is a material with rich topological properties: it is a 2D topological insulator as a monolayer and a Weyl-semimetal and higher-order topological insulator in a bulk form. Inducing superconductivity in topological materials is a way to obtain topological superconductivity, which lays at the foundation for many proposals of fault tolerant quantum computing. Here, we demonstrate the emergence of superconductivity at the interface between and the normal metal palladium. The superconductivity has a critical temperature of about 1.2 K. By studying the superconductivity in a perpendicular magnetic field, we obtain the coherence length and the London penetration depth. These parameters correspond to a low Fermi velocity and a high density of states at the Fermi level. This hints to a possible origin of superconductivity due to the formation of flatbands. Furthermore, the critical in-plane magnetic field exceeds the Pauli limit, suggesting a non-trivial nature of the superconducting state.
Topological materials attract a lot of attention in modern condensed matter physics. This interest stems from intriguing fundamental properties and great potential for practical applications. The especially interesting class of topological materials is topological superconductors, promising to revolutionize quantum computing due to the inherent error protection.1 Topological superconductivity could be obtained by inducing superconductivity in a topologically non-trivial system. There are several theoretical predictions of different topological superconducting states in Dirac and Weyl-semimetal based systems, including Fulde–Ferrell–Larkin–Ovchinnikov superconductors,2–4 the time-reversal invariant topological superconductor,5 chiral non-Abelian Majorana fermions,6 and flatband superconductivity.7
is a layered transition-metal dichalcogenide with rich topological properties. As a bulk material, it is a type-II Weyl semimetal with bulk Weyl nodes connected by Fermi-arc surface states.8,9 Recently, it has been predicted to be a higher-order topological insulator with one-dimensional hinge states,10 and experimental evidence of these states has been obtained.11–13 In a single layer form, is a two-dimensional topological insulator with helical edge states.14,15 In addition to all these topological phases, has a tendency of becoming superconducting under different conditions: under pressure,16,17 electron doping,18 or electrostatic gating.19,20 The combination of these properties makes a particularly promising candidate for topological superconductivity.
In this paper, we demonstrate the emergence of superconductivity at the interface between the normal metal palladium and few-layer thick . Studying the transport properties in magnetic field and at different temperatures, we deduce the main parameters characterizing the superconducting state including the critical temperature, the coherence length, and the London penetration depth. These parameters correspond to a low Fermi velocity and a high density of states at the Fermi level. This hints to a possible origin of superconductivity due to the formation of flatbands. Moreover, the measured in-plane critical field exceeds the Pauli limit, suggesting non-trivial superconducting pairing. The coexistence of the observed superconductivity with topological states in makes it a promising platform for studying topological superconductivity and applications for quantum computing.
The single crystals of were grown with a flux growth method.21 We obtained few-layer thick flakes by mechanically exfoliating single crystals with an adhesive tape on an oxidized Si substrate with a 295 nm layer. To avoid oxidation of , the exfoliation has been carried out in a glovebox with low oxygen content. We selected few-layer thick (5–12 single layers) stripe shaped flakes. Suitable flakes have been identified with an optical contrast method22 and were picked up and transferred using the polycarbonate assisted pick-up technique23 on the device chip that already contained prepatterned contacts. The contacts were defined before using standard e-beam lithography and metal deposition of 3 nm titanium and 12 nm palladium. In the final stack, is protected from oxidation by an hBN layer that covers the . All the measurements were performed in a dilution refrigerator with a base temperature of 60 mK. Similar superconducting properties have been observed in multiple devices, and data presented in the paper were collected from 3 samples.
RESULTS AND DISCUSSION
Figure 1(a) shows an optical image of an encapsulated crystal with a contact pattern that resembles a standard Hall-bar configuration. Note that the visible Pd contacts are at the bottom, followed by a few-layer crystal with a rectangular shape and a high-aspect ratio oriented vertically, followed by an hBN layer that has the weakest contrast in the image. The drawn electrical schematics correspond to the measurement of the longitudinal resistance given by .
Figure 1(b) displays as a function of perpendicular magnetic field . At 4 K, the resistance shows a non-saturating magnetoresistance characteristic for .24 The small thickness (7 layers) of our crystal results in a relatively small magnetoresistance.25 Another evidence of the high quality of our samples is the presence of Shubnikov–de Haas oscillations at low temperature. The frequency of the oscillations T corresponds to an electron density cm and a Fermi wavevector nm (here, the two electron pockets of are taken into account). The oscillation visibility at around 5 T suggests a mobility of at least 2000 cm V s, which yields an electron mean free path of nm.
