Hall Conductance Of Open Two-band Systems

The discovery of the Hall effect(especially the integer quantum Hall effect)has great significance in the development history of physics.People have gradually tried to use many methods to study the topological characteristics of topological insulators(TIs)in the theoretical and experimental aspects.The concept of Chen numbers was used to prove the Hall conductivity of quantum system.As a new topological quantum state,topological insulators have become the focus of people's investigation.With the continuous advancement of scientific research,we all know that quantum systems are inevitably interacted with the environment,which are called open quantum systems.The response of open systems is different from the response of closed systems.When the system is the open system,the exchange of energy and information occurs between the system and the environment.Linear response theory has been widely used in many aspects,because it can be used to calculate the response when the environment slightly perturbs the system.The quantum Hall conductance is the linear response to the current due to electric field is applied.The investigation of quantum Hall conductance of open systems is one of the hot topics that have attracted much attention.In this thesis,we combine the linear response theory of open quantum systems to explore the Hall conductance of open two-band systems.Starting from the total Hamiltonian and inducing the influence of the quantum electric field and classical electric field at the beginning,we obtain the expression of an open two-band quantum system master equation from a microscopic angle,which has distinctions with the master equation and perturbation induced phenomenologically.We got the steady-state solution and the analytical formula of the Hall conductance of this system.In particular,the dissipation rate is depended on the Bloch wave vector,which has led to more new features for Hall conductance.The results show that the quantum Hall conductance in this case can no longer be expressed by Chern number.The topological phase transition still exists.