Condensed Matter Seminar

When a small quantum system is subject to multiple periodic drives, it may realize multidimensional topological phases. In my talk, I will explain how to make such constructions, and show how a spin-1/2 particle driven by two elliptically-polarized light beams could realize the Bernevig-Hughes-Zhang model of 2 topological insulators. The observable consequence of such construction is quantized pumping of energy between the two drive sources. I will demonstrate this effect, and discuss the surprising features that emerges in such a topological quantum-optics system.

Nonequilibrium steady state behavior in driven, open quantum systems has generated significant interest in recent years. I will discuss certain aspects of dissipation and decoherence in quantum systems, leading to the emergence of the Kraus map and the GKLS (“Lindblad”) Master equation. Under GKLS dynamics, the density matrix for boundary driven quantum systems - for example, a chain coupled to different heat baths at either end - relaxes to a nonequilibrium steady state (NESS), the properties of which depend on whether the bulk Hamiltonian is integrable or not.

Symmetry protected topological (SPT) phases are generalizations of topological band insulators; they are quantum phases of matter with a bulk energy gap and characteristic edge or surface properties. Over the past few years, exciting progress has been made in the theory of SPT phases with strong interactions, and, separately, SPT phases with crystalline symmetry. The intersection of these two directions — strongly interacting crystalline SPT phases — has potential experimental relevance but has remained rather poorly understood.

The thermoelectric effect is a phenomenon in which a temperature difference applied to a conducting material induces a voltage difference. This effect has a range of important applications, since it allows one to convert waste heat into useful electric power. In conventional metals and semiconductors, however, the strength of the thermoelectric effect faces fundamental limitations. In this talk I consider whether these same limitations apply to the three-dimensional nodal semimetals.

When system dimension and size go down, many interesting phenomena can happen. Both experimental and numerical works in recent years have shown that phonon/heat transport in low (quasi 1D and 2D) dimensional nano structures like nanotube, nanowire, polymer chain, graphene, and other 2D materials show anomalous behavior: 
(a) heat conduction due to phonons does not follow the Fourier law; 
(b) heat transports may break down the reciprocal principle, namely heat flows asymmetrically.

Topological quantum matter typically arises in gapped (massive) systems, where topological invariants and their associated quantized experimental signatures are protected by the energy gap separating ground- and excited- state(s). Understanding topological properties of such gapped systems has led to tremendous progress in theoretically classifying and characterizing gapped phases of matter, even in the presence of strong correlations.

Novel universal quantities can arise in scaling terms sub-leading to the area law, in the entanglement entropy in quantum critical theories in d > 1+1. These depend crucially on the geometry of the entangled bipartition. In some cases, they are known to be related to scaling dimensions obtained from conventional n-point functions, but in some cases no clear relationships are yet known.

I discuss the interplay between non-Fermi liquid behaviour and superconductivity near a quantum-critical point (QCP) in a metal. It is widely thought that the tendency towards superconductivity and towards non-Fermi liquid behaviour compete with each other, and if the pairing interaction is reduced below a certain threshold, the system displays a naked non-Fermi liquid QC behaviour. I show that the situation is more complex as there are multiple solutions for Tc at a QCP. For all solutions, except one, Tc vanishes when the pairing interaction drops below the threshold.