Conductance calculations for quantum wires and interfaces: Mode matching and Green’s functions

Abstract

Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green function techniques and an expression first derived by Caroli. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated originally by Ando, is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived and it is shown how all the Green function results can be derived from the mode matching technique. We illustrate this for a simple model which can be studied analytically, and for an Fe|vacuum|Fe tunnel junction which we study using first-principles calculations.

Zigzag nanoribbons of two-dimensional silicene-like crystals: magnetic, topological and thermoelectric properties

“…47 The total transmission, T tot (E), as a function of electron energy E is then defined as the sum of transmissions for all incident Bloch waves for a given wave-number k, and is a piece-wise constant function equal to the number of energy bands for a given energy E. In turn, the spin transmission, T spin , is equal to the sum of the mean values of the Pauli operatorσ z . More detailed description of the transmission calculation is presented in Ref.…”

Thermal electric effects in Fe|GaAs|Fe tunnel junctions

“…The self-consistent calculations are performed with the tight-binding linear muffin-tin orbital [32][33][34][35] (TB-LMTO) surface Green's function method 36,37 with coherent potential approximation 38,39 to deal with the disorder or impurities. The transport properties are evaluated by the Keldysh nonequilibrium Green function including nonequilibrium vertex correction.…”

Of interfaces and spin transport across nanoscale layers

“…In matrix form this expression reads 18) with obvious definitions for the matrices. Using straight-forward, but somewhat lengthy, algebra, one can rewrite this expression in terms of Green's function matrices [37] 19) where G r S , G a S are the matrix blocks pertaining to the scattering region, Fig 2.1, of the retarded, respectively the advanced (independent-particle) Green function G r,a =…”

“…is the retarded (advanced) Green's function matrix block connecting the right and left leads via the scattering region, and Γ σ R(L) = −2ImΣ σ R(L) , with Σ σ R(L) the self-energy matrix connecting the scattering region to the right (left) lead [39,37].…”

“…sponding advanced Green's function matrix block, and Γ σ R(L) = −2ImΣ σ R(L) , with Σ σ R(L) the self-energy matrix connecting the quantum conductor to the ideal right (left) lead [36,39,37].…”