Majorana zero modes choose Euler numbers - revealed by full counting statistics

We study transport properties of a quantum dot coupled to a Majorana zero mode and two normal leads. We investigate the full counting statistics of charge tunneling events which allows one to extract complete information about current fluctuations. Using a Keldysh path-integral approach, we compute the cumulant generating function. We first consider a noninteracting spinless regime, and find that for the symmetric dot-lead couplings, the zero-frequency cumulants exhibit a universal pattern of Euler numbers, independent of the microscopic parameters. For a spinful case, the Coulomb interaction effects are discussed for both strong interaction (single-electron occupancy regime) and weak interactions (perturbative regime). Compared to the case without Majorana coupling, we show that, while the tunneling conductance might exhibit zero-bias anomaly, the full counting statistics is qualitatively different in the presence of the Majorana coupling.