The Study Of Spin Chern Pump In Low-dimensional Topological Systems

Traditionally, the electronic transportation is only related to charge transport, but ignores its another intrinsic freedom-spin. This makes it possible for semiconductor industry to get into a new field in which the transport processes consider the freedom of spin as a new object. Meanwhile, there are many possible applications of spin related transport. As a consequence, in the past few years the new field of spintronics have been attracting a great deal of interest, and practical realization of devices in which spin can be well controlled and spin currents can be stable or even quantized has becoming an important subject in the field of mesoscopic transport. In the early 80’s, Thouless and Niu put forward the quantized adiabatic particle transport in gapped fermi systems in which an adiabatical variation of the periodic electrostatic potential pumps up an in-teger number of electrons per cycle. Since then, an adiabatic quantum pumping that transmits an integral number of electrons per cycle through an unbiased system in re-sponse to a periodic deformation of the system potential, which can be described by some parameters and varies slowly, has been continuously reported. In recent years, pumping of spin polarization with little or no dissipation has become a focus of atten-tion. One option to design an adiabatic spin pump involves that the periodic variation of some control parameters leads to the transfer of spin across an insulating structure. Such a spin pump has been came true in quantum dot structures. The another option involves using the spin Hall effect to generate a spin current which may be precisely quantized due to its topological properties. Based on the later option, Fu and Kane pro-pose a Z2 adiabatic spin pump in the limit of weak coupling, who consider a class of one-dimensional insulating Hamiltonians which get through an adiabatically deforma-tion in an appropriate closed cycle, and then show that Z2 pump function as they defined transmits a finite but not integer quantized spin in each cycle. As the Chern number that characterizes a topological charge pump, the Z2 pump is characterized by a Z2 topolog-ical invariant. Which means that the Z2 pump is closely related to the quantum spin Hall effect and protected by the time-reversal symmetry. However, how this fictitious model could be implemented is still unknown, and such theory is not applicable to sys-tems without time-reversal symmetry. Furthermore, from the viewpoint of application, generalization of the idea of the Z2 pump to higher dimension is meaningless. There-fore, it is crucial to determine whether the topological spin pump remain robust as the time-reversal symmetry has been broken, e.g., robust spin pump protected by topolog-ical alone, independent of any symmetries, is still awaited. Fortunately, based on the spin Chern numbers, it was shown that the bulk topological properties remain intact even when the TR symmetry is broken. In this dissertation, we investigate an open system as the same model of Fu and Kane, and with a finite coupling between the pump and electrode by using the scattering matrix method, and then found that the topological spin pumping is still robust in the absence of time-reversal symmetry. For this reason, such spin pumping process can no longer be explained by the theory of Z2 pump, or even has no association with the appearance of gapless end states. Instead, it is only dependent on the bulk topological properties and related to the spin Chern numbers. As a result, we also call such spin pump as spin Chern pump in contrast to Z2 pump. This dissertation consists of three chapters:In the first chapter, we give an introduction for the related experimental and theo-retical background, theoretical methods and a brief outline of some fundamental con-ceptions.In the second chapter, a one-dimensional electron model with parameters modu-lated adiabatically in closed cycles is proposed which can continuously pump spin to leads. By Fourier transform, the energy structure of this one-dimensional system ex-ists energy gap and a boundary state across this gap, which means that it has nontrivial topology. Moreover, by defining the spin-polarized Wannier functions, we reveal that the spin pumping process is protected by the spin Chern numbers and independent of any symmetries, so that it is stable to perturbations violating the time-reversal symme-try and spin conservation. We also calculate the spin pump function by using scattering matrix method, and found that the spin polarization pumped per cycle is quantized, even though there are weak magnetic disorder. Finally, we make a comparison with previ-ous theories, such as Z2 pump, and put forward a method to experimentally observe the spin Chern numbers by using a half-metallic lead.The last chapter presents a summary of this dissertation, and then gives some out-look for the investigation.