Majorana-Josephson interferometer

We propose an interferometer for chiral Majorana modes where the interference effect is caused and controlled by a Josephson junction of proximity-induced topological superconductors, hence, a Majorana-Josephson interferometer. This interferometer is based on a two-terminal quantum anomalous Hall bar, and as such its transport observables exhibit interference patterns depending on both the Josephson phase and the junction length. Observing these interference patterns will establish quantum coherent Majorana transport and further provide a powerful characterization tool for the relevant system.

Figure 1

(a) Schematic of a Majorana-Josephson interferometer. A quantum anomalous Hall bar (gray) is in contact with two conventional superconductors (cyan) on its top and two normal metals (yellow) at its ends. The two superconducting contacts are grounded and maintain a tunable phase difference $\varphi$. The arrowed lines represent generic scattering of chiral Majorana modes in the interferometer. (b) Typical two-terminal conductance $G$ as a function $\varphi$ in a Majorana-Josephson interferometer when the superconducting junction is long (blue line) and short (red line), respectively.

Figure 2

Scattering picture of the chiral Majorana modes in the long-junction limit of a Majorana-Josephson interferometer at $\mu =0$. Regions with different superconducting order parameters are labeled by A–E. The full scattering matrix can be obtained by first analyzing the composite regions ABC and CDE (in gray dashed frames) individually, and then connecting them by taking into account the $\varphi$-dependent local basis. Labels for the incoming ($a$'s) and the outgoing ($b$'s) Majorana modes are indicated.

Figure 3

(a) Two-terminal conductance $G$ as a function of $\varphi$ for different junction lengths $l_C$ with the chemical potential $\mu =0$. The solid lines are numerical results, whereas the dashed lines are analytical results for the long-junction and the short-junction limits, respectively. (b) $G$ as a function of $l_C$ with different $\mu$ at $\varphi =0$. The solid lines are numerical results, whereas the dashed lines are analytical results for the long-junction limit plotted from $l_C=60a$. (c) $G$ as a function of $\varphi$ for different inverse quasiparticle life time $\mathrm{\Gamma }$ with $\mu =0.04$, in the long-junction (blue line, $l_C=100a$) and the short-junction (red line) limits, respectively. All plots here share the following parameters: $W=200a, x_2-x_1=x_4-x_3=100a, b=v=1, {\mathrm{\Delta }}_0=3m=0.3$. With these parameters we estimate ${\xi }_{\mathrm{QAH}}/a\approx v/\left(2m\right)=5$.