# Fano Resonances in Majorana Bound States - Quantum Dot Hybrid Systems

## TL;DR

This paper investigates Fano resonances in conductance and noise in a quantum wire with Majorana bound states coupled to a quantum dot, revealing unique signatures that distinguish Majorana states from regular fermionic states.

## Contribution

It introduces an effective low-energy model and confirms its robustness using a Kitaev chain, providing new insights into Majorana bound state signatures in hybrid systems.

## Key findings

- Fano resonance line shapes depend on QD energy and MBS overlap.
- Asymmetry parameter changes sign with bias voltage tuning.
- Distinct coupling signatures differentiate MBS from fermionic bound states.

## Abstract

We consider a quantum wire, containing two Majorana bound states (MBS) at its ends that are coupled to a current lead on one side and to a quantum dot (QD) on the other side. Using the method of full counting statistics we calculate the conductance and the zero-frequency noise. Using an effective low-energy model, we analyze in detail the Andreev reflection probability as a function of the various system parameters and show that it exhibits a Fano resonance (FR) line shape in the case of a weakly coupled QD as a function of the QD energy level when the two MBS overlap. The asymmetry parameter changes sign as the bias voltage is tuned through the MBS overlap energy. The FR is mirrored as a function of the QD level energy as long as tunneling to the more distant MBS is negligible. However, if both MBS are coupled to the lead and the QD, the height as well as the asymmetry of the line shapes cease to respect this symmetry. These two exclusive cases uniquely distinguish the coupling to a MBS from the coupling to a fermionic bound state that is shared between the two MBS. We complement the analysis by employing a discretized one-dimensional p-wave superconductor (Kitaev chain) for the quantum wire and show that the features of the effective low-energy model are robust towards a more complete Hamiltonian and also persist at finite temperature.