Abstract
In nonmagnetic bulk materials, inversion symmetry protects the spin degeneracy. If the bulk crystal structure lacks a centre of inversion, however, spin–orbit interactions lift the spin degeneracy, leading to a Rashba metal whose Fermi surfaces exhibit an intricate spin texture. In superconducting Rashba metals a pairing wavefunction constructed from these complex spin structures will generally contain both singlet and triplet character. Here we examine the possible triplet components of the order parameter in noncentrosymmetric BiPd, combining for the first time in a noncentrosymmetric superconductor macroscopic characterization, atomicscale ultralowtemperature scanning tunnelling spectroscopy, and relativistic firstprinciples calculations. While the superconducting state of BiPd appears topologically trivial, consistent with Bardeen–Cooper–Schrieffer theory with an order parameter governed by a single isotropic swave gap, we show that the material exhibits Diraccone surface states with a helical spin polarization.
Introduction
In noncentrosymmetric superconductors, the spin–orbit interactions can give rise to a mixing of spinsinglet and spintriplet pairing components^{1,2,3} and to a topologically nontrivial superconducting phase^{4,5}, which is characterized by protected Majorana surface states^{5,6,7,8,9}. While in several materials indications for a triplet component of the order parameter have been detected, unambiguous evidence remains scarce. Scanning tunnelling microscopy (STM) and spectroscopy (STS) can help to identify the symmetry of the order parameters^{10}, however, it requires highquality surfaces, which have not previously been obtained for any noncentrosymmetric superconductor.
The noncentrosymmetric compound BiPd^{11,12,13}, which becomes superconducting below T_{c}≃3.8 K (refs 14, 15, 16, 17), offers the opportunity to study the interplay of the aforementioned spin–orbit coupling (SOC) effects with superconductivity. The large atomic spin–orbit interaction of the heavy element Bi results in a sizeable Rashbalike spin splitting of the calculated bulk bands and, moreover, may give rise to nontrivial band topologies and unconventional superconducting pairing symmetries. Here the term Rashba is used very broadly to denote any antisymmetric SOC that leads to band dispersions with nontrivial spin textures and a dominant linear term at timereversal invariant momenta of the Brillouin zone (BZ, a classification of spin–orbit interactions in terms of pointgroup symmetries is discussed in ref. 18). This may give rise to nontrivial band topologies and unconventional superconducting pairing symmetries. Recent pointcontact Andreevreflection measurements have detected zerobias anomalies and signs of multigap superconductivity^{16}. The former have been interpreted as evidence for Majorana midgap states predicted in topological superconductors.
In the following, we study the interplay of spin–orbit interactions with superconductivity in BiPd using scanning tunnelling spectroscopy and relativistic firstprinciples calculations. Tunnelling spectroscopy, performed on atomically flat surfaces, shows that superconductivity in BiPd is entirely consistent with conventional swave pairing. While the superconducting state of BiPd is topologically trivial, our electronic structure calculations show that the large atomic SOC of Bi alters the normalstate band topology of BiPd, leading to the appearance of a Diraccone surface state. The existence of these Dirac surface states is confirmed by our scanning tunnelling measurements of the surface density of states.
Results
Topographic images and surface terminations
αBiPd has a noncentrosymmetric monoclinic crystal structure with space group P2_{1} (refs 11, 12, 13). As shown in Fig. 1a the unit cell contains 16 atoms with four inequivalent sites for each element. The structure is characterized by two double layers stacked along the b axis, related by a 180° screw symmetry. The crystal cleaves preferentially along (010) planes between the Bi layers; due to the lack of inversion symmetry, the (010) and surfaces (facing up and down, respectively, in Fig. 1a) are not equivalent. Topographic STM images obtained on the samples cleaved in cryogenic vacuum show atomically flat terraces up to hundreds of nanometres in lateral size separated by steps (Fig. 1b). Line cuts show a step size of ~5.3 Å between terraces (Fig. 1c), corresponding to half the height of the unit cell along b^{13}. In atomic resolution images, we observe two different kinds of surfaces. Figure 1d shows a twin boundary between the two. By comparing the surface structures and the atomic corrugations (Fig. 1e) with the expected Bi terminations, we deduce that the surfaces shown in Fig. 1d correspond to (010) on the left and on the right. The main structural difference between the two terminations is the displacement of the atoms in the surface plane: the termination exhibits predominantly lateral displacement of Bi atoms at the surface, whereas for the (010) terminated surface, there is little lateral distortion but substantial vertical buckling of the neighbouring Bi atoms (Supplementary Fig. 1). The atomic resolution indicates highquality surfaces free from reconstruction, making this the first noncentrosymmetric superconductor suitable for singleparticle spectroscopies.
