Proposal to measure the quasiparticle poisoning time of Majorana bound states

We propose a method of measuring the fermion parity lifetime of Majorana fermion modes due to quasiparticle poisoning. We model quasiparticle poisoning by coupling the Majorana modes to electron reservoirs, explicitly breaking parity conservation in the system. This poisoning broadens and shortens the resonance peak associated with Majorana modes. In a two-lead geometry, the poisoning decreases the correlation in current noise between the two leads from the maximal value characteristic of crossed Andreev reflection. The latter measurement allows for calculation of the poisoning rate even if the temperature is much higher than the resonance width.

Figure 1

Sketch of the experimental setup: Two tunneling current leads at the same bias, $V$, are connected to the ends of a grounded superconducting wire which supports Majorana bound states at its ends. The Majoranas are split by energy 2$E_M$. In addition, reservoirs are coupled to the Majorana bound states with matrix elements ${\delta }_L$ and ${\delta }_R$ to simulate the effect of quasiparticle tunneling.

Figure 2

The zero-temperature cross-correlation differential Fano factor, $F_{LR}$, for ${\Gamma }_t^L={\Gamma }_t^R=\Gamma$ and $E_M=100\Gamma$, without poisoning (dashed) and with poisoning rate ${\Gamma }_p^L={\Gamma }_p^R=\Gamma$ (solid).

Figure 3

The zero-temperature differential Fano factors for the left lead, $F_{LL}$, ${\Gamma }_t^L={\Gamma }_t^R=\Gamma$ and $E_M=100\Gamma$, without poisoning (dashed), and with poisoning rate ${\Gamma }_p^L={\Gamma }_p^R=\Gamma$ (solid).

Figure 4

The correlation differential Fano factor at fixed low bias $eV=10{\Gamma }_t<E_M=100{\Gamma }_t$ as a function of poisoning. We show curves at temperatures $T=0,4,8,12\Gamma$. Note that the curves for $T=0$ and $T=4{\Gamma }_t$ are nearly overlapping. Only when $k_{B}T\sim eV$ is the temperature effect strong.