Condensed Matter Physics
Topological phenomena are the phenomena which are determined by some topological structure in the physical system, which are thus usually universal and robust against perturbations. For example, two famous topological phenomena are the flux quantization in superconductors and Hall conductance quantization in the Quantum Hall states. Recent discovery of topological insulators and topological superconductors in different symmetry classes bring the opportunity to study a large family of new topological phenomena. For example the three-dimensional topological insulator provides a condensed matter realization of the important theoretical concepts in high energy physics such as ”θ-vacuum” and “axion”. The interplay of topological insulators and superconductors with conventional phases of matter such as ferromagnets and superconductors lead to richer topological phenomena.
Nanoscience and Quantum Engineering
Quantum entanglement is the unique feature of quantum mechanics, which is essential for quantum information and quantum computation. The understanding of quantum entanglement provides a new probe to the physical properties of the many-body systems compared to the conventional response properties such as conductivity, spin susceptibility, etc. On the other hand, more systematical understanding of quantum entanglement in many-body systems may also lead to breakthrough in building a quantum computer. It is far more difficult to study entanglement properties in many-body systems compared to few-body systems. There are a lot of open questions for which the answer is not known or only known for specific systems. For example, what is the general relation between entanglement properties and other physical observables in a given system? What is the relation between quantum entanglement and topological states of matter? Besides the known description of entanglement such as von Neumann entropy, what other measure can be defined to provide more refined characterization of entanglement? I am pursuing these directions.