Aspects of Localisation in OffDiagonally Disordered Systems.
Abstract
Available from UMI in association with The British Library. Requires signed TDF. The method of numerical finitesize scaling implemented on strips and bars is extended to the case of offdiagonal disorder. Systems where the diagonal and offdiagonal matrix elements of the Hamiltonian were correlated with a Goldstone symmetry, and also where only the offdiagonal elements were random, were studied. The oneparameter scaling theory of localisation is confirmed for these systems with some idea of the limits of its validity, and this leads to a determination of the critical behaviour for the localisation length for a variety of energies, and of the critical disorder of the Anderson transition. The results thus obtained are consistent with other estimates on diagonally disordered systems, and in particular no transition is found in two dimensions. Results for the mobility edge, given by an extension of this method into the full energydisorder plane are also presented. Using scaling assumptions and the behaviour of the density of states, many features of the observed behaviour can be at least qualitatively explained. All of these investigations are improved by a correction to scaling analysis which removes many of the systematic errors in the simple finitesize scaling approach. For comparison, a method which combines the coherent potential approximation with an equivalence between potential wells and localised systems is used to calculate the mean free path 1, and ultimately extract the localisation length and mobility edge. The shortcomings of this method for offdiagonal systems are also discussed. The conductivity obtained using both finitesize scaling and potential well methods are also presented, and the results discussed along with a brief review of the current state of experiments on localisation.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT.......239S
 Keywords:

 Physics: General