Parametric Glassiness in Graphene-based Electronic Lévy Glass

Abstract

Complex disordered conductors can display highly structured and parameter-sensitive transport even in the absence of a thermodynamically stable glass phase. Overlap distributions originally developed for replica symmetry breaking (RSB) provide a useful diagnostic of this organization, provided that their interpretation is distinguished from the equilibrium Parisi construction. In this study, we report RSB-like overlap phenomenology and parametric mesoscopic glassiness in a graphene-based electronic Lévy glass, a device that mimics optical phenomena via electronic processes. By tuning the Fermi energy, we can control the number of propagating wave modes and observe reentrant changes from narrowly centered to broad or bimodal overlap distributions. The phenomenology is observed in both graphene-based and conventional two-dimensional electron-gas electronic Lévy glasses, indicating its generality. Sample-resolved overlap distributions show that the effect is intrinsic to each disorder landscape, whereas the normalized conductance variance shows that the growth of the absolute variance is mainly caused by the increasing mean conductance. We therefore interpret the overlap as a measure of correlation among hierarchically organized transport pathways and the reentrant behavior as evidence of pinning, parameter-induced reorganizations, and mesoscopic chaos in coherent transport.