Quantum transport in dynamically disordered continuum tight binding systems

Abstract

We consider the continuum limit of three distinct models describing tightly bound electron systems in one dimension. The first model is the usual tight binding hamiltonian for monatomic lattices with nearest-neighbour hopping between sites. The second model describes a two-subband tight binding system involving two different atoms per unit cell. Finally, the third model represents a monatomic system with two energy levels per atomic site and different nearest-neighbour hopping parameters for hopping between equivalent and non-equivalent levels. The continuum limits of these models result in field-theoretic hamiltonians showing similarities with the Dirac hamiltonian. Assuming the different types of site energies to be dynamically disordered with gaussian whitenoise spectra, we calculate exactly the quantum mechanical mean square displacement <x ²(t)>. Due to the use of Novikov's theorem for the evaluation of configuration averages our analysis for the two-band models is restricted to the degenerate case, where the average positions of the two types of atomic levels coincide. Fort→∞ we find coherent motion, <x ²(t)>∼t ², for the one-band model and disorder induced diffusive contributions for the two-band models. However, for the two-level atomic model the diffusive term is dominated by at ²-term describing coherent hopping between equivalent levels. These findings are discussed in relation to previous results for both discrete and continuum models.