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.