Anomalous Electronic Spin-orbit Properties In Condensed Matter Physics

In this thesis,we study the anomalous electronic spin-orbit properties in condensed matter physics.In particular,we emphasize these properties in different Hall effects and in several thermodynamical physical quantities.The former includes the anomalous Hall effect,the quantum Hall effect,and the spin-Hall effect,while the latter includes the orbital rnagnetization,the magnetic netic susceptibility.The physical systems,in which we study these anomalous properties,are the two-dimensional(2D) ferromagentic kagomélattice,the three-dimensional(3D) antiferromagnetic face-centered-cubic(fcc) lattice,the Haldane model,the 2D electron gas(2DEG),the 2D hole gas system(2DHG) and the Luttinger model.The results show that the(anomalous,quantum,spin-) Hall effects and the novel properties of the orbital magnetization have a tight relation with these spin-orbit properties.In chaptersâ…¡andâ…¢,using the general multi-band formula for finite-temperature orbital magnetization,we theoretically investigate the orbital magnetization and its effects on thermoelectric transport of the 2D kagomélattice with spin anisotropies included and of the 3D ferromagnetic distorted fcc lattice.It is found that the two parts in orbital magnetization,the conventional part M_c and the Berry phase correction part M_Ω,opposite each other.In particular,we show that M_c and M_Ωyield the paramagnetic and diamagnetic responses,respectively.It is further shown that the orbital magnetization displays fully different behavior in the metallic and insulating regions, which is due to the different roles M_c and M_Ωplay in these two regions.The anomalous Nernst conductivity is also calculated,which displays a peak-valley structure as a function of the electron Fermi energy.In chapterâ…£,we investigate the orbital magnetization in several semiconductor models.In chapterâ…¤,we study the de Haas-van Alphen(dHvA) oscillations in the magnetization of a 2DEG under the influence of the edge states and/or the Rashba spin-orbit interaction(SOI) in the sample.The inclusion of SOI changes the well-defined sawtooth behavior of the dHvA oscillations in the magnetization,while no presence of edge states.When the edge effect is included while the SOI is excluded,the center of sawtooth-iike magnetization oscillation does not tend to vanish. This behavior is different from that without the edge effect.The magnetic field is weaker,the destruction of the edge effect and/or the spin-orbit coupling is larger.In chapterâ…¥,we investigate the chiral edge states in the 2D ferromagntic kagomélattice with spin anisotropies included.In the strong spin-coupling case,the Harper equation for solving the energies of edge states is derived.We find that there are two edge states in each bulk energy gap, corresponding to two zero points of the Bloch function on the complex-energy Riemann surface (RS).The edge-state energy loops parainetrized by the momentum cross the holes of the RS. When the Fermi energy lies in the bulk energy gap,the quantized Hall conductance is given by the winding number of the edge states across the holes,which reads asσ_xy^edge=-e²/h sgn(sinφ),whereφis the spin chiral parameter.In the weak spin-coupling case,the quantum Hall effect can also be obtained.Even the quantum will be equal to 2 under a certain condition.These results keep consistent with those based on the topological bulk theory.In chaptersâ…¦andâ…§,we study the conserved spin Hall conductivity in the 2DHG modeled by a combined bulk Luttinger and SIA Rashba spin-orbit coupling and in the 2DEG within a perpendicular magnetic field.In the former,it is shown that the two components in spin Hall conductivity usually have the opposite contributions.While in the absence of Rashba spin splitting, the spin Hall transport is dominated by the conventional contribution,the presence of Rashba spin splitting stirs up a large enhancement of the spin torque dipole correction,leading to an overall sign change for the total spin Hall conductivity.In the latter,it is shown that the spin-orbit coupling competes with Zeeman splitting by introducing additional degeneracies between different Landau levels at certain values of magnetic field.These degeneracies,if occurring at the Fermi level,turn to give rise to resonances in bothsσ_μν^sοandσ₍μν_<sup>sÏ„ in spin Hall conductance.Remarkably,both of these two components have the same sign in the wide range of variation in the magnetic field,which result in an overall enhancement of the total spin Hall current.In particular,the magnitude ofσ₍μν_<sup>sÏ„ is much larger than that ofσ_μν^sο around the resonance.In the last chapter,we study the anomalous Hall effect of heavy holes in Semiconductor Quantum Wells in the intrinsic transport regime,where the Berry curvature dictates the Hall current properties.A derivation based on the first-order perturbation of wave function gives the same expression of the Hall conductivity as that from the semiclassical equation of motion of the Bloch particles.The dependence of Hall conductivity on the system parameters is shown.The amplitude of Hall conductivity is found to be balanced by a competition between the Zeeman splitting and the spin-orbit splitting.