Blackman-Esterling-Berk based FCS-CPA method in off-diagonal disorder system

Abstract

In real world, the unexpected impurities or intentional doping are universally existed in nano electronic devices, which strongly influence the quantum transport behaviors in mesoscopic systems. As a result, the quality of fabricated devices could be unstable. On the other hand, the transport properties in quantum systems can be affected by disorder in a fundamental way. For instance, the universal conductance fluctuation in disordered systems is one of the hallmarks of mesoscopic physics. It’s important to study and control the transport behaviours in disorder systems. The evaluation of electronic transport properties focuses on different transport quantities considering the stochastic nature. These quantities are random variables and can be characterized by the distribution function. In full counting statistics theory (FCS), full information about desired quantities can be derived by simply taking derivatives on the cumulant generating function (CGF). The expression of these interested transport quantities in FCS can be derived from non-equilibrium Green’s function (NEGF) method, which is widely studied. A traditional brute force (BF) method to handle the disorder problem is to generate a large ensemble of disorder distribution configurations and directly calculate the desired statistical quantities. However, this method is time consuming and has its application is restricted. To mitigate the problem, the coherent potential approximation (CPA) method was proposed long time ago and widely used to approximate the transport quantities in the presence of disorder. Previous work adopts CPA and FCS to approximate the CGF in diagonal disorder system. However, in real situation,impurities may influence the coupling energy between different atoms, leading to the off-diagonal disorder. The previous FCS-CPA method would face trouble when solving off-diagonal disorder problem. In this thesis, we extend the FCS-CPA method to solve off-diagonal disorder problem. We use Blackman-Esterling-Berk formalism to transform the Green’s function into augmented dimension space, and eliminate the randomness in off diagonal part. The modified CGF can then be approximated by the CPA method. We perform the numerical experiments using the BEB based FCS-CPA to calculate serval important transport quantities with both diagonal and off diagonal disorder systems and compare the results with what is calculated from BF method. The comparisons show that our method could reach acceptable accuracy without large computational cost.