Phase-controlled quantum transport signatures in a quantum dot-Majorana hybrid ring system

TL;DR

This work addresses identifying Majorana bound state signatures in a quantum-dot–topological-superconducting-nanowire ring threaded by magnetic flux. It employs the dissipaton equation-of-motion (DEOM) method to model phase-controlled transport, treating normal tunneling and anomalous tunneling channels whose interference is tuned by the flux phase φ through the couplings (1+e^{iφ}) and (1−e^{iφ}). Key findings include a π-periodic conductance when $ε_D ε_M=0$ and a 2π-periodic response otherwise, a zero-bias peak at φ = (2m+1)π/2 under balanced NT/AT, and a distinctive shot-noise landscape featuring a giant Fano factor at zero bias that decays to Poissonian statistics with increasing bias; these signatures are thermally sensitive and provide supplementary criteria for MBS detection. Overall, the results illuminate how flux-controlled interference in a QD–MBS ring reveals robust transport and noise features that can aid experimental identification of Majorana states in hybrid mesoscopic systems.

Abstract

We investigate the quantum transport in a hybrid ring system consisting of a quantum dot (QD) coupled to two Majorana bound states (MBSs) hosted in a topological superconducting nanowire, threaded by a magnetic flux. Utilizing the dissipaton equation-of-motion approach, we demonstrate that the differential conductance shows periodic behavior and its periodicity depends on both the QD energy level and the MBS overlapping. A zero-bias peak (ZBP) emerges as a result of the balance between normal and anomalous tunneling processes, associated with the presence of a single MBS. Beyond the phase-dependent periodic behavior, the shot noise exhibits voltage-dependent transitions between sub-Poissonian ($F = 0.5$), Poissonian ($F = 1$), and super-Poissonian ($F > 1$) regimes. Strikingly, we find a giant Fano factor ($F\gg1$) emerging at the balance point, accompanied by a peak in the shot noise. This distinctive feature may serve as a supplementary signature for MBS detection. However, both ZBP in the differential conductance and shot noise peak are degraded by thermal effects.

Figures (4)

• Figure 1: Schematic diagram for the transport through the QD-wire hybrid ring system. The QD is contacted by the two electron reservoirs under the bias voltage ($V=\mu_{\hbox{\tiny L}}-\mu_{\hbox{\tiny R}}$) with the tunneling rates $\Gamma_{\rm L}$ and $\Gamma_{\rm R}$. It is further side coupled to the two Majora modes ($\gamma_1$ and $\gamma_2$) at the two ends of a 1D topological superconductor nanowire with the coupling coefficients $\lambda_1$ and $\lambda_2$, respectively. $\Phi$ is the magnetic flux through the loop.
• Figure 2: Differential conductance $G$ as a function of bias voltage tuned by the flux phase $\phi$ for different $\varepsilon_{\hbox{\tiny D}}$ and $\varepsilon_{\hbox{\tiny M}}$. The conductance $G$ exhibits a period of $\pi$ when $\varepsilon_{\hbox{\tiny D}}\varepsilon_{\hbox{\tiny M}}=0$, whereas its period is $2\pi$ when $\varepsilon_{\hbox{\tiny D}}\varepsilon_{\hbox{\tiny M}}\neq0$. We classify the phase-dependent behavior into four cases: (ia) $\phi=2m\pi$, (ib) $\phi=(2m+1)\pi$, (ii) $\phi= (2m+1)\pi/2$, and (iii) other phase values.
• Figure 3: Physical quantities as functions of the phase $\phi$. (a) Resonance energy positions $E_j$ calculated using Eq. (\ref{['G00']}). (b) Shot noise (solid line) and steady-state current (dashed line) under different bias voltages. (c) Fano factor $F=S/\bar{I}$. (d) Peak characteristics of the shot noise (solid line) and steady-state current (dashed line) at low bias voltages.
• Figure 4: Differential conductance $G$ as a function of bias voltage for $\phi=0.5\pi$ and $\varepsilon_{\hbox{\tiny D}}=\varepsilon_{\hbox{\tiny M}}=0$. The evaluations are based on QME approach (black solid-line) given by the analytical expression Eq. (\ref{['G00']}) and exact DEOM theory (red dash-line) with (a) $\Gamma= k_{\hbox{\tiny B}}T=0.1$, (b) $\Gamma=0.1$ and $k_{\hbox{\tiny B}}T=0.2$, (c) $\Gamma=0.05$ and $k_{\hbox{\tiny B}}T=0.1$, and (d) $\Gamma=0.05$ and $k_{\hbox{\tiny B}}T=0.2$.