| In the 1980s,the phenomenon of electron transport related to electron spin in solid-state devices was discovered,and a new discipline,spintronics,began to emerge.In re-cent years,with the development of technology,spintronic devices with advantages of small size,high speed,and low power consumption have become more and more pop-ular,and then they are expected to become an alternative to traditional charge-based semiconductor devices.Spin-orbit coupling,intimately uniting a electron's spin with it momentum has attracted widespread attention in spintronics since it provides a whole electrical way to control spin.In the electron transport,the disorder effect is of great significance.Disorder affect on the propagation characteristics of waves has always been one of the research topics in condensed matter physics.Especially when multiple scattering between impurities plays a major role,complex quantum interference effects often cause many interesting physical phenomena.Therefore,it is highly required to explore the disorder effect on the spin-orbit coupling systems,which will provide an im-portant theoretical basis for the related experiments and applications of novel spintronic devices.This dissertation for Ph.D degree contains the following five chapters.In Chapter 1,we briefly introduce the Hamiltonian model of two-dimensional(2D)spin-orbit coupling systems,the realization and control of such systems in real materi-als,as well as the recent investigations of disorder effect.Many previous studies on the disorder effect of density of states show that,when Fermi energy approaches band tail,the system enters strong scattering region where the multiple scattering off many impu-rity centers plays a major role.In this region,the density of states decays exponentially with energy,which called Urbach tail.This result cannot be obtained in the traditional perturbation theory method based on Feynman diagram.When the disorder is weak,due to the change in symmetry caused by the spin-orbit coupling,the system still be-longs to the diffusion metal state,and the transport properties are mainly determined by the diffusion conductivity.In the 2D Rashba spin-orbit coupling system,the direct current(DC)diffusion conductivity shows a significant difference between the high-energy regime and the low-energy regime.In the 2D ferromagnetic Rashba spin-orbit coupling system,there is a non-quantized anomalous Hall conductivity in the pseudo-gap regime.With the increase of disorder,the system will be localized.According to the early Anderson localization theory and single-parameter scaling theory,metal-insulator phase transitions only exist in three-dimensional systems.For one-dimensional and 2D systems,arbitrarily small disorder will make the system localize.However,the spin-orbit coupling will transform the traditional 2D electron gas from orthogonal symmetry to symplectic symmetry,resulting in the system wave function being extended under weak disorder.The system will undergo metal-insulator phase transition until disor-der strength reaches a threshold value.The introduction of the ferromagnetic exchange term will then change the system from symplectic symmetry to unitary symmetry.The disorder-induced quantum phase transitions in unitary symmetry are still inconclusive,although several researches have found that there is a novel Kosterlitz-Thouless(KT)type phase transition in these systems.In Chapter 2,we in detail introduce some basic concepts of the 2D nonmagnetic and ferromagnetic Rashba spin-orbit coupling systems.Here,we deduce the expres-sion of eigenenergy,eigenstates,velocity operators,Green's function,and the conver-sion matrices within the spin and eigenstate representations.These quantities and the related expressions will be directly used in this dissertation in the following chapters.At the same time,we introduce the discretization scheme of continuous model to lattice tight binding model,which is necessary for the numerical simulations.What's more,we examine four common types of disorder considered in this dissertation including the short-range Anderson disorder,the short-range Gaussian disorder,the long-range Gaus-sian disorder and the spin-related disorder.Via the Hamiltonian expressions,averaged strength and quasi-particle relaxation time,we try to explore the differences and con-nections among four different disorders.We also show connection between continuous and discrete representations for them.In Chapter 3,we systematically study the direct current(dc)diffusion conductivity of the 2D Rashba spin-orbit coupling system and the anomalous Hall conductivity of the 2D ferromagnetic Rashba spin-orbit coupling system.Firstly,by comparing the re-sults of dc diffusion conductivity of the 2D Rashba spin-orbit coupling system from the semi-classical Boltzmann transport theory and the Kubo