Finite-temperature conductance in one dimension

Abstract

The Landauer formula and its finite-temperature extension are used to obtain the temperature-dependent conductance G(T) of a one-dimensional system. Large resonant structure in G as a function of Fermi energy, a manifestation of a zero-temperature quantum-mechanical eigenstate tunneling phenomenon, persists to finite temperature. The resulting statistical properties of G, lnG, R1G, and lnR are studied. At intermediate temperatures, the mean dependence of lnG on T follows the one-dimensional T-12 Mott law, with lnG displaying large nonthermodynamic fluctuations about this mean behavior. We verify these observations with numerical simulations on a one-dimensional Kronig-Penney model. The mean Mott-like behavior is reproduced, and the relationship between the Mott temperature T0 and the localization length L0 is verified. At higher temperature we show that the energy dependence of L0 or of the density of states s can cause G(T) to deviate from the T-12 behavior, and we derive expressions for the modified temperature dependence of G. © 1984 The American Physical Society.