Numerical studies of conductance fluctuations in disordered metals

We compute conductance fluctuations in a variety of disordered mesoscopic systems through direct numerical evaluation of the Kubo-Greenwood formula for the conductivity.Our model Hamiltonian is quite different from the Anderson tight-binding Hamiltonian which has been most commonly used in studies of electronic structure and properties of disordered systems. It is reminiscent of the Kronig-Penney model in that $ delta$-like atomic potentials are specified by a single parameter.Our model structures range from substitutional binary alloys to topologically disordered "glasses", and include systems where the disorder is caused by random small displacements of atoms from their crystalline lattice positions.We test the universal nature of conductance fluctuations for the model with substitutional disorder. We study systems which are always larger than the elastic mean free path, but not always smaller than the localization length of the electron wavefunctions. In those systems where universality is expected, we confirm the ergodic theorem of Lee and Stone and observe the universal amplitudes of the fluctuations both in two-dimensional systems with and without a magnetic field, and in quasi-one-dimensional geometry.We have also performed the first studies of conductance fluctuations in strongly disordered systems and observed a universal relationship between the amplitude of the fluctuations and the value of the conductance itself: this relationship does not depend upon the nature of the disorder