Coulomb interaction unlocks Majorana-mediated electron teleportation between Quantum dots

Abstract

We investigate quantum transport in a hybrid system composed of two quantum dots (QDs) coupled through a pair of spatially separated Majorana zero modes (MZMs) with negligible coupling energy. We focus on nonlocal correlations mediated by the MZMs, particularly the role of Coulomb interaction U between the QDs and the Majorana wire. Using the numerically exact fermionic dissipation equation of motion (DEOM) method, we compute both the transient current and the current-current cross-correlation noise spectrum. In the non-interacting case (U=0), destructive interference between the degenerate normal tunneling and anomalous tunneling channels suppresses electron teleportation between the dots. Introducing a finite Coulomb interaction $U$ lifts this channel degeneracy, enabling strong nonlocal correlations and inter-dot electron teleportation. This effect manifests as a robust signal in the cross-correlation noise spectrum, which is significantly stronger than that induced by a finite Majorana coupling energy $\varepsilon_{M}$. Our findings propose Coulomb interaction as an efficient and experimentally accessible control parameter for generating and detecting Majorana-mediated nonlocal transport in the topologically relevant long-wire limit ($\varepsilon_{M}\rightarrow0$).

Figures (5)

• Figure 1: Schematic of the transport setup for a hybrid quantum dot-Majora zero mode (QD-MZM) system. Two QDs are coupled to a pair of Majorana modes ($\gamma_1$ and $\gamma_2$), located at the ends of a superconducting nanowire, with coupling strengths $\lambda_1$ and $\lambda_2$, respectively. Each QD is contacted by an electron reservoirs via tunneling amplitudes $t_{\hbox{\tiny L}}$ and $t_{\hbox{\tiny R}}$.
• Figure 2: Coherent electron transitions between the states within the odd-parity subspace (a) and the even-parity subspace (b). The dynamics in each subspace are governed by the Hamiltonian $H_-$ [Eq. (\ref{['Hodd']})] and $H_+$ [Eq. (\ref{['Heven']})], respectively. Both involve two distinct tunneling process: normal tunneling (NT) via the electron channel $\varepsilon_{\hbox{\tiny M}}$ and anomalous tunneling (AT) via the hole channel $-\varepsilon_{\hbox{\tiny M}}$.
• Figure 3: The time evolution of the occupation probability in the right dot $P_2(t)$ for (a) various $\lambda_1$ with $U=0.5$ and (b) various $U$ for $\lambda_1=0.5$. The initial state is $|110\rangle$ with $P_{110}(0)=1$.
• Figure 4: The time evolution of the occupation probability in the right dot $P_2(t)$, and the transport current through the right electrode $I_R(t)$. (a) For viarious $\lambda_1$ with $U=0.5$; (b) For various $U$ for $\lambda_1=0.5$. The initial state is $|110\rangle$ with $P_{110}(0)=1$.
• Figure 5: The cross-correlation noise spectrum ${\rm Re}[{S_{\hbox{\tiny L}\hbox{\tiny R}}(\omega)}]$ (in units of $e\lambda_2/\hbar$). In the up panels, we consider $\varepsilon_{\hbox{\tiny M}}=0$ for (a) different Coulomb interaction $U$ with $\mu_{\hbox{\tiny L}}=\mu_{\hbox{\tiny R}}=4$, and (b) different chemical potential configurations with $U=0.5$. For comparison, we also plot the result of $U=0$ but finite $\varepsilon_{\hbox{\tiny M}}$ in the low panels: for (c) different $\varepsilon_{\hbox{\tiny M}}$ values, and (d) different chemical potential configurations with $\varepsilon_{\hbox{\tiny M}}=0.5$.