$\pi$ and $4\pi$ Josephson Effects Mediated by a Dirac Semimetal

${\mathrm{Cd}}_3{\mathrm{As}}_2$ is a three-dimensional topological Dirac semimetal with connected Fermi-arc surface states. It has been suggested that topological superconductivity can be achieved in the nontrivial surface states of topological materials by utilizing the superconductor proximity effect. Here we report observations of both $\pi$ and $4\pi$ periodic supercurrents in aluminum-${\mathrm{Cd}}_3{\mathrm{As}}_2$-aluminum Josephson junctions. The $\pi$ period is manifested by both the magnetic-field dependence of the critical supercurrent and the appearance of half-integer Shapiro steps in the ac Josephson effect. Our macroscopic theory suggests that the $\pi$ period arises from interference between the induced bulk superconductivity and the induced Fermi-arc surface superconductivity. The $4\pi$ period is manifested by the missing first Shapiro steps and is expected for topological superconductivity.

Figure 1

Experimental configuration and observation of supercurrents in ${\mathrm{Cd}}_3{\mathrm{As}}_2$. (a) The resistance of a superconductor-${\mathrm{Cd}}_3{\mathrm{As}}_2$-superconductor junction versus temperature at zero magnetic field. A zero-resistance state is reached below $T_c=0.8\mathrm{K}$. Inset shows a scanning electron microscopy image of a Josephson junction. (b) The current-voltage ($I\text{−}V$) characteristic of junction A measured at $T=12\mathrm{mK}$. Supercurrent is observed with a critical current $I_c=4.6\mu \mathrm{A}$.

Figure 2

Current-phase measurements of an $\mathrm{Al}\text{−}{\mathrm{Cd}}_3{\mathrm{As}}_2\text{−}\mathrm{Al}$ Josephson junction. (a) 2D color plot of $dV/dI$ with respect to the magnetic field and the dc current to better demonstrate the current-phase relationship. The blue area represents the superconducting state and the edge exhibits critical current $I_c$. (b) The magnetoresistance of junction A measured at 12 mK. The resistance remains zero around $B=0$ and starts to increase at $B=30\mathrm{mT}$. At $B>40\mathrm{mT}$, the superconductivity is completely destructed and the junction is in the normal state. (c) $I_c$ in junction $A$ is plotted as a function of magnetic field. $I_c$ enhancement induced by the magnetic field has been observed in the low magnetic-field regime due to the strong spin-orbit coupling. The weak minimum at $B=22\mathrm{mT}$ labeled by the arrow corresponds to $\mathrm{\Phi }={\mathrm{\Phi }}_0/2$, indicating a $\pi$-period supercurrent.

Figure 3

Observation of the ac Josephson effect in an $\mathrm{Al}\text{−}{\mathrm{Cd}}_3{\mathrm{As}}_2\text{−}\mathrm{Al}$ Josephson junction. (a) $I\text{−}V$ curves measured with microwave irradiation $f=6.5\mathrm{GHz}$ for different irradiation power values. Integer Shapiro steps are clearly visible at $V_{\mathrm{dc}}=Nhf/2e$ due to the ac Josephson effect. (b) $I\text{−}V$ curves measured with microwave irradiation $f=10.5\mathrm{GHz}$. Integer Shapiro steps are observed for low irradiation power $P=-3\mathrm{dBm}$ (blue trace). With increasing irradiation power, fractional Shapiro steps emerge. The green trace shows the $I\text{−}V$ curve measured with $P=2\mathrm{dBm}$. Half-integer Shapiro steps are marked by the red arrows. (c) $I\text{−}V$ curves for microwave irradiation of low frequency $f=3\mathrm{GHz}$. For high irradiation power, all integer steps are visible. When the power is lowered, step $N=1$ is missing, indicating a $4\pi$ periodic Josephson effect.

Figure 4

The SQUID diagram used in our macroscopic model. (a) Schematic sideview of the superconductor-${\mathrm{Cd}}_3{\mathrm{As}}_2$-superconductor device structure used in our experiment. (b) Schematic circuit diagram showing the coexistence of bulk-state (indicated by the blue color) and surface-state (indicated by the red color) channels in the Dirac semimetal. $L_{s(b)}$, $R_{s(b)}$, and $I_{s(b)}$ are the surface (bulk) inductance, resistance, and current.