Surface states with Rashbalike spin splitting
The spatial and energy dependence of the local density of states was systematically measured using differential conductance (dI/dV) spectroscopy. While the spectra do not vary significantly as a function of STM tip position, they display pronounced features in their energy dependence. A typical differential conductance measurement covering a large energy range recorded at T~1.5 K is shown in Fig. 2a,b. The spectra exhibit a sharp peak at ~0.4 V, which, by comparison with band structure calculations (Fig. 2c,d), we associate with a van Hove singularity due to the dispersion of a Dirac surface state near the point of the surface BZ. For a parabolic twodimensional band with Rashbalike spin splitting, the width of the peak in the density of states, here 24 mV, is an estimate for the spin–orbit splitting^{19}. In Fig. 2c,d, we show the projected bulk bands together with the dispersion of the surface states near E_{F} of (010) and terminated surfaces obtained from a slab calculation along highsymmetry lines of the surface BZ of BiPd. A Diraccone surface state appears at the point within the projected band gap opened by SOC (see Supplementary Figs 2 and 3). This suggests that spin–orbit interactions change the band topology near the timereversal invariant momentum Γ from trivial to nontrivial. The lower branch of the Dirac state is almost completely buried inside the four bulk p_{1/2} bands and the Dirac point, which is protected by timereversal symmetry, lies just above the top of these bands. Due to the absence of inversion symmetry, the shape of the Dirac states at the top and bottom sides of (010) BiPd are inequivalent. That is, the Dirac state at the surface is shifted downwards by ~75 meV as compared with that at the (010)terminated surface. Similarly the spin textures of the Dirac states at opposite sides are expected to be dissimilar and not simply related by symmetry (Fig. 2c,d). As a result, the Dirac electrons of these surface states fractionalize into two inequivalent halves at the top and bottom sides of BiPd.
Properties of the superconducting state
The next question is whether the Rashbalike spin–split band structure of BiPd manifests exotic superconductivity when cooled. We have characterized the superconducting state in BiPd by ultralowtemperature STM and STS, transport, specific heat and magnetic susceptibility. Resistivity and magnetic susceptibility (Supplementary Fig. 4a, b), which are in good agreement with previously published results ^{15,16,17,20}, as well as specific heat (Fig. 3a) show that BiPd becomes superconducting below T_{c}≃3.8 K (Supplementary Note 2). The specific heat data reveal a slightly larger discontinuity at T_{c} than expected from Bardeen–Cooper–Schrieffer (BCS) theory, while the lowtemperature behaviour indicates a full, nodeless gap. Most importantly, the measurements reveal a significant discrepancy between the upper critical field H_{c2} determined from specific heat and transport measurements, as can be seen in Fig. 3a,b. While the magnetic fielddependent resistivity at 1.4 K (Fig. 3b) shows three distinct transitions at 0.1, 0.17 and 0.7 T, the temperature dependence of the specific heat (Fig. 3a) shows no indication of bulk superconductivity at magnetic fields of 0.07 or 0.1 T. This indicates that the transitions observed in the resistance at 0.17 and 0.7 T do not represent bulk behaviour. We note that in ref. 15 the upper critical field based on transport measurements alone was reported as 0.7 T, suggesting a similar nonbulk contribution to the electrical transport may have been present also in those samples. To elucidate the nature of the superconducting order parameter and confirm this result, we have performed STS at temperatures down to 15 mK.
