Abstract
The effects of a finite value of the Green-function damping parameter η on the Kubo-Greenwood conductance are treated exactly in several lattice models. Simple closed-form formulas for the conductance of a finite segment of length L of an infinite one-dimensional (1D) chain are extended to give conductance expressions for quasi-1D ribbons, for quantum wires of triangular cross section, and for 2D square and 3D simple-cubic lattices. For the 1D chain, the conductance at fixed energy for finite η decays away precisely exponentially as a function of L. In other cases, the L dependence is not exponential. Expressions given here for the length, energy, and damping dependence of the conductance of these lattices are important for assessing the effects of disorder or of varying model geometry whenever Green functions are used in the calculation.
- Received 3 June 1991
DOI:https://doi.org/10.1103/PhysRevB.45.1770
©1992 American Physical Society