Quantum transport through a quantum dot side-coupled to a Majorana bound state pair in the presence of electron-phonon interaction

• Main Authors: Máthé, Levente, Sticlet, Doru, Zârbo, Liviu P
• Format: Journal Article
• Language: English
• Published: 22-04-2022
• Subjects: Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.2107.05410

Phys. Rev. B 105, 155409 (2022) We theoretically study quantum transport through a quantum dot coupled to
Majorana bound states confined at the ends of a topological superconducting
nanowire. The topological superconductor forms a loop and is threaded by a
tunable magnetic flux, which allows one to control the electron transport in
the system. In particular, we investigate phonon-assisted transport properties
in the device when the central quantum dot interacts with a single long-wave
optical phonon mode. We find that when the two Majorana bound states are
unhybridized, the zero-temperature linear conductance has a $2\pi$ periodicity
as a function of magnetic flux phase, independent of the electron-phonon
interaction, the quantum dot energy, or the finite values of dot-Majorana
couplings. For a finite overlap between the Majorana bound states, the linear
conductance periodicity generally changes to $4\pi$ either due to a finite
electron-phonon coupling strength, or a dot energy level that is tuned away
from the Fermi level. Additionally, the differential conductance periodicity
changes from $2\pi$ to $4\pi$ when the Majorana bound states hybridize and the
electron-phonon coupling is finite. Our results provide insight into transport
signatures expected in topological quantum computational platforms that
integrate quantum dots as a means for Majorana qubit readout. The energy
exchange with an environmental bath, here a single phonon mode, significantly
alters the current signatures expected from Majorana modes.