Highresolution tunnelling spectroscopy within a narrow energy range of ±1.25 mV around E_{F} as shown in Fig. 3c displays a fullygapped superconducting density of states with sharp coherence peaks. We have fitted a Dynes equation for a single isotropic gap to the tunnelling spectrum, using an effective temperature T_{eff}=130 mK (as determined previously to be the energy resolution of the experiment^{21}) and an adjustable broadening parameter Γ accounting for impurity scattering, finite quasiparticle lifetime and a possible anisotropy of the order parameter. The fit to the spectrum in Fig. 3c yields a gap with amplitude Δ=601 μeV and Γ=12 μeV. The tunnelling spectra and hence the gap size exhibit very little spatial variation, even across step edges. The temperature dependence of the superconducting gap shows the disappearance of the gap at temperatures close to the bulk transition temperature T_{c}, with temperature dependence in excellent agreement with the BCS theory (Fig. 3d). As opposed to pointcontact spectroscopy^{16}, our data show no evidence for zerobias peaks when measuring with nonsuperconducting tips.
Tunnelling spectra (Fig. 4a) at 10 mK reveal a complete suppression of the superconducting gap in fields of only 70 mT and indicate an upper limit of the lower critical field H_{c1} of about 20 mT. The field dependence of the gap size, as shown in Fig 4b, confirms that the gap vanishes at an upper critical field H_{c2}≃75 mT (extrapolated to T=0 K), which is consistent with the magnetization measurements (compare Supplementary Note 2 and ref. 20) and specific heat. From the tunnelling spectra we extract a ratio of gap size to critical temperature of Δ_{0}/(k_{B}T_{c})≈1.9, slightly larger than the weak coupling BCS prediction of 1.764. Recalculating the behaviour of the specific heat with the experimental gap magnitude results in significantly improved agreement with experiment, confirming that specific heat detects the same superconducting gap size as tunnelling spectroscopy (Fig. 3a, see also Supplementary Note 3 and Supplementary Fig. 5). The level of quantitative agreement among these techniques confirms that tunnelling in BiPd is sensitive to the bulk superconducting properties.
Imaging of vortex cores and vortex bound states
In typeII superconductors with nontrivial normalstate band topology, Majorana zeroenergy modes can emerge in vortex cores even in the absence of unconventional pairing symmetries^{22,23}. To test this possibility, we performed extensive fielddependent STM measurements on the vortex state of BiPd. Figure 4c shows a spatial map of the differential conductance at zero bias, revealing a vortex pinned at a step edge. At the centre of the vortex core we detect a strong zerobias peak in the differential conductance (Fig. 4d), which we attribute to Carolide Gennes–Matricon (CdGM) bound states, of which zeroenergy Majorana states are a special case^{24,25,26}. These vortex bound states decay outside the vortex core on the scale of the coherence length ξ_{0}. From the radial dependence of the spectra (see Fig. 4e), ξ_{0} is estimated to be ~60 nm, in good agreement with the value obtained from the Ginzburg–Landau expression (Φ_{0} being the magnetic flux quantum h/(2e)), reconfirming the extrapolated H_{c2}. To distinguish possible zeroenergy Majorana modes from ordinary CdGM states with finite energy, a resolution on the order of the level spacing ε_{0}=Δ^{2}/E_{F} of the CdGM states is required. For BiPd, we estimate ε_{0}≃100 neV, which cannot be resolved due to limitations of the energy resolution of the instrument, but will also likely be exceeded by the intrinsic broadening of the quasiparticle states. Observation of Majorana modes may require a superconductor with a larger pairing gap.
