Multichannel decoherent transport.

C. J. CATTENA, R. A. BUSTOS-MARUN, H. M. PASTAWSKI

Salinas de Maragogi, Brasil.

Simposio; 20th Latin American Symposium on Solid State Physics (SLAFES XX), Salinas de Maragogi, Brasil.; 2011

In this work we present an extension of the minimal parametrization method of D?Amato and Pastawski model of incoherent transport, to multichannel electronic transport [1]. This model, which is based on the B ̈ttiker?s scattering formulation of incoherent transport [2], relies on theassumptions that: 1) Coupling the environment to a system in a Fermi?s golden rule is equivalent to add a fictitious lead to the system. 2) Due to charge conservation, the current through the fictitious leads must be zero. 3) In a non-interacting scheme, as the wave function of the returning electrons must have random phases, the sum of transmittances between different paths must be done classically, i.e. according to Kirchhoff?s current law [1]. The result of this reasoning is aeffective transmittance which includes all possible decoherent events that can be suffered by the passing electrons. This minimal parametrization and computationally cheap method (compared with explicit treatment of coupling with all phonon degrees of freedom for example) have showntheir worth in numerous works [3]. However, there are certain cases were it can not be applied in its original form, which gives only one effective transmittance. In this work we show that the effective transmittance between any given pair of physical leads isgiven by the decimation of the transmittance matrix that include all the fictitious and real leads. Moreover, we show how to take advantage of n-diagonal Hamiltonians in the calculation of all possible transmittance between system?s sites. Possible applications of this method are: electronic transport processes where some phonon degrees of freedom can?t be treated in a Fermi?s Golden Rule while others can, time dependent transport under ac bias using Floquet?s theory, and any general multichannel transport process where decoherence must be taken into account.[1] J. L. D?Amato and H. M. Pastawski, Phys. Rev. B 41, 7411 (1990).[2] M. Buttiker, Phys. Rev. B 32, 3020 (1986).[3] X. Q. Li and Y. Yan, Appl. Phys. Lett. 79, 2190 (2001); D. Nozaki, Y. Girard, and K. Yoshizawa, J. Phys. Chem. C 112, 17408 (2008); Juyeon Yi, Phys. Rev. B 77, 193109 (2008); C. J. Cattena, R. A. Bustos-Marun, and H. M. Pastawski, Phys. Rev. B 82, 144201 (2010).