Universal conductance fluctuation of mesoscopic systems in the metal-insulator crossover regime

Abstract

We report a theoretical investigation on conductance fluctuation of mesoscopic systems. Extensive numerical simulations on quasi-one-dimensional, two-dimensional, and quantum dot systems with different symmetries [circular orthogonal ensemble, circular unitary ensemble (CUE), and circular symplectic ensemble (CSE)] indicate that the conductance fluctuation can reach a universal value in the crossover regime for systems with CUE and CSE symmetries. The conductance distribution is found to be a universal function from diffusive to localized regimes that depends only on the average conductance, dimensionality, and symmetry of the system. The numerical solution of DMPK equation agrees with our result in quasi-one dimension. Our numerical results in two dimensions suggest that this universal conductance fluctuation is related to the metal-insulator transition. In the localized regime with average conductance $⟨G⟩<0.3$, the conductance distribution seems to be superuniversal independent of dimensionality and symmetry.