Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and theory nonlinear response yet be fully developed. Here, we extend nonlinear-response regime. We show that while linear conductance is directly related transmission probability, given by derivatives with respect energy. This sensitivity energy shown produce unique transport phenomena mesoscopic systems including disordered topological materials. By way illustration, investigate chains identify their universal behavior according symmetry. In particular, find large singular for zero modes, Majorana modes in superconductors. also critical around mobility edges due Anderson transitions. Moreover, study graphene as prime example materials featuring quantum anomaly. Furthermore, considering geometry electronic wave functions, develop Hall effect. establish new connection between nonequilibrium fluctuations. discuss influence disorder localization on Our work opens avenue physics beyond