Experimental observation of the mobility edge in a waveguide with correlated disorder

Abstract

The tight-binding model with correlated disorder introduced by Izrailev and Krokhin [PRL 82, 4062 (1999)] has been extended to the Kronig-Penney model. The results of the calculations have been compared with microwave transmission spectra through a single-mode waveguide with inserted correlated scatterers. All predicted bands and mobility edges have been found in the experiment, thus demonstrating that any wanted combination of transparent and non-transparent frequency intervals can be realized experimentally by introducing appropriate correlations between scatterers.PACS numbers: 72.15. Rn, 72.20.Ee, 73.20.Jc Starting from the pioneering paper by Anderson [1], a lot of progress has been achieved in the theoretical study of 1D tight-binding models. This model includes a wide range of different physical situations lying in between two limit cases: ideal periodic lattices where all states are extended, and completely random lattices where any state is exponentially localized. Specific interest has been paid to the so-called pseudo-random (or deterministic aperiodic) potentials which demonstrate either localization or delocalization, depending on their parameters [2][3][4]. A widely used model is described by the Harper equation with the site potential V n = ǫ cos(2παn). For α irrational, the incommensurability of the potential gives rise to a localization-delocalization transition (for all states) when the amplitude ǫ passes through the critical value ǫ cr = 2, see e.g., Ref. [5]. For fixed ǫ the energy spectrum of the Harper equation exhibits the famous Hofstadter butterfly [6] when α scans the interval [0, 1]. This rather exotic spectrum was recently observed experimentally [7] by making use of the equivalence of the Harper equation and the wave equation in a single-mode electromagnetic waveguide with point-like scatterers.For a long time a coexistence of localized and extended states in the spectrum of eigenenergies of 1D random potentials was considered to be impossible. However, it was shown in Refs. [8,9] that a discrete set of delocalized states appears if short-range correlations are introduced in a random potential. This is done by repeating twice each value of site potential (dimer model). Recently discrete extended states have been observed in the experiment with GaAs-AlGaAs random superlattices [10].A general case of 1D potential in tight-binding approximation with arbitrary correlations was considered in Ref. [11]. A direct relation between the pair correlation function and the localization length has been derived. This relation shows that the mobility edge does exist in 1D geometry. A few examples of potentials with correlated disorder were given. All these potentials necessarily contain the long-range correlations which thus give rise to a continuum set of delocalized states and to mobility edge.

Resistance of a 1D random chain: Hamiltonian version of the transfer matrix approach

“…These results have been also extended to a single-mode waveguide with random surface profiles [8]. The predictions of the theory [6] have been verified experimentally [9], when studying transport properties of a singlemode electromagnetic waveguide with point-like scatterers. The latter were intentionally inserted into the waveguide in a way to provide a random potential with slowly decaying binary correlator.…”

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

“…In other words, controllable long-range correlations facilitate the observation of the metal-insulator transition. 30 Therefore, transparency windows can be observed in the transmission line, if one fabricates either a transmission line with a locally changeable external current and apply j n with desirable correlations, or a junction array with fixed appropriate correlations of J c n . There exist several methods of generating partially random sequences with desirable correlation functions.…”

Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential

“…[9] Since late eighties, however, it has been realized that extended states may survive on 1D systems if the disorder distribution is correlated. [10,11,12,13,14,17,15,16,18] Thus, a short-range correlated disorder was found to stabilize the extended states at special resonance energies. In the thermodynamic limit, such extended states form a set of null measure in the density of states, [10,11,12,13,14] implying the absence of mobility edges in these systems.…”

“…Theoretical predictions of localization suppression on 1D geometries, due to correlations of the disorder distribution, were confirmed experimentally in semiconductor superlattices with intentional correlated disorder, [17] as well as in single-mode waveguides with correlated scatterers. [18] Among 1D models with extended states, aperiodic Anderson models [19] with an incommensurate site potential represent a class of particular interest. These models have been extensively investigated in the literature, [20,21,22,19,23] and the localized or extended nature of the eigenstates has been related to general characteristics of aperiodic site-energy distributions.…”