The Matching Conditions for the Distribution Functions of Boltzmann Equation in Nonequilibrium Transport

Zhengchuan Wang

Department of Physics, Graduate School of the Chinese Academy of Sciences, Beijing, China.

DOI: 10.4236/jmp.2013.41004                

Abstract

Based on the equation of motion in nonequilibrium Green function formalism, the matching conditions for the distribution functions of Boltzmann equation at interfaces of metallic multilayers are investigated in the nonequlibrium transport procedure. We also explore the matching conditions when the current-induced spin accumulation is accounted for, the contribution of coulomb interaction due to accumulated electrons is included. In order to study the matching conditions in the position space, we generalize the tunneling Hamiltonian to the formalism in position space, the matching conditions in this case is then obtained, which is convenient for us to match the usual distribution function of Boltzmann equation.

Keywords

Matching Conditions; Distribution Funtion; Boltzmann Equation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. E. Camley and J. Barnas, “Theory of Giant Magnetoresistance Effects in Magnetic Layered Structures with Antiferromagnetic Coupling,” Physical Review Letters, Vol. 63, No. 6, 1989, pp. 664-667. doi:10.1103/PhysRevLett.63.664
[2]	J. Barnas, A. Fuss, R. E. Camley, P. Grǔnberg and W. Zinn, “Novel Magnetoresistance Effect in Layered Magnetic Structures: Theory and Experiment,” Physical Review B, Vol. 42, No. 13, 1990, pp. 8110-8120. doi:10.1103/PhysRevB.42.8110
[3]	T. Valet and A. Fert, “Theory of the Perpendicular Magnetoresistance in Magnetic Multilayers,” Physical Review B, Vol. 48, No. 10, 1993, pp. 7099-7113. doi:10.1103/PhysRevB.48.7099
[4]	S. Zhang and P. M. Levy, “Interplay of the Specular and Diffuse Scattering at interfaces of Magnetic Multilayers,” Physical Review B, Vol. 57, No. 9, 1998, pp. 5336-5339. doi:10.1103/PhysRevB.57.5336
[5]	A. Shapiro and P. M. Levy, “Resistance across an Interface, and That Measured Far from It,” Physical Review B, Vol. 63, No. 1, 2000, Article ID: 014419. doi:10.1103/PhysRevB.63.014419
[6]	M. Johnson and R. H. Silsbee, “Spin-Injection Experiment,” Physical Review Letters, Vol. 37, No. 10, pp. 5326-5335. doi:10.1103/PhysRevB.37.5326
[7]	P. C. van Son, H. van Kempen and P. Wyder, “Boundary Resistance of the Ferromagnetic-Nonferromagnetic Metal Interface,” Physical Review Letters, Vol. 58, No. 21, 1987, pp. 2271-2273. doi:10.1103/PhysRevLett.58.2271
[8]	G. E. W. Bauer, Y. Tserkovnyak, D. Huertas-Hernando and A. Brataas, Advances in Solid State Physics, Vol. 43, 2003, p. 383.
[9]	J. Zhang and P. M. Levy, “Layer by Layer Approach to Transport in Noncollinear Magnetic Structures,” Physical Review B, Vol. 71, No. 18, 2005, Article ID: 184426. doi:10.1103/PhysRevB.71.184426
[10]	P. M. Levy and J. Zhang, “Erratum: Current-Induced Spin Flip Scattering at Interfaces in Noncollinear Magnetic Multilayers [Phys. Rev. B 70, 132406 (2004)],” Physical Review B, Vol. 73, No. 6, 2006, Article ID: 069901. doi:10.1103/PhysRevB.73.069901
[11]	H. Haug and A. P. Jauho, “Quantum Kinetics in Transport and Optics of Semiconductor,” Springer-Verlag Berlin Heidelberg, New York, 1996, p. 160.
[12]	L. P. Kadanoff and G. Baym, “Quantum Statistical Mechanics,” Benjamin, New York, 1962.
[13]	G. D. Mahan, “Quantum Transport Equation for Electric and Magnetic Fields,” Physics Reports, Vol. 145, No. 5, 1987, pp. 251-318. doi:10.1016/0370-1573(87)90004-4
[14]	J. Rammer and H. Smith, “Quantum Field-Theoretical Methods in Transport Theory of Metals,” Review of Modern Physics, Vol. 58, No. 2, 1986, pp. 323-359. doi:10.1103/RevModPhys.58.323