Anomalous Low-Temperature Enhancement of Supercurrent in Topological-Insulator Nanoribbon Josephson Junctions: Evidence for Low-Energy Andreev Bound States

We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator ${\mathrm{BiSbTeSe}}_2$ nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature $T$, the increasing critical current $I_c$ exhibits a sharp upturn at a temperature $T_{*}$ around 20% of the junction critical temperature for several different samples and various gate voltages. The $I_c$ vs $T$ demonstrates a short junction behavior for $T>T_{*}$, but crosses over to a long junction behavior for $T<T_{*}$ with an exponential $T$ dependence $I_c\propto \exp (-k_{B}T/\delta )$, where $k_B$ is the Boltzmann constant. The extracted characteristic energy scale $\delta$ is found to be an order of magnitude smaller than the induced superconducting gap of the junction. We attribute the long-junction behavior with such a small $\delta$ to low-energy Andreev bound states arising from winding of the electronic wave function around the circumference of the topological insulator nanoribbon.

Figure 1

(a) Two-terminal $R$ vs $V_g$ measured at $T=14.5\mathrm{K}$, above the critical temperature $T_c^{\mathrm{Nb}}=7.5\mathrm{K}$ of the Nb electrodes. Shaded regions highlight n and p doping of TINR. (b) $V_{\mathrm{dc}}$ vs $I_{\mathrm{dc}}$ for different $V_g$’s at $T=20\mathrm{mK}$. Inset: AFM image of sample 1 (from which all data in this figure are measured), a TI (${\mathrm{BiSbTeSe}}_2$) nanoribbon Josephson device with superconducting Nb electrodes. Scale bar is $0.5\mu \mathrm{m}$. (c) Color map of the two-terminal $dV/dI$ vs $V_g$ and $I_{\mathrm{dc}}$ at $T=20\mathrm{mK}$. An ac excitation current $I_{\mathrm{ac}}=1\mathrm{nA}$ was used for the $dV/dI$ measurement. Solid white line marks the junction critical current $I_c$ vs $V_g$. Data in (b)–(c) is measured by sweeping $I_{\mathrm{dc}}$ from -300 to 300 nA.

Figure 2

(a) Temperature dependence of $I_c$ for different $V_g$’s for sample 1. (b) Normalized $I_c/I_c^{\max }$ vs normalized $T/T_c$ for data in (a) in log-linear scale. The solid blue line is the normalized $I_{c1}/I_{c1}^{\max }$ [Eq. (2)] divided by factor 2.2 and the solid red line is a fit to $\exp (-k_{B}T/\delta )$ with $\delta \sim 0.08\mathrm{\Delta }$. The symbols have the same legends as in (a). Inset: cartoons of the TINR JJ depicting the current $I_1$ corresponding to the modes on the top surface and the current $I_2$ corresponding to the modes that extend around the circumference and flow through the bottom surface. (c) $I_c/I_c^{\max }$ vs $T/T_c$ in a log-linear scale for five different TINR-based Josephson devices measured at a few (1–3) $V_g$’s for each device. The exponential fit and the experimental data in (b) are also included in this plot as the solid red line and black symbols, respectively.

Figure 3

(a) False-colored scanning electron microscope image of an asymmetric SQUID used to measure the current-phase relations (CPR) in our TINR-based JJs. (b) Normalized current $I/I_c$ vs normalized flux $\mathrm{\Delta }\mathrm{\Phi }/{\mathrm{\Phi }}_0$, where ${\mathrm{\Phi }}_0=h/2e$ is the flux quantum, at $V_g=20\mathrm{V}$ and $T=20\mathrm{mK}$. As the absolute value of the flux inside the superconducting SQUID is unknown, the experimental curve is shifted along the horizontal axis for comparison with a sinusoidal function.