At low temperature, additional features develop in : at zero field, the resistance goes to zero, and in small fields, it has an intermediate state between zero and high-temperature values. The asymmetry in is defined by the sweep direction and rate; thus, it is likely connected with heating during the magnetic field sweep. The intermediate resistance state in Fig. 1(b) is a result of the formation of a superconducting state in above the Pd leads. Furthermore, these superconducting regions could be connected by the Josephson effect, as illustrated in Fig. 1(c), leading to a zero longitudinal resistance. The zero resistance state appears only for smaller distances between the contacts, excluding intrinsic superconductivity in our samples. This explanation is further supported by dependence in Fig. 1(d). With decreasing temperature, the first superconducting transition takes place in the range of 1.05–1.2 K, followed by the gradual developing of the Josephson effect at lower temperature achieving zero resistance below 350 mK.
To understand the properties of the superconducting state, we studied the evolution of with increasing temperature, as shown in Fig. 2(a). Upon temperature increase, both transitions in the resistance are shifting toward zero field. The zero resistance state connected to the Josephson coupling disappears first above 0.75 K, and the second transition connected to the suppression of superconductivity by magnetic field persists up to 1.1 K. We define as the magnetic field where the crosses the fixed resistance value , which approximately corresponds to half of the resistance step. Figure 2(b) shows the extracted dependence of the critical magnetic field as a function of temperature . The dependence is linear as expected for a 2D superconductor,
where is the magnetic flux quantum, is the Ginzburg–Landau coherence length at zero temperature, and is the critical temperature at zero magnetic field. Fitting the experimental data with Eq. (1), we obtain K and relatively short nm.
Disorder can cause the reduction of the coherence length, but we do not think this is the case in our samples since we have found and non-saturating magnetoresistance. In the clean limit at low temperatures, the Ginzburg–Landau coherence length is similar to the Bardeen–Cooper–Schrieffer (BCS) coherence length . Knowing the coherence length and the critical temperature, we can estimate the Fermi velocity , where we take for the BCS relation , yielding ms. The obtained small value of Fermi velocity could suggest superconductivity due to the formation of flatbands.26
We further investigate the superconducting properties by looking at the dependence on the in-plane magnetic field , as shown in Fig. 3(a). Compared with the perpendicular field, both changes in the resistance have shifted to higher magnetic fields. We extracted the critical field values as a function of temperature and plotted them in Fig. 3(b). In this case, follows the known empirical law for superconductors ,27 as evident from the very good agreement between measured points and the fit. Both fits of the critical field as a function of and converge to the same temperature K.
A notable feature of the parallel critical field is its large value, which exceeds the Pauli paramagnetic limit . The latter is given by T. This expression is based on the BCS theory for weak-coupling superconductors and a free electron -factor of .28 This effect has also been observed in a gated monolayer19,20 and doped bulk 18 and ultrathin films of other materials.29,30 Several mechanisms could be responsible for superconductivity exceeding the Pauli limit, including Ising-type superconductivity28 or a diminishing of the effective -factor due to strong spin–orbit coupling.31 Further studies are required to resolve this.
The London penetration depth is another important characteristic of a superconductor. While RF-measurements are a common way of measuring the penetration depth,32 it can also be estimated by measuring the critical current of a Josephson junction in a magnetic field . A Josephson junction placed in a perpendicular magnetic field demonstrates an oscillating critical current. One period of the oscillations corresponds to the magnetic flux quantum through the effective area of the junction , where and are the junction’s width and length, respectively, and is the magnetic field penetration depth;27 see Fig. 4(a). For a bulk superconductor , but for a thin film superconductor with thickness , the penetration depth is a function of the thickness .32 In the limit of small thickness , the previous expression is equal to the Pearl’s penetration depth .
