Abstract
The one-dimensional self-similar alloys are presented to study electron properties of binary alloys intermediate between periodicity and randomness. The systems studied are represented by tight-binding Hamiltonians with self-similar diagonal potentials with self-similar atomic configurations. The Hamiltonian is exactly renormalized with the use of a decimation technique. Band structures and densities of states are calculated by recursion relations. It is shown that each band of the alloy with (,,...,) periods breaks up into m subbands when N becomes N+1 where m,N are integers. As N→∞, the density of states approaches a limit with an infinite number of very narrow bands which have self-similar structures, the total bandwidth goes to zero and all states are localized.
- Received 1 April 1985
DOI:https://doi.org/10.1103/PhysRevB.32.2049
©1985 American Physical Society