Revealing the nonlocal coherent nature of Majorana devices from dissipative teleportation

The recent observations of Majorana resonance increase our confidence in the realization of the first topological qubit. The nonlocal coherent nature of Majorana devices is the key factor for the topological protection of these qubits from decoherence. Direct observation of this coherent nature could provide a first-step benchmarking scheme to validate Majorana qubit quality, which could be the next experimental milestone. We propose a simple transport scheme with a Majorana island device along with a dissipative environment in the electrodes. We find that the dissipative environment renormalizes the quantum transport in significantly different ways: As the temperature is reduced, while the conductance for Majorana coherent teleportation increases, all other incoherent signals are strongly suppressed due to dissipation. This unique conductance scaling behavior is a clear benchmark to reveal the nonlocal coherent nature of Majorana devices.

Figure 1

(a) Illustration of the system setup. (b), (c) Majorana teleportation and normal-state sequential tunneling. (d) An equivalent circuit of (a). The two tunneling junctions are characterized by capacitance $C_{l,r}$ and dimensionless conductance $g_{l,r}$ (conductance $G_{l,r}=g_{l,r}2e^2/h$). (e) Phase diagram of the proximitized nanowire. The trivial and topological gaps are labeled by ${\mathrm{\Delta }}_{\mathit{B}}$ and ${\mathrm{\Delta }}_{\mathrm{Topo}}$.

Figure 2

The dissipative CB conductance as a function of dimensionless central gate potential $n_g\equiv V_g{C}_g/e$ for different temperatures in regions (i)–(iii) of Fig. 1. (a) A schematic drawing of the dissipative CB conductance in Majorana phase [region (i)] by fitting the results in [46, 63] with $T\ll {\mathrm{\Gamma }}^{\mathit{M}},{\omega }_R$. The inset shows the peak conductance as a function of $T$ in a larger range. (b) The dissipative CB conductance in normal-metal phase [region (ii)] with ${\mathrm{\Delta }}_{\mathit{B}}<\delta$. (c) The dissipative CB conductance of a superconductor in region (iii) where $T\ll {\mathrm{\Delta }}_{\mathit{B}}<E_c$ with ${\mathrm{\Delta }}_{\mathit{B}}/E_c=0.37$. The peak positions shift about $N_{\mathrm{\Delta }}$ with $N_{\mathrm{\Delta }}\equiv \mathrm{\Delta }/\left(2E_c\right)$. $N_0$ represents an integer.

Figure 3

(a) The Majorana CB conductance when there is a splitting ${\epsilon }_0$ as shown in (b). The solid and dashed lines represent the conductance with and without splitting, respectively. The peak position will be shifted by $N_{\epsilon }\equiv {\epsilon }_0/\left(2E_c\right)$ when splitting occurs. (c) The dissipative CB conductance of a superconductor in region (iv) of Fig. 1 where ${\mathrm{\Delta }}_{\mathit{B}}>E_c$ with ${\mathrm{\Delta }}_{\mathit{B}}=3\text{K}, E_c=2.32\text{K}$. (b), (d) Single-terminal tunneling conductance as a function of bias voltage $V$ and Zeeman energy $V_Z$ of the proximitized nanowire, with MZM (b) and ABS (d) at the wire end, respectively. The splittings at $V_Z=3\text{meV}$ are labeled as ${\epsilon }_0$ and ${\epsilon }_A$.