Transport Properties Of The Quantum Dot Coupled Lead In The Kondo Regime With Magnetic Field

The research of strongly correlated electron system have had a great progress no matter in theory or in experimental physics,especially the discovery of electron system which is constitute by Quantum Dot.There are,however,so many exotic phenomena which is important in Condensed Matter Physics should be explored for us and that is one of the reason why physicists are committed to research the system of Quantum Dot.There are many important physical effects,such as Kondo effect,Coulomb Blockade effect,Quantum Tunneling effect and so on,in low dimensional quantum system and Kondo Effect which is caused by the interaction of electrons of the system is one of the most significant physical effects.So the research of electron transport properties of low dimensional quantum system has far-reaching significance,and get more and more attentions of people.In addition,the motion of electrons is bound to be affected by the magnetic field,so considering the effect of magnetic field,the results are more convincing.In experiment,it is very sophisticated to control the factor of magnetic field,however,the advantage of quantum dot system is that it can be adjusted,so the one-dimensional quantum wire and quantum dot coupling system based on the Luttinger model can be used to study the influence of the magnetic field on the electron transport properties of the system.First,we study the nature of the system of quantum dot coupled to Luttinger liquid leads,and explore the effect of the interaction between the electrons and the magnetic field on the density of states in the Kondo region.We use non-equilibrium Green's function method,Bose,and Motion equation to deduce the formula of the density of states.We found that under the weak electron interaction,the Kondo peak split into two asymmetric Kondo peak,the peak position of the splitting peak is at the Zeeman energy level,representing the spin up and down respectively.For weak electron interaction,the Kondo dip also occurs splitting in the same way.However,for the strong electronic interaction,the Zeeman splitting behavior disappeared and produce power-law scattering behavior.Second,based on the study of the density of States,we further study the effects of a magnetic field and intralead electron interaction on the transport of a strongly interacting quantum dot coupled to Luttinger liquid leads in the Kondo regime by using the nonequilibrium Green function method.Detailed predictions are made for the differential conductance as a function of voltage bias.We find that for very weak intralead electron interaction,the Kondo peak splits in two peaks by an applied magnetic field and a minima appears.When the intralead interaction increases and becomes the moderately strong interaction,the peaks at the positive and negative values of V disappear and turn into the two dips.There is a sharp local minimum in the differential conductance at a finite field dependent voltage.When the intralead interaction increases to the limit of extremely strong interaction,Kondo peaks and dips disappear and the differential conductance as a function of voltage bias becomes a smooth curve.Because of our work in this thesis,we now have a new understanding of density of states and differential conductance of quantum dot coupled to Luttinger liquid leads in the Kondo region under the external magnetic field.It also lays the foundation for the experimental and theoretical work in the future.