Electronic states in a one-dimensional system with incommensurate lattice potentials

The authors present some new and interesting results on the localisation of electronic states in a one-dimensional lattice with an incommensurate lattice potential. The system studied is represented by a tight-binding Hamiltonian with diagonal elements given by V₀ cos(qn). V₀ is the modulation strength and q is the wavenumber. They introduce the concept of quasilocalisation to clarify inconsistencies in previous work on the existence of mobility edges. Their technique allows very precise calculation of the resolvent operator without the problem of numerical instability. Thus they are able to present accurate results for the density of states even when the widths of the energy bands are extremely small.