The concept of exciton and its condensation in semiconductor is reviewed in this thesis. The theoretical method of using a BCS like ground state trial wave function to study exciton condensation is summarized. My work focused on the calculation of exciton condensation in model 2D topological insulators. From argument, the effect of s wave pairing exciton mainly modified the parameters of effective Hamiltonian near Γ point. More interesting problem is to find the possibility of p wave pairing that breaks time reversal symmetry spontaneously. With a simple 4 parameters model, p wave pairing phase was found to be energetically preferable when Rashba spin orbit coupling is larger than a critical value. The p wave exciton can close the bulk band gap and change the topological propert...[ Read more ]

The concept of exciton and its condensation in semiconductor is reviewed in this thesis. The theoretical method of using a BCS like ground state trial wave function to study exciton condensation is summarized. My work focused on the calculation of exciton condensation in model 2D topological insulators. From argument, the effect of s wave pairing exciton mainly modified the parameters of effective Hamiltonian near Γ point. More interesting problem is to find the possibility of p wave pairing that breaks time reversal symmetry spontaneously. With a simple 4 parameters model, p wave pairing phase was found to be energetically preferable when Rashba spin orbit coupling is larger than a critical value. The p wave exciton can close the bulk band gap and change the topological properties of the ground state. The total Chern number of this phase was calculated to be -2. We found that this phase may be not realizable for the known 2DTI materials. A proposal is made to find p wave exciton pairing in usual 2D semiconductor with Rashba spin orbit coupling.