Unconventional Josephson Effect in Hybrid Superconductor-Topological Insulator Devices

We report on transport properties of Josephson junctions in hybrid superconducting-topological insulator devices, which show two striking departures from the common Josephson junction behavior: a characteristic energy that scales inversely with the width of the junction, and a low characteristic magnetic field for suppressing supercurrent. To explain these effects, we propose a phenomenological model which expands on the existing theory for topological insulator Josephson junctions.

Figure 1

(a) Schematic of a topological insulator Josephson junction. Two superconducting leads are patterned on top of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ forming a junction with length $L$ and width $W$. Along the width of the device, resulting in a one-dimensional wire of Majorana fermions (in between superconducting leads). (b) Scanning-electron micrograph of a device similar to the ones measured in this Letter. (c) (main) $V$ vs $I$ for a devices of dimensions $(L,W)=(45\mathrm{nm},1\mu \mathrm{m})$ for $B=0$, 2, 3, 5, 8, 10 mT and at a temperature of 12 mK. At $B=0$, $I_C$ is 850 nA, which is reduced upon increasing $B$. For this device, the product $I_C{R}_N=30.6\mu \mathrm{V}$, much lower than theoretically expected for conventional JJs. (upper-left inset) $I\mathrm{\text{−}}V$ curves overlap for all values of $B$ at $V\ge 2\Delta /e\sim 300\mu \mathrm{V}$. (lower-right inset) Sweeps up and down in $I$ show little hysteresis, indicating that the junction is in the overdamped regime.

Figure 2

(a) A comparison of two devices with similar $R_N$ (56.1 and $51.5\Omega$) and different widths $W$, 0.5, and $1\mu \mathrm{m}$. The device with $W=0.5\mu \mathrm{m}$ exhibits a larger $I_C$, in contrast to conventional JJs, where similar resistances lead to similar values of $I_C$. (b) $I_C{R}_N$ vs $1/W$ for all 14 devices (synthesized via two methods: a binary melt and VLS) showing the general trend of $I_C{R}_N\propto 1/W$. In addition, $I_C{R}_N$ data points from Refs. 3, 4, 5 (symbols) are shown in comparison to the results of this Letter.

Figure 3

(a) Differential resistance $dV/dI$ as a function of $B$ and $I$ showing an anomalous magnetic diffraction pattern for a $W=1.5\mu \mathrm{m}$ junction. Two features are of note: a smaller-than-expected value of $B_C$ at 1.70 mT and a nonuniform spacing between minima at values $B=1.70$, 6.50, 11.80 mT. (b) (main) $I_C(B)$ (dashed line with circles) extracted from $dV/dI$ in (a) is compared to the expected Fraunhofer pattern for the junction (solid line) where a reduction of the scale of the pattern and the nonuniform spacing are evident. (inset) A comparison of the simulated Frauhofer pattern for a sinusoidal and an empirically determined, peaked CPR. The narrowing of the diffraction pattern and the aperiodic minima observed in (a) are captured this CPR.

Figure 4

(a) Energy levels near $\phi =\pi$ before momentum quantization along $W$ (solid line) and after, where the topological state remains at $E=0$ (solid circle) and the first quantized energy level at the value $E_C$ (empty circle). (b) Current-phase relation resulting from momentum quantization, producing an anomalous peak at $\phi =\pi$. The location and shape of the peaks in the current-phase relation depend on the details of energy spectrum of the Andreev bound pairs and in 9 we consider several possible scenarios for this spectrum.