Discussion
Our tunnelling spectra, their temperature and magnetic field dependence together with the specific heat data strongly suggest that superconductivity in BiPd behaves rather conventionally, consistent with BCS predictions for a nearly isotropic swave order parameter and dominant spinsinglet pairing. A sizeable triplet pairing component, which was recently discussed in the context of topological superconductivity^{16,27}, is expected to lead to zerobias anomalies due to Majorana surface states. From our data there is no evidence of a finite surface density of states at zero energy in zero field. While the transition seen in transport at fields >0.5 T (Fig. 3b) is consistent with a previously reported critical field of H_{c2}≈0.6 T (ref. 15), STM data and especially specific heat are not. Both yield a substantially smaller critical field H_{c2}~75 mT, which is also consistent with the vortex core size. This suggests that transport at magnetic fields larger than 75mT and small currents is governed by superconductivity near defects. If the anomalies seen in transport were due to surface effects as might be expected for topological superconductivity, they should leave strong signatures in tunnelling spectra. Point defects or impurities appear unlikely candidates, because a rather large density would be required to dominate the transport. Therefore the more likely explanation is that superconductivity near extended defects, for example twin boundaries, is more robust against magnetic field than in the bulk. In fact, our resistivity measurements come into agreement with other techniques if highdrive currents are used (Supplementary Fig. 4), suggestive of the suppression of critical currents along filamentary pathways. Enhanced critical fields near twin boundaries in noncentrosymmetric superconductors have recently been posited to occur due to magnetoelectric effects^{28}, while the formation of orbital currents would be suppressed by scattering at the boundaries or by the limited spatial extent of the superconductivity nucleated at such a defect.
In summary, these first temperature and fielddependent tunnelling spectra on a noncentrosymmetric superconductor show that BiPd is well described with a single gap, an isotropic swave order parameter and the predictions of BCS theory, confirmed by bulk measurements. Our results suggest that the coupling mechanism that mediates Cooper pairing in BiPd favours swave superconductivity, leading to a negligible triplet component^{29}. While the superconducting phase of BiPd appears to be topologically trivial, its normalstate band structure exhibits nontrivial features. By means of electronic structure calculations, we have shown that the large atomic SOC of Bi alters the band topology near the Γ point, leading to the appearance of a Diraccone surface state, the existence of which is confirmed by our STM measurements of the surface density of states. Our results highlight the importance of a characterization both at the macroscopic and microscopic scales to establish a complete picture of the physical properties, while the ability to apply STM to noncentrosymmetric superconductors will open new avenues of exploration in this exciting field.
Methods
Crystal growth
Large single crystals of BiPd were grown by a modified Bridgman–Stockbarger technique. Stoichiometric quantities of Bi (Alfa Aesar, 99.999%) and Pd (Degussa, 99.95%) were sealed under vacuum in a quartz ampoule having a conical end, then suspended in a vertical tube furnace. While maintaining a temperature gradient over the length of the quartz tube, the furnace was heated well above the melting point to ensure homogeneity. BiPd melts congruently at 600 °C. The ampoule was subsequently cooled through the melting temperature at a rate of 0.2 °C h^{−1}, then cooled through the α–β phase transition at 189 °C at 0.5 °C h^{−1} to maximize the domain size of the lowtemperature α phase. The resulting crystal readily cleaves perpendicular to the unique monoclinic b axis. Analysis of the composition by energy dispersive Xray spectroscopy suggests a bismuth deficiency of 1–2%, comparable to the technique’s uncertainty. Additional characterization is presented in Supplementary Fig. 4 and Supplementary Note 2.
Electronic structure calculations
The electronic structure of BiPd was obtained by a fully relativistic linear muffintin orbital calculation^{30,31} using the experimental crystal structure of ref. 13. Relativistic effects, including spin–orbit interactions, were fully taken into account by solving the fourcomponent Dirac equation inside each atomic sphere. The latter is crucial to obtain accurate results for the p_{1/2} bands of heavy elements such as Bi^{32}. Figure 2c,d show a sketch of the electronic structure, the full calculations are shown in Supplementary Figs 2 and 3 and Supplementary Note 1.
All band structure calculations were performed using the inhouse PY LMTO computer code as described in ref. 31. The code is available on demand.
STM measurements
All experiments were performed using a homebuilt STM, operating in cryogenic vacuum at temperatures down to 10 mK and in magnetic fields up to 14 T (ref. 21). Singlecrystal samples of BiPd were cleaved in situ at low temperatures. We used STM tips cut from a platinum–iridium wire. Bias voltages were applied to the sample with the tip at virtual ground. Differential conductance spectra were recorded through a standard lockin technique with frequency f=433 Hz.
