Full counting statistics of conductance for disordered systems

Quantum transport is a stochastic process in nature. As a result, the conductance is fully characterized by its average value and fluctuations, i.e., characterized by full counting statistics (FCS). Since disorders are inevitable in nanoelectronic devices, it is important to understand how FCS behaves in disordered systems. The traditional approach dealing with fluctuations or cumulants of conductance uses diagrammatic perturbation expansion of the Green's function within coherent potential approximation (CPA), which is extremely complicated especially for high order cumulants. In this paper, we develop a theoretical formalism based on nonequilibrium Green's function by directly taking the disorder average on the generating function of FCS of conductance within CPA. This is done by mapping the problem into higher dimensions so that the functional dependence of generating a function on the Green's function becomes linear and the diagrammatic perturbation expansion is not needed anymore. Our theory is very simple and allows us to calculate cumulants of conductance at any desired order efficiently. As an application of our theory, we calculate the cumulants of conductance up to fifth order for disordered systems in the presence of Anderson and binary disorders. Our numerical results of cumulants of conductance show remarkable agreement with that obtained by the brute force calculation.