Figure 4(b) demonstrates several examples of dependencies for Josephson junctions in where the superconducting regions on top of Pd play the role of superconducting contacts. These dependencies have a SQUID-like character due to hinge states11 with a rapidly decaying Fraunhofer contribution due to the Fermi-arc surface states33,34 or the bulk conductivity. The SQUID-like oscillations with many visible periods allow one to determine the period with a high precision. For junctions 1 and 2, with m and m, we obtain a period of mT. This period corresponds to m and a penetration depth of nm. For junction 3 ( nm, m), we obtain mT, yielding nm. The obtained penetration depth is much larger than the thickness of the flakes nm (approximately 10-layer thick) so that the extracted penetration depth is given by Pearl’s limit . Using this expression, we estimate the London penetration depth to be nm. The ratio between the London penetration depth and the coherence length is , suggesting type-II superconductivity.27
The obtained London penetration depth is comparable to typical values for metals and is surprisingly small considering the semimetalic nature of . This additionally speaks against the presence of disorder in our samples since the penetration depth is expected to be higher in dirty superconductors.27 An estimate of the superconducting electron density yields a quite high value cm, where is the effective mass of the electrons in .35 This value is higher than the typical carrier densities in cm36 and corresponds to a density per single layer of cm, which is an order of magnitude higher than the electron density in monolayer with gate induced superconductivity19,20 but comparable to the predicted optimal charge carrier density.37 Furthermore, a large superconducting carrier density implies a high density of states at the Fermi level cm eV, which is a signature of flatbands.
The emergence of superconductivity at the interface of two non-superconducting materials is quite surprising despite the fact that it has been observed previously in different Weyl and Dirac semimetals.38–42 While the underlying mechanism for the superconductivity is unclear, in our case of the /Pd interface, several material specific reasons for the superconductivity could be proposed. First, the structural change at the interface could lead to the superconductivity similar to the pressure induced superconductivity in .16,17 Second, electron doping from palladium43 could create a superconducting state similar to what was seen in monolayer19,20 or bulk doped .18 The latter seems to be the more probable explanation since the in-plane critical field exceeds the Pauli limit, which has been observed in doped 18–20 but not in the pressure induced superconductivity.16,17 Another possibility is interdiffusion of Pd and Te with a formation of superconducting , which has been recently reported in samples with Pd deposited on .44 We think that this mechanism is unlikely in our case since and Pd are merely placed in contact by stacking and the samples were never heated above 180 C.
Even more intriguing is the possibility of the flatband superconductivity,45,46 as suggested by the small Fermi velocity and high density of states at the Fermi level. Flatbands are ubiquitous in van der Waals (vdW) heterostructures. For example, high carrier density combined with a low Fermi velocity has been observed close to van-Hove singularities in the band structure of superlattices formed in hBN-encapsulated graphene.47 Also, the presence of the flatbands is known to stimulate superconductivity.26,48,49
Establishing the presence of the flatband superconductivity at the /Pd interface and understanding the reasons for it will require further experiments, but some explanations could be outlined already. Flatband superconductivity can be formed as a result of a topological phase transition due to strain at the interface.7,46 Furthermore, flatband superconductivity has been observed in vdW systems with a Moiré pattern.26 This possibility is feasible since the mismatch between the lattice constant in Pd (0.389 nm50) and the a-axis lattice constant in (0.349 nm17) is only about 10%. However, we deem this scenario unlikely since Moiré patterns strongly depend on the mutual orientation of the lattices, while we observe superconductivity in multiple samples without any intentional alignment of the lattices.
An alternative explanation for the experimental data could be a multiband superconductivity in our samples. In this situation, a sublinear dependence of and an exceeding Pauli limit by could be expected in the dirty limit of the superconductivity,51 which seems not to be the case in our samples.
We demonstrate the emergence of superconductivity at the interface between type-II Weyl-semimetal and normal metal palladium. Studying the transport properties in a magnetic field and at different temperatures, we deduce the key parameters that characterize the superconducting state, including the critical temperature , the coherence length , and the London penetration depth . The combined set of parameters hint to a possible origin of superconductivity being due to the formation of flatbands. Moreover, the measured in-plane critical field exceeds the Pauli limit, suggesting non-trivial superconducting pairing. The coexistence of superconductivity with topological states makes a promising platform for topological superconductivity and applications for quantum computing.
We thank A. Baumgartner for helpful discussions. A.K. was supported by the Georg H. Endress foundation. This project has received further funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 787414 TopSupra), by the Swiss National Science Foundation through the National Centre of Competence in Research Quantum Science and Technology (QSIT), and by the Swiss Nanoscience Institute (SNI). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan and the CREST (JPMJCR15F3), JST. D.G.M. and J.Y. acknowledge support from the U.S. Department of Energy (U.S. DOE), Office of Science—Basic Energy Sciences (BES), Materials Sciences and Engineering Division. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative (Grant No. GBMF9069).