Analytical approach to spin-dependent transport in a mesoscopic magnetic conductor

Zheng-Chuan Wang and Gang Su

Department of Physics, Graduate School of the Chinese Academy of Sciences, P. O. Box 3908, Beijing 100039, China

~Received 9 December 2002; revised manuscript received 21 May 2003; published 30 July 2003!

Instead of obtaining the Hartree self-consistent potential numerically, we develop a method to solve analytically this potential which satisfies the Poisson and the Schro¨dinger equations. It is convenient for us to explore the effect of electron-electron interactions on the spin-dependent transport properties in a mesoscopic magnetic conductor. When we express the wave function in the Schro¨dinger and Poisson equations as C(x) 5R(x)exp(iS(x)/\), then the self-consistent potential and the wave function can be expressed analytically when we neglect the higher-order terms of the Planck constant \ and choose the function R(x) to be unity. The electric current, differential conductance, and quantum capacitance can thus be obtained readily. In this paper, the electron-electron interaction is only considered on the basis of the semiclassical approximation.

DOI: 10.1103/PhysRevB.68.024421 PACS number~s!: 75.70.Cn, 72.10.Bg, 73.23.2b