Subtle leakage of a Majorana mode into a quantum dot

TL;DR

This paper demonstrates that Majorana modes in a topological superconductor can leak into a quantum dot, causing a conductance signature that can be used to detect Majorana states even when the dot level is off-resonance.

Contribution

It reveals a unique Majorana-induced pinning of the quantum dot level at the Fermi energy, leading to a distinctive conductance signature for Majorana detection.

Findings

Majorana mode leaks into the quantum dot, pinning its level to the Fermi energy.

Conductance of e^2/2h observed even when the dot level is off-resonance.

Pinning effect is specific to Majorana modes, not ordinary fermionic states.

Abstract

We investigate quantum transport through a quantum dot connected to source and drain leads and side-coupled to a topological superconducting nanowire (Kitaev chain) sustaining Majorana end modes. Using a recursive Green's function approach, we determine the local density of states (LDOS) of the system and find that the end Majorana mode of the wire leaks into the dot thus emerging as a unique dot level {\it pinned} to the Fermi energy $\varepsilon_F$ of the leads. Surprisingly, this resonance pinning, resembling in this sense a "Kondo resonance", occurs even when the gate-controlled dot level $\varepsilon_\text{dot}(V_g)$ is far above or far below $\varepsilon_F$. The calculated conductance $G$ of the dot exhibits an unambiguous signature for the Majorana end mode of the wire: in essence, an off-resonance dot [$\varepsilon_\text{dot}(V_g)\neq \varepsilon_F$], which should have $G=0$, shows instead a conductance $e^2/2h$ over a wide range of $V_g$, due to this pinned dot mode. Interestingly, this pinning effect only occurs when the dot level is coupled to a Majorana mode; ordinary fermionic modes (e.g., disorder) in the wire simply split and broaden (if a continuum) the dot level. We discuss experimental scenarios to probe Majorana modes in wires via these leaked/pinned dot modes.