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.

Three-dimensional topological insulators (TI's) in proximity with superconductors are expected to exhibit exotic phenomena such as topological superconductivity (TSC) and Majorana bound states (MBS), which may have applications in topological quantum computation. In superconductor-TI-superconductor Josephson junctions, the supercurrent versus the phase difference between the superconductors, referred to as the current-phase relation (CPR), reveals important information including the nature of the superconducting transport. Here, we study the induced superconductivity in gate-tunable Josephson junctions (JJs) made from topological insulator BiSbTeSe2 with superconducting Nb electrodes. We observe highly skewed (non-sinusoidal) CPR in these junctions. The critical current, or the magnitude of the CPR, increases with decreasing temperature down to the lowest accessible temperature (T ~ 20 mK), revealing the existence of low-energy modes in our junctions. The gate dependence shows that close to the Dirac point the CPR becomes less skewed, indicating the transport is more diffusive, most likely due to the presence of electron/hole puddles and charge inhomogeneity. Our experiments provide strong evidence that superconductivity is induced in the highly ballistic topological surface states (TSS) in our gate-tunable TI- based JJs. Furthermore, the measured CPR is in good agreement with the prediction of a model which calculates the phase dependent eigenstate energies in our system, considering the finite width of the electrodes as well as the TSS wave functions extending over the entire circumference of the TI.

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 $T_*$ around 20$\%$ of the junction critical temperatures for several different samples and various gate voltages. The $I_c$ vs. $T$ demonstrates a short junction behavior for $T>T_*$, but crosses over to a long junction behavior for $T<T_*$ 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.

Over the past few years, there has been a growing interest in layered transition metal dichalcogenides (TMD) such as molybdenum disulfide (MoS2). Most studies so far have focused on the electronic and optoelectronic properties of single-layer MoS2, whose band structure features a direct bandgap, in sharp contrast to the indirect bandgap of thicker MoS2. In this paper, we present a systematic study of the thickness-dependent electrical and thermoelectric properties of few-layer MoS2. We observe that the electrical conductivity () increases as we reduce the thickness of MoS2 and peaks at about two layers, with six-time larger conductivity than our thickest sample (23-layer MoS2). Using a back-gate voltage, we modulate the Fermi energy () of the sample where an increase in the Seebeck coefficient () is observed with decreasing gate voltage () towards the subthreshold (OFF state) of the device, reaching as large as in a four-layer MoS2. While previous reports have focused on a single-layer MoS2 and measured Seebeck coefficient in the OFF state, which has vanishing electrical conductivity and thermoelectric power factor (), we show that MoS2-based devices in their ON state can have as large as in the two-layer sample. The increases with decreasing thickness then drops abruptly from double-layer to single-layer MoS2, a feature we suggest as due to a change in the energy dependence of the electron mean-free-path according to our theoretical calculation. Moreover, we show that care must be taken in thermoelectric measurements in the OFF state to avoid obtaining erroneously large Seebeck coefficients when the channel resistance is very high. Our study paves the way towards a more comprehensive examination of the thermoelectric performance of two-dimensional (2D) semiconductors.