We report on the observation of gate-tunable proximity-induced superconductivity and multiple Andreev reflections (MARs) in a bulk-insulating BiSbTeSe2 topological insulator nanoribbon (TINR) Josephson junction with superconducting Nb contacts. We observe a gate-tunable critical current (IC) for gate voltages (Vg) above the charge neutrality point (VCNP), with IC as large as 430 nA. We also observe MAR peaks in the differential conductance (dI/dV) versus DC voltage (Vdc) across the junction corresponding to sub-harmonic peaks (at Vdc = Vn = 2ΔNb/en, where ΔNb is the superconducting gap of the Nb contacts and n is the sub-harmonic order). The sub-harmonic order, n, exhibits a Vg-dependence and reaches n = 13 for Vg = 40 V, indicating the high transparency of the Nb contacts to TINR. Our observations pave the way toward exploring the possibilities of using TINR in topologically protected devices that may host exotic physics such as Majorana fermions.
Three-dimensional topological insulators (TIs) are a new class of quantum matter with insulating bulk and conducting surface states, topologically protected against time-reversal-invariant perturbations (scattering by non-magnetic impurities such as crystalline defects and surface roughness).1,2 Topological superconductors (TSCs) are another important class of quantum matter and are analogous to TIs, where the superconducting gap and Majorana fermions of TSCs replace the bulk bandgap and Dirac fermion surface states of the TI, respectively.2 Controlling the Majorana modes is considered one of the important approaches for developing topologically protected quantum computers. Three-dimensional (3D) TIs in proximity to s-wave superconductors have been proposed as one of the promising platforms to realize topological superconductivity and Majorana fermions.3 In this context, it has been pointed out that TI nanowires (TINWs) possess various appealing features for such studies.4–8 However, the first important step is to understand how TI nanowires, including nanoribbons (TINRs), behave in contact with superconducting leads.
Superconductor-normal-superconductor (SNS) Josephson junctions (JJs), with topological insulators as the normal material, have been experimentally realized on 3D-TIs.9–22 However, TI materials used in many of the previous experiments have notable bulk conduction, making it challenging to distinguish from the contribution of the topological surface states. In this letter, we study S-TINR-S Josephson junctions, where S = Niobium (Nb) and the TINRs are mechanically exfoliated from bulk BiSbTeSe2 (BSTS) TI crystals. Our BSTS is among the most bulk-insulating TIs with surface state dominated conduction and chemical potential located close to the surface state Dirac point in the bulk bandgap.23,24 Therefore, our study enables us to investigate the proximity effects and induced superconductivity in such “intrinsic” (bulk-insulating) and gate-tunable TINRs with both electron (n) and hole (p) dominated surface transport. Moreover, we are able to investigate the transparency of our superconducting contacts to TINRs both in n- and p-dominated transport regimes through the observation of multiple Andreev reflections (MARs).
High-quality single crystals of BSTS were grown by the Bridgman technique as described elsewhere.23,24 Devices fabricated on the exfoliated flakes from these crystals exhibit surface dominated conduction with ambipolar field effects, half-integer quantum hall effects, and π Berry's phase.23,24 We obtain BSTS nanoribbons using a standard mechanical exfoliation technique and transfer them onto a 500-μm thick highly doped Si substrate (used as the back gate) covered with 300-nm SiO2 on top. We locate BSTS nanoribbons, which are randomly dispersed on the substrate, using an optical microscope. An atomic force microscopy (AFM) image of a representative JJ is shown in Fig. 1(a). Multiple electrodes, with electrode separation L < 100 nm between the adjacent electrodes, are defined by e-beam lithography for each TINR. We then deposit 30-nm thick Nb contacts by a DC sputtering system. A short (∼5 s) in situ Ar ion milling prior to the metal deposition is used to remove any residues left from the lithography step and native oxides on the TINR surface. Our results presented here are taken from a TINR sample with a thickness of ∼20 nm, a width of ∼250 nm, and an electrode separation of ∼60 nm.
