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 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 $T_{\ast }$ around 20$\mathrm{\%}$ of the junction critical temperatures for several different samples and various gate voltages. The $I_c$ vs. $T$ demonstrates a short junction behavior for $T>T_{\ast }$, but crosses over to a long junction behavior for $T<T_{\ast }$ with an exponential $T$-dependence $I_c \propto \exp\big(-k_B T/\delta \big)$,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 (ABS) arising from winding of the electronic wavefunction around the circumference of the topological insulator nanoribbon (TINR). Our TINR-based Josephson junctions with low-energy ABS are promising for future topologically protected devices that may host exotic phenomena such as Majorana fermions.