Conserved Currents, The Spin-orbit Coupling System

Recently,the study on spin-orbit coupling effects in semiconductor systems,especially their novel transport properties attracted many scientists' interest.And the expressions of charge currents and spin currents are the bases for the study on corresponding transport properties.In this thesis,we mainly concern the analytic expressions of charge currents in typical spin-orbit coupling semiconductor systems.Further, taking into account the extra terms in the expression of conserved charge current,we rigorously explain the integer quantum Hall effect in 2D k-cubic Rashba system.Chapter 1 roughly reviews the mechanism of spin-orbit coupling effects in semiconductor systems and introduces typical models in spin-orbit coupling semiconductor systems.Chapter 2 discusses the expressions of conserved currents in Rashba,Luttinger and Dresselhaus systems based on continuity equation of Schroedinger equation.Further, by extended Noether's theorem,we discuss the origin of extra terms in the expression of conserved currents,which is the cubic dependence of momentum k to the Hamiltonian. The results derived from the above two methods are consistent with each other.Our result is the conventional expressions of currents,widely used in several literatures,are not complete.In Dresselhaus system,the particle currents needs extra terms besides the conventional ones.While,in Rashba and Luttinger systems,the expression of particle currents need not the extra terms.Chapter 3 studies extra terms in the expression of particle currcnt of 2D k-cubic Rashba spin-orbit coupling systems based on the methods provided in Chapter 2.Further, noticed that this system is realizable for the experiment of integer quantum Hall effects,and,in fact,the existence of integer quantum Hall effects strongly depends on the expression of current.Then we answer the question that why integer Hall effects will remain in this system in the presence of extra terms in particle currents.