Many-terminal The Transport Properties Of Two-Dimensional Systems

In recent years, most of the researching works on the transport of mesoscopic systems based on semiconductor heterostructures study the spin Hall effect and the measurement spin current under consideration of the spin-orbit coupling interaction. In this thesis we investigate the thermoelectric effect such as Nernst effect and the spin Nernst effect, simultaneously considering Rashba and Dressehaus spin-orbit interactions in two-dimensional electron gas. The main contents are as follows:In the first chapter, a brief introduction of the mesoscopic system and its characteristics such as Nernst effect etc is given firstly. Then the Rashba and Dresselhaus spin-orbit coupling interaction is derived in detail from the free-electron Dirac equation, and the Landauer-Buttiker formula used to study the electron transport property is present.The second chapter describes the numerical methods, finite difference method and surface Green function. Taking an example of one-dimensional harmonic oscillator, its eigenvalues are tested by the finite difference method. Derived the surface Green’s function from the definition of the Green’s function, and the conductance and the band structure of ideal graphene nanoribbons is calculated.In the third chapter, we study the influence of the spin-orbit coupling on the thermoelectric effect of the two-dimensional electron gas systems. The Nernst coefficient and the spin Nernst coefficient are numerically discussed. The results show that:(1) If the middle scattering region and the four electrodes are all imposed the Rashba and Dressehaus spin-orbit coupling and the strength of two is equal, the variation of Nernst coefficient with the reciprocal of the magnetic field appears a series of peaks. When the coupling strength is not equal, every peak of Nernst coefficient will be split. With increasing of the difference between two kinds of spin-orbit coupling or weakening of the magnetic field, the more obvious to be split.(2) Only if the middle scattering region is imposed the Rashba and Dressehaus spin-orbit coupling, an associated small peaks appear at the side of resonant peaks when the strength of two is equal. For different strength of two kinds of spin-orbit interaction the spin Nernst effect is produced. The resonant amplitude of spin Nernst coefficient is dependent on the spin-orbit interaction and the magnetic field.(3) At the end of this chapter, the characteristic of the Nernst coefficient in the limit of temperature tending infinitely to0K is analyzed. It is found that the Nernst coefficient is linear with temperature in low-temperature limit.