Monte Carlo study of single-barrier structure based on exclusion model full counting statistics

Different from the usual full counting statistics theoretical work that focuses on the higher order cumulants computation by using cumulant generating function in electrical structures, Monte Carlo simulation of single-barrier structure is performed to obtain time series for two types of widely applicable exclusion models, counter-flows model, and tunnel model. With high-order spectrum analysis of Matlab, the validation of Monte Carlo methods is shown through the extracted first four cumulants from the time series, which are in agreement with those from cumulant generating function. After the comparison between the counter-flows model and the tunnel model in a single barrier structure, it is found that the essential difference between them consists in the strictly holding of Pauli principle in the former and in the statistical consideration of Pauli principle in the latter.

Topological quantum-phase coherence in full counting statistics of transport electrons with two-body interaction

The full counting statistics of electron transport through two parallel quantum dots with antiparallel magnetic fluxes is investigated as a probe to detect the topological quantum-phase coherence （TQPC）, which results in the characteristic oscillation of the zero-frequency cumulants including the shot noise and skewness. We show explicitly the phase transition of cumulant spectrum-patterns induced by the topology change of electron path-loops while the pattern period, which depends only on the topology （or Chern number）, is robust against the variation of Coulomb interaction and interdot coupling strengths. Most importantly we report for the first time on a new type of TQPC, which is generated by the two- particle interaction and does not exist in the single-particle wave function interference. Moreover, the accurately quantized peaks of Fano-factor spectrum, which characterize the super- and sub-Poissonian shot noises, are of fundamental importance in technical applications similar to the superconducting quantum interference device.

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation(CPA)within full counting statistics(FCS)formalism is shown to be a suitable method to investigate average electric conductance,shot noise as well as higher order cumulants in disordered systems.We develop a similar FCS-CPA formalism for phonon transport through disordered systems.As a byproduct,we derive relations among coefficients of different phonon current cumulants.We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders.For binary disorders as well as Anderson disorders,we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method.The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio.Collective features of phonon current cumulants are also revealed.

A theoretical extraction scheme of transport information based on exclusion models

In order to explore how to extract more transport information from current fluctuation, a theoretical extraction scheme is presented in a single barrier structure based on exclusion models, which include counter-flows model and tunnel model. The first four cumulants of these two exclusion models are computed in a single barrier structure, and their characteristics are obtained. A scheme with the help of the first three cumulants is devised to check a transport process to follow the counter-flows model, the tunnel model or neither of them. Time series generated by Monte Carlo techniques is adopted to validate the abstraction procedure, and the result is reasonable.