Figure 1(b) depicts R vs. the back-gate voltage (Vg) at T = 10 K (above the critical temperature of our deposited superconductor, ). The charge neutrality-point voltage (VCNP) is ∼4 V for this device. The electron- and hole-dominated regimes can be easily observed in Fig. 1(b) as we tune Vg away from VCNP. Using BCS theory, we estimate the T = 0 K superconducting gap as .
When the sample is cooled down below , the electronic transport in the junction is strongly affected by the superconducting proximity effect. The evidences of this effect manifest themselves as the flow of a supercurrent in the junction and the appearance of multiple Andreev reflections (MARs).25,26 Figure 2(a) shows the colormap of the differential resistance (dV/dI) vs. Vg and Idc at T = 30 mK. The DC voltage vs. current (Vdc vs. Idc) characteristic of the junction at T = 30 mK for a few different Vg's is also presented in Fig. 2(b). As we increase Idc from zero, the junction is in its superconducting state and its resistance is zero. However, once Idc is increased above a critical value [IC, marked by an arrow in Fig. 2(b)], the junction transitions from the superconducting state to a normal state with a non-zero resistance. The junction critical current, IC, is highlighted by a white curve in Fig. 2(a). First, we observe that IC is gate tunable, with larger IC for Vg > VCNP. However, when Vg is tuned near the charge neutrality point (VCNP ∼ 4 V), IC decreases and eventually saturates for more negative Vg's as previously observed in Bi2Se3 flakes27 and graphene.28,29 One possible explanation for the saturation of IC for Vg below VCNP is that the Nb electrodes electron-dope the underlying material (TINR). Therefore, when Vg < VCNP, a p-n junction is formed in the TINR. This p-n junction can weaken and eventually break the induced superconductivity as was shown in graphene.30 Furthermore, despite that the total charge of the system is neutral close to the CNP, the top and bottom surfaces may be oppositely charged due to the difference in their coupling to the back gate. This charge inhomogeneity may also contribute to the saturation of IC for Vg ≤ VCNP. Another plausible explanation may be the poor injection of the holes into TINRs by Nb, as will be demonstrated from the low transparency of the contacts for Vg < VCNP from our analysis of MARs (Fig. 3). The inset of Fig. 2(b) shows the dependence of IC on the Fermi momentum (kF), where and Cox is the parallel plate capacitance per unit area of 300-nm SiO2 (∼12 nF/cm2). For kF > 0.4 nm−1, we observe that IC varies linearly with kF, as experimentally demonstrated in ballistic graphene Josephson junctions.31 The measured mean free path of BSTS flakes is ∼100 nm.23,24 Given the channel length L ∼ 60 nm, we believe our junctions to be in the ballistic limit, corroborating the linear dependence of IC with kF. We also observe that the junction critical temperature (TC, the temperature below which the junction resistance goes to zero and supercurrent starts to flow in the junction) changes with Vg from TC = 1.6 K for Vg = 40 V to TC = 0.7 K for Vg = 10 V. Using BCS theory, we extract the induced superconducting gap (Δ) in the TINR as Δ = 1.76kBTC = 242 μeV and 106 μeV for Vg = 40 V and Vg = 10 V, respectively. The superconducting coherence length varies from 600 nm to 260 nm for Vg = 10 and 40 V, respectively. We note that the resistance (dV/dI) of the junction does not change as we increase Vdc above ΔNb/e (∼975 μV) and even slightly beyond 2ΔNb/e as will be discussed later. As a result, the normal resistance (RN) in our junctions is obtained at Vdc slightly above ΔNb/e. We obtain ICRN ∼ 304 μV and 266 μV for Vg = 40 V and 10 V, respectively. Such large ICRN products (compared to Δ) again point towards the ballistic nature of superconducting transport in our sample as recently reported in other TI junctions.32
Figure 3(a) displays dI/dV vs. Vdc for Vg = 40 V at T = 30 mK. Several peaks (within the Nb superconducting gap) in dI/dV are observed at Vdc = Vn = 2ΔNb/en (where n = 2, 3, 4, 5, 6, 9, and 13) as marked by the arrows in Fig. 3(a). These dI/dV peaks are consistent with MARs.25 We note that these peaks are symmetric around Vdc = 0 V, and thus, below we focus only on the positive peaks. No feature in dI/dV vs. Vdc is identified for n = 1, and RN is achieved for V > ΔNb/e instead of V > 2ΔNb/e. The absence of the first (n = 1) MAR peak has been noted in some SNS junctions20,26 and may be related to the presence of mid-gap zero-energy states as described elsewhere.33,34 From the linear fit of dI/dV peaks vs. 1/n, we obtain ΔNb ∼ 900 μeV, which is in excellent agreement with ΔNb obtained from the BCS theory and . Moreover, the observed dI/dV peaks are reproducible and independent of the Vdc sweep direction. While we do not observe any dI/dV peaks corresponding to n = 7 and 8, higher-order peaks (n = 9 and 13) are present, a feature that has been previously observed26 and requires further investigation. The observation of the high-order MAR peaks is an indication of high transparency of contacts in our junction.
