Majorana signatures in an asymmetrically coupled quantum dot--topological superconducting nanowire junction

Abstract

We present a theoretical study of the quantum transport through a nanoscale system in which a central quantum dot (QD) is coupled asymmetrically to normal leads and to two Majorana bound states (MBSs) localized at the ends of a topological superconducting nanowire threaded by a tunable magnetic flux. The effects of the leads--QD coupling asymmetry parameter $\alpha$ and the bias voltage asymmetry parameter $q$ on the system's linear conductance are considered for the case of unhybridized and hybridized MBSs. In the zero-temperature limit, for unhybridized MBSs the system's linear conductance is finite only when the magnetic flux phase $\phi = (2n+1)\pi$ ($n\in\mathbb{Z}$) and it scales as $\mathcal{G}=2q\alpha e^2/[h(\alpha+1)]$, while for hybridized MBSs it presents a complicated dependence on the system's parameters. At finite temperature, for unhybridized MBSs, the system's linear conductance oscillates as a function of the magnetic flux phase $\phi$ with a period of $2\pi$, and the position of the linear conductance maxima can be shifted from $\phi=2n\pi$ to $\phi=(2n+1)\pi$ by simply varying the value of the bias voltage asymmetry parameter $q$. For hybridized MBSs, the conductance exhibits a similar behavior when the energy level of the central QD, $\varepsilon_d$, is tuned at the leads' Fermi level ($\varepsilon_d=\varepsilon_F$), although when $\varepsilon_d\neq\varepsilon_F$ the oscillation period changes to $4\pi$, and the position of the linear conductance maxima depends on the actual value of $\varepsilon_d$ and other parameters in the system. Our results highlight the experimental importance of the leads-QD and bias voltage asymmetry parameters, which are often present in realistic experimental setups, and can strongly affect the identification and observation of MBSs transport signatures.