Superdielectrics: Disorder-induced perfect screening in insulators

We study the relationship between the quantities that encode the insulating properties of matter: the ground-state quantum metric, the average localization length, and the electric susceptibility. By examining the one-dimensional Anderson insulator model and the Su-Schrieffer-Heeger chain with chiral disorder, we demonstrate that the former two measures are proportional in one-dimensional systems near criticality, and both are determined by the properties of the hybridized localized states around the Fermi energy. We employ these insights to demonstrate that the behavior of the electric susceptibility is drastically different in the bond-disordered SSH chain, with the possibility that it may diverge even when the localization length and the quantum metric remain finite. This divergence, caused by the proliferation of impurity resonances at a particular energy, leads to a novel regime that exhibits mixed characteristics of metals and insulators. We term this regime superdielectric: an insulating state characterized by a finite quantum metric and divergent static electric susceptibility, which implies perfect screening in the absence of the dc conductivity. We demonstrate that the superdielectric phase also emerges in higher-dimensional materials, such as graphene with vacancies and Kekul\'e bond distortion.