Electronic states and transport properties in the Kronig–Penney model with correlated compositional and structural disorder

Abstract

We study the structure of the electronic states and the transport properties of a Kronig-Penney model with weak compositional and structural disorder. Using a perturbative approach we obtain an analytical expression for the localisation length which is valid for disorder with arbitrary correlations. We show how to generate disorder with self-and cross-correlations and we analyse both the known delocalisation effects of the long-range self-correlations and new effects produced by cross-correlations. We finally discuss how both kinds of correlations alter the transport properties in Kronig-Penney models of finite size.

Transmission in waveguides with compositional and structural disorder: experimental effects of disorder cross-correlations

“…As for cross-correlations, they can either enhance or reduce the opacity of the low-transmittivity intervals. Numerical studies confirmed these expectations [20]. They also showed that the effects of self-and cross-correlations can be detected in random samples of moderate size, as can be seen in figure 2, which represents the transmission coefficient T of a random Kronig-Penney model of N = 40 sites for a specific realization of the disorder.…”

“…The weak-disorder case is identified by the conditions [18][19][20] with n = a n+1 − a n representing the relative displacement of two contiguous barriers. If disorder is weak, one can obtain an analytical expression for the localization length l loc of the electronic states ψ of the model (1) [18][19][20]. Following the Hamiltonian map approach, one can show that, within the second-order approximation, the electronic states have an inverse localization length equal to…”

“…Since slabs of both types can have random widths, each structure is characterized not by one but by two random sequences which, in addition to self-correlations, can exhibit cross-correlations. Another model exhibiting two types of disorder is the aperiodic Kronig-Penney model with both compositional and structural disorder [18][19][20]. For this model, it was possible to work out a perturbative expression for the localization length of the quantum states valid for weak disorder with any kind of selfand cross-correlations [18].…”

Localisation and transport in bidimensional random models with separable Hamiltonians

“…[52]). An analytical expression for the inverse localisation length (22) was derived for the case of weak disorder in [53][54][55]. As shown in [53], disorder can be considered weak provided that…”

“…It is possible to construct sequences of self-and cross-correlated random variables u n and Δ n such that the corresponding power spectra(25) vanish over pre-defined intervals. A way to produce such sequences was presented in [55]; for the sake of completeness, we outline the main steps in appendix B.…”