formula based on the Green's function.We find the these results from two methods are completely consistent under the first-order Born approximation.As for two methods,the conductivity is linearly dependent on the carrier density when the Fermi level is above the Dirac point,which is equal to the traditional 2D electron gas without spin-orbit coupling,while the conduc-tivity is related to the square and biquadrate of the carrier density when the Fermi level is below the Dirac point.However,when the accurately calculated self-energy term is introduced into the Kubo formula,we find that near the band edge the conductivity and the charge density satisfy a power-law relation,with the exponent linearly dependent on the Rashba spin-orbit strength(but independent of the disorder strength).Moreover,some unphysical behaviors obtained by perturbation methods(i.e.the saturation of mo-bility near the band edge and the conductivity plateaus in the ultralow density regime)disappear in the exact calculations.These observations clearly reveal that the multi-ple scattering off many impurity center in the tail region has an important influence on the transport properties.Then we turn to study the anomalous Hall conductivity of the 2D ferromagnetic Rashba spin-orbit coupling system in the presence of Gaussian short-range disorder under the mean field approximation.In this case,the anomalous Hall conductivity is composed of intrinsic and side-jump scattering contributions.Here,the intrinsic contribution is closely related to the band structure.Comparing the disorder effect on the intrinsic contribution of Hall conductivity and the spectral function of the system,we find that the change in the intrinsic contribution conductivity mainly origi-nate from the overlapping of band broadening caused by disorder.On the other hand,the side-jump scattering plays a significate role in canceling the whole anomalous Hall conductivity in the regime above the pseudo-gap,which is much less than the intrinsic part in remaining range.As a result,the nonzero anomalous Hall conductivity only ex-ist in the pseudo-gap and the regime below the pseudo-gap,which mainly comes from the intrinsic contribution.In Chapter 4,we focus on the disorder-induced quantum phase transitions in these systems.In the 2D Rashba spin-orbit electron gas,we observe a metal-insulator phase transition with the critical exponent and the form of the correlation function are con-sistent with the results in other 2D symplectic systems.As for the 2D ferromagnetic Rashba spin-orbit electron gas,we find a novel critical phase,called marginal metal,between the metal and insulator through calculating the conductance and fractal di-mension.With the change of the disorder strength or the Fermi level,the system will undergo two KT-type quantum phase transitions(one is the metal to marginal phase transition,and the other is the marginal to insulator phase transition.In the metal and insulator phases closing to the marginal metal phase,the conductance meets the single-parameter scaling law,and the correlation length diverges exponentially when the dis-order strength or the Fermi energy approaches critical point.Besides,we calculate the fractals of dimension as a function of the disorder strength,and find that D=1.90 for the critical phase,while the extended states in the diffusive metal phase spread over the entire lattice(D=2),and all states localized in the insulator phase(D=0).In Chapter 4,we focus on the disorder-induced quantum phase transitions in these systems.In the 2D Rashba spin-orbit electron gas,we observe a metal-insulator phase transition with the critical exponent and the form of the correlation function are con-sistent with the results in other 2D symplectic systems.As for the 2D ferromagnetic Rashba spin-orbit electron gas,we find a novel critical phase,called marginal metal,between the metal and insulator through calculating the conductance and fractal dimen-sion.With the change of disorder strength or the Fermi level,the system will undergo two KT-type quantum phase transitions(one is the metal to marginal phase transition,and the other is the marginal to insulator phase transition).In the metal and insulator phases closing to the marginal metal phase,the conductance meets the single-parameter scaling law,and the correlation length diverges exponentially when the disorder strength or the Fermi energy approaches the critical point.Besides,we calculate the fractal di-mension as a function of the disorder strength,and find that D=1.90 for the critical phase,while the extended states in the diffusive metal phase spread over the entire lattice(D=2),and all states localized in the insulator phase(D=0).In the last chapter of this doctoral dissertation,we give a brief summary and out-look. |
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