernst signal in superconducting films above the critical temperature.
We investigate the entanglement spectra of topological insulators which have gapless edge states on their spatial boundaries. In the physical energy spectrum, a subset of the edge states that intersect the Fermi level translates to discontinuities in the trace of the single-particle entanglement spectrum, which we call a `trace index'. We find that any free-fermion topological insulator that exhibits spectral flow has a non-vanishing trace index, which provides us with a new description of topological invariants.
Time-reversal invariant band insulators can be separated into two categories: `ordinary' insulators and `topological' insulators. Topological band insulators have low-energy edge modes that cannot be gapped without violating time-reversal symmetry, while ordinary insulators do not. A natural question is whether more exotic time-reversal invariant insulators (insulators not connected adiabatically to band insulators) can also exhibit time-reversal protected edge modes.
Strongly correlated electron systems are play grounds for exotic quantum states such as high Tc superconductivity, quantum spin liquids, non-fermi liquids and so on. Recently high Tc superconductivity has been observed in an iron based compound K2Fe4Se5. I will present a model and outline an effective theory  that describes physics of this complex system - a non linear O(3) sigma model in 2 + 1 dimensions coupled to Dirac fermions. Topological solitons and induced quantum numbers are well known in Skyrme model for protons and neutrons.
We discuss bulk and holographic features of black hole solutions of 4D anti de Sitter Einstein-Maxwell-Dilaton gravity. At finite temperature the field theory holographically dual to these solutions has a rich and interesting phenomenology reminiscent of electron motion in metals:
phase transitions triggered by nonvanishing VEV of scalar operators, non-monotonic behavior of the electric conductivities etc. Conversely, in the zero temperature limit the transport properties for these models show an universal behavior.
The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench.
We will discuss the effect of non-equilibrium drive near a quantum
critical point in itinerant electron systems. Non-equilibrium field
theory is formulated in terms of the Keldysh functional integral.
The renormalization group approach is used to study the universality
class of the non-equilibrium phase transition in the steady state system.
The role of the non-equilibrium drive in the quantum-classical crossover
will be discussed using the example of the Hertz-Millis theory and
the generalization thereof.