Majorana zero modes choose Euler numbers as 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 and obtain complete information on current fluctuations through the dot. Using the Keldysh path-integral approach, we compute the cumulant generating function of the current. We first consider a spinless case and find that for the symmetric dot-lead couplings, the zero-frequency cumulants are independent of the microscopic parameters and exhibit a universal pattern described by Euler numbers. We then consider the spinful system and investigate the effect of both weak and strong Coulomb interactions. We show that cases with and without Majorana coupling exhibit qualitatively different full counting statistics of charge tunneling events despite the fact that differential linear conductance might have zero-bias features in both cases.