Fano resonances in Majorana bound states–quantum dot hybrid systems

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.

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires

“…5. We can associate these additional levels with QD-like bound states arising in the attractive regions of the induced potential that anticross with the Majorana levels when their energies are on resonance [35–36 43–44]. …”

“…For the shown values of V Z , only the central part of the wire is in the topological regime (), corresponding to an effectively shorter Majorana wire, whereas the outer parts are trivial (), corresponding to two effective QDs attached to it. Specific details of how QD levels interact with Majorana nanowire ones can be found in [35–36 43–45]. …”

Transport signatures of Majorana bound states in superconducting hybrid structures

“…In this section, we want to report on our findings already summarized in Ref. [62], in which we considered a setup where two MBSs are contacted by a normal conducting lead on one side and a quantum dot on the other side. By including not only a coupling to the closest MBS we can tune the system between Majorana-like (only coupling to one MBS) and Dirac-like (coupling to both MBSs with the same amplitude) couplings.…”

“…The details of these calculations can be found in Refs. [62,146]. At zero temperature, the CGF is given by…”

“…Also, the current noise and the Fano factor can be readily obtained with this formalism [62]. The differential conductance has local maxima and minima which we call resonances and antiresonances.…”