Full counting statistics of charge transport for disordered systerms

Abstract

In principle, quantum transport can be viewed as a stochastic process. Therefore, all order cumulants of the conductance are needed to give a fully description of the transport properties of the system. The full counting statistics (FCS) is a powerful method to compute arbitrary order of cumulants $\kappa_n$, since the cumulant can be easily obtained by taking derivative of the cumulant generating function (CGF). In fabrication processes of nano-devices, disorders will be unavoidable introduced into the system. The disorder effect may have a significant influence on the transport behaviour and thus it is important to study transport behaviours in disordered systems. Although the brute force approach can be used to compute any disorder averaged physical quantities, the huge number configurations are needed and this will be not acceptable in dealing with large systems. Several approaches have been put forward to compute disorder averaged cumulants of conductance $\langle \kappa_n \rangle$ within coherent potential approximation (CPA). However, these approaches will become extremely complicated and unpractical to implement when $n$ is large. In this thesis, a theoretical method are presented to compute disorder averaged cumulants $\langle \kappa_n \rangle$. In our method, the CGF has become linear dependent on Green's function and thus the disorder average can be performed within CPA method. Once the disorder averaged CGF is obtained, the averaged cumulant can be computed by taking derivatives of it and the complicated diagrammatic perturbation expansion can be avoid. This method offers an efficient way to compute arbitrary order cumulants of conductance. The numerical simulation has been performed to compute $\langle \kappa_n \rangle$ up to fifth order for Anderson and binary types disorder. The numerical results demonstrate the good performance of our FCS-CPA method from ballistic regime to diffusive regime.