# Research

## Overview

As a condensed matter theory group, we find ideas and motivations from experiments. Naturally, our projects evolve with experimental developments. Condensed matter physics is nestled in the intersection where material science, nanotechnology, chemistry, physics and mathematics meet. Rapid experimental developments fueled by new materials and probing techniques offer many opportunities to work on new problems and impact experimental research. We enjoy bringing real world materials together with mathematical and beautiful theoretical concepts and calculations.

We tend to focus on the physics of strongly correlated systems. In weakly correlated systems, such as semiconductors and most metals, the electron-electron interaction energy is far smaller than individual electron's kinetic energy. Hence the system can be successfully thought in terms of the motion of independent electrons: electrons behave like molecules in gas. On the other hand, interaction energy is either more dominant or on par with kinetic energy in strongly correlated systems. As a result, the system as a whole display properties that cannot be boiled down to the properties of individual electrons: electrons behave like molecules in liquid, well aware of each other. Examples of such systems include electrons in a two-dimensional(2D) plane under strong magnetic field (quantum Hall regime), high temperature superconductors, and low-dimensional (1D or 2D) systems in the clean limit. Strongly interaction effect open up many new possibilities for the material properties. For instance, they may lead to exotic ground states and excitations that act like a fraction of an electron. We may need to use sophisticated mathematics to describe such excitations. Also, analogies to seemingly unrelated systems can be very useful in understanding new phenomena. For example, the concept of electronic analogue of liquid crystals is turning out to be quite useful in describing a number of systems.

We take "holistic approach" in our research. On one hand, we search for the common thread within experimental observations and use it as the foundation and check for our theoretical research. At the same time, we combine various analytical methods such as field theory and renormalization group, with computational techniques such as quantum Monte Carlo through collaborations.

## Research Areas

The diversity of emergent phenomena and opportunities to connect theoretical ideas and calculations to experimentally observed phenomena are major attractions for condensed matter theory. While much effort of our group go into the study of strongly correlated systems such as high temperature superconductors and quantum Hall effect, we work on a diverse set of topics as you can see from our publication list. For instance, we have worked on fractional vortices in chiral superconductors, curvature effects on graphene, edge states of topological insulator, topological quantum phase transition, charge density waves in rare-earth-Tellurides, nodal nematic quantum phase transition, and intra-unit-cell nematicity in high Tc superconductors. See below for topics of current research.