Spin Transport In Low-dimenional Systems With Spin-orbit Coupling

This dissertation focuses on the spin transport in low-dimensional systems with spin-orbit coupling. In the first two chapters, we briefly review the de-velopment of spintronics and introduce some spin-orbit-coupling dependent spin transport phenomena. Then we show the details of our following investigations.We study the spin current in systems with spin-orbit coupling from the point of view of SU(2) gauge fields for the first time. We find that the naturally defined spin current obeys the covariant continuity equation. By means of the Noether theorem, we obtain the conserved total spin current. We argue that the spin density and spin current density are the sources of SU(2) gauge fields which in turn exert spin force on them. This leads to the nonconservation of the spin current. Thus the conserved spin current should include the contributions from SU(2) gauge fields. By introducing the SU(2) field strength tensor, we can easily obtain the spin force which reduces to the Stern-Gerlach force. We investigate the orbit current in the presence of U(1)×SU(2) gauge fields. We point out that due to the spatially dependent spin-orbit coupling, the total angular momentum does not conserve. Hence the nonconservation parts of the spin and orbit currents can not counteract each other precisely.Starting from the fluid mechanics, we construct a classical picture for the spin transport in SU(2)×U(1) fields. Based on this picture, we derive the clas-sical analogy of the covariant continuity equation which the spin current obeys. Considering that the electron experiences both Lorentz force and spin force, we obtain the classical equations of motion for an electron moving in SU(2)×U(1) fields. From these equations, we can directly obtain the condition for the occur-rence of the infinite spin relaxation time. On the other hand, these equations show that even though the SU(2) gauge fields do not vary with respect to time, the electron can feel an effective time-dependent spin force due to the coupling between the spin and SU(2) gauge fields. We also formulate the diffusion equa- tions for the charge and spin densities. We find that the Zitterbewegung makes these equations couple to each other. Besides, we study the spin precession in one-dimensional ballistic system with three different forms of spin-orbit coupling. The results manifest that the spin precession strongly depends on the initial con-ditions.We investigate the SU(2) Kubo formula which describes the linear response to the nonabelian external fields. We find that the covariant continuity equation for the spin current plays a key role in keeping the consistency of the SU(2) Kubo formula with different gauge fixings. We calculate the linear responses of the spin density and spin current density to the SU(2) external fields. It is shown that if the system possesses the parabolic dispersion relation in the absence of the spin-orbit coupling, the SU(2) spin conductivity still vanishes even without the impurities. This is due to the anticommunication relation between the SU(2) generators. Moreover, we generate the SU(2) Kubo formula to the spin 3/2 representation. It facilitates the discussions of the spin transport in the Luttinger model and coupled bilayer two-dimensional gas.We study the spin Hall conductivity and tunneling spin current in the bi-layer two-dimensional electron gas. The results demonstrate that the spin Hall conductivity shows a sharp peak around the energy degenerate point. This peak can not be suppressed to zero by the infinitesimal concentration of nonmagnetic impurities. We also propose a experimental scheme to detect this magnification effect of the spin Hall conductivity. On the other hand, we find that the tunnel-ing spin conductivity exhibits a double-peak structure in the twin-layer situation. Taking the difference of strengthes of impurity potentials between layers, we find out that the tunneling spin current is asymmetric with respect to the gate voltage. It makes the bilayer system a candidate for the spin diode.We discuss the low-energy excitation of nuclear spins in quantum dots. Using the path integral approach, we obtain the action of this system. After integrating out the electron degrees of freedom, we derive the effective action describing the nuclear spins and the propagator for the spin wave. This helps us to further investigate the spin decoherence caused by the hyperfine interaction in quantum dots.