### Edge current/angular momentum in nonequilibrium electron systems

When systems are out of thermal equilibrium, unexpected effects appears. One is that we expect angular momentum near the edge, but not in the bulk. The project starts with a Hall system, i.e., free electrons in a magnetic field, and study its edge effect. When this is done, we look into other models, such as the Haldane model. Finally, we see if a driven current can lead to angular momentum near the edge of a graphene. The student is expected to have a good foundation in quantum mechanics, statistical mechanics, solid state physics, and computer skills, such as MATLAB or python. This is theoretical/computational project.

### Emissivity of graphene and multi-layer graphene, and graphite

The emissivity is defined as the ratio of thermal radiation to the blackbody value according to the Stefan-Boltzmann law of T to the 4-th power of temperature. Graphene has a well-known 2 percents for emissivity. This project aims first to reproduce this value and then going on for multi-layer graphenes, and study the layer number dependence of emissivity. When the layers approach infinity, we expect the result of graphite. In addition to the concrete calculations, we also develop theory based on the Boltzmann transport for coupled electron-photon system. The student is expected to have a good background in solid state physics.

### "Capacitor physics" of near-field radiative heat transfer

The capacitor serves as a model system for the simplest possible quantum system for heat transfer mediated by the Coulomb interaction. In this project, we study a capacitor with three layers, i.e., the problem of three parallel plates, each connected independently to a battery. Each of the plate is treated as a quantum dot of one degree electron. By controlled the temperature and chemical potential of each one, as well as the two distances between the plates, we explore possible interesting new physics. The student should have a solid fundation is quantum mechanics, and some numerical computation skills, such as MATLAB or Python.