Abstract
We prove for a one-dimensional tight-binding Hamiltonian with only off-diagonal randomness that the state at the middle of the band is extended, regardless of the probability distribution of the hopping matrix elements and also derive a sum rule for the density of states. In particular, for the case where the probability distribution of the hopping matrix elements is a generalized Poisson distribution, we derive an expression for the localization length near the middle of the band. We also calculate the localization length for a chain of potential wells with randomly fluctuating depths, separated by regions of zero potential, the length of the latter being also random.
Original language | English (US) |
---|---|
Pages (from-to) | 4597-4601 |
Number of pages | 5 |
Journal | Physical Review B |
Volume | 13 |
Issue number | 10 |
DOIs | |
State | Published - 1976 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics