# Honours/MPT/311/PhD projects

### Electron surface Green's function in a 2D lattice

The Green's function for electrons is the starting point for many
calculations. This project aims to find exact expression for simple
systems such as square lattice for an semi-fininite system.
The result will be used in the following projects for energy transport.

All students in my group are expected to have a good foundation in quantum mechanics,
statistical mechanics, solid state physics, and computer skills,
such as MATLAB or python. This (and the all the rest) 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.

### Super-Planckian heat transfer

This project aims to compute the energy transfer between two flat sheets
(say square lattices) side by side (not face to face), using the Green's functions
in the first project. The approach is based on the nonequilibrium Green's function
for photon transport. This project requires substantial knowledge in condensed
matter physics and good programming skill (such as Fortran and parallel
programming with MPI).

### Energy, momentum, and angular momentum transfer in electron systems

This is an open-ended PhD level project based on our recent review article
here.
We need to identify good systems to work on, and implement the theory as
numerical codes for predictions.

For more information, contact Prof. Wang Jian-Sheng, phywjs@nus.edu.sg.