Figure 3(b) depicts the differential conductance (dI/dV, normalized by 1/RN) vs. (positive) Vdc for T = 30 mK at three different Vg's. First, we observe that the position of the dI/dV peaks remains relatively constant with Vg, in contrast to the oscillatory behavior of dI/dV peaks around a resonant level in a quantum dot.35,36 This suggests the absence of localized states in our TINR devices. The high-order dI/dV peaks observed for Vg > VCNP further indicate that the contacts are highly transparent. Even though the large ICRN product and the linear dependence of IC vs. kF point towards the ballistic nature of transport, the small amplitude of MAR peaks [as shown in Fig. 3(b)] has been previously attributed to a diffusive transport regime in graphene JJs.37 Such discrepancies require further investigations. For Vg < VCNP, the amplitude of the dI/dV peaks decreases with more negative Vg, e.g., with vanishing peak amplitudes for n = 3, 4, 5, 6, and 9 at Vg = −40 V. The vanishing of dI/dV peaks for Vg < VCNP may be related to the pinning of the Fermi level to the electron-doped regime under the Nb electrodes and hence the formation of p-n junctions for Vg < VDP, where VDP is the Dirac point voltage, as has been observed in graphene JJs.28,29
Figure 4(a) depicts the T-dependence of dI/dV (normalized by 1/RN) vs. Vdc for Vg = 40 V, exhibiting a reduction of the Nb superconducting gap with increasing T. Dashed lines are guides to the eye corresponding to the expected T-dependence of dI/dV peak positions (Vn) from BCS theory. We observe a nearly flat and featureless dI/dV vs. Vdc for T = 6.6 K (slightly above ). We also observe that while dI/dV peaks are noticeable up to high temperatures (∼5.2 K), the amplitude of the peaks reduces with increasing T, and some of the peaks merge together at higher T (e.g., peaks for n = 3 and 4 merge at T = 3.5 K). Figure 4(b) shows the T-dependence of Vn for n = 2, 3, 4, and 6. Using the BCS theory to fit Vn vs. T, we extract TC ∼ 6 K, in fair agreement with . Figure 4(c) displays the T-dependence of ΔNb extracted from each dI/dV peak (for n = 2, 3, 4, and 6), where ΔNb = neVn(T)/2, together with the fit of ΔNb vs. T obtained from the BCS theory, which is seen to describe the data well.
We demonstrated Josephson junctions based on mechanically exfoliated bulk-insulating 3D topological insulator nanoribbons in proximity to superconducting Nb electrodes. We observe high-order (n = 13) multiple Andreev reflections, demonstrating that charge transport in the TINR channel is coherent. Furthermore, the critical current exhibits gate effects and can be gate-tuned around one order of magnitude from ∼50 nA to ∼430 nA at 30 mK. Our measurements of supercurrent in Josephson junctions based on TINRs help to better understand the nature of induced superconductivity in these junctions and pave the way toward exploration of the envisioned topologically protected devices based on superconductor-TINR-superconductor junctions.
We acknowledge support from NSF (DMR No. 1410942). The TI material synthesis was supported by the DARPA MESO Program (Grant No. N66001-11-1-4107). L.A.J. also acknowledges support from a Purdue Center for Topological Materials fellowship. L.P.R. and A.K. acknowledge support from the U.S. Department of Energy under Award No. DE-SC0008630.