Shot noise from which-path detection in a chiral Majorana interferometer

Abstract

We calculate the full counting statistics of charge transfer in a chiral Majorana interferometer - a setup where a Dirac mode (an electron-hole mode) is split into two Majorana modes that encircle a number of h/2e vortices in a topological superconductor. Without any coupling to the environment it is known that the low-energy charge transfer is deterministic: An electron is transferred either as an electron or as a hole, dependent on the parity of the vortex number. We show that a stochastic contribution appears if which-path information leaks into the environment, producing the shot noise of random 2e charge transfers with binomial statistics. The Fano factor (dimensionless ratio of shot noise power and conductance) increases without bound as the which-path detection probability tends to unity.

5 pages, 3 figures

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