Additional information
How to cite this article: Sun, Z. et al. Dirac surface states and nature of superconductivity in Noncentrosymmetric BiPd. Nat. Commun. 6:6633 doi: 10.1038/ncomms7633 (2015).
References
 1
Bauer, E. & Sigrist, M. NonCentrosymmetric Superconductors: Introduction and Overview, vol. 847, Lecture Notes in Physics Springer Berlin (2012) .
 2
Yip, S. Noncentrosymmetric superconductors. Ann. Rev. Cond. Matt. Phys. 5, 15–33 (2014) .
 3
Bauer, E. et al. Heavy Fermion superconductivity and magnetic order in noncentrosymmetric CePt3Si. Phys. Rev. Lett. 92, 027003 (2004) .
 4
Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B 78, 195125 (2008) .
 5
Sato, M. & Fujimoto, S. Topological phases of noncentrosymmetric superconductors: edge states, Majorana Fermions, and nonAbelian statistics. Phys. Rev. B 79, 094504 (2009) .
 6
Iniotakis, C. et al. Andreev bound states and tunneling characteristics of a noncentrosymmetric superconductor. Phys. Rev. B 76, 012501 (2007) .
 7
Vorontsov, A., Vekhter, I. & Eschrig, M. Surface bound states and spin currents in noncentrosymmetric superconductors. Phys. Rev. Lett. 101, 127003 (2008) .
 8
Tanaka, Y., Mizuno, Y., Yokoyama, T., Yada, K. & Sato, M. Anomalous Andreev bound state in noncentrosymmetric superconductors. Phys. Rev. Lett. 105, 097002 (2010) .
 9
Sato, M. & Fujimoto, S. Existence of Majorana Fermions and topological order in nodal superconductors with spinorbit interactions in external magnetic fields. Phys. Rev. Lett. 105, 217001 (2010) .
 10
Hanaguri, T. et al. Coherence factors in a highT c cuprate probed by quasiparticle scattering of vortices. Science 323, 923–936 (2009) .
 11
Zhuravlev, N. Structure of superconductors. X thermal, microscopic, and xray investigation of the bismuthpalladium system. Zh. Eksp. Teor. Fiz 5, 1064–1072 (1957) .
 12
Bhatt, Y. & Schubert, K. Kristallstruktur von PdBi.r. J. LessCommon Met. 64, P17–P24 (1979) .
 13
Ionov, V. M. et al. Anisotropy of physical properties and crystal structure of PdBi in the interval 293–570K. Sov. Phys. Crystallogr. 34, 496–499 (1989) .
 14
Kheiker, D., Zhdanov, G. & Zhuravlev, N. Xray investigation of the structure of BiPd. Zh. Eksp. Teor. Fiz 25, 621–627 (1953) .
 15
Joshi, B., Thamizhavel, A. & Ramakrishnan, S. Superconductivity in noncentrosymmetric BiPd. Phys. Rev. B 84, 064518 (2011) .
 16
Mondal, M. et al. Andreev bound state and multiple energy gaps in the noncentrosymmetric superconductor BiPd. Phys. Rev. B 86, 094520 (2012) .
 17
Matano, K. et al. NMR and NQR studies on noncentrosymmetric superconductors Re7B3, LaBiPt, and BiPd. J. Phys. Soc. Jpn 82, 084711 (2013) .
 18
Samokhin, K. Spinorbit coupling and semiclassical electron dynamics in noncentrosymmetric metals. Ann. Phys. 324, 2385–2407 (2009) .
 19
Ast, C. R. et al. Local detection of spinorbit splitting by scanning tunneling spectroscopy. Phys. Rev. B 75, 201401 (2007) .
 20
Joshi, B., Thamizhavel, A. & Ramakrishnan, S. Probing anisotropy in a new noncentrosymmetric superconductor BiPd. JPS Conf. Proc. 3, 015010 (2014) .
 21
Singh, U. R., Enayat, M., White, S. C. & Wahl, P. Construction and performance of a dilutionrefrigerator based spectroscopicimaging scanning tunneling microscope. Rev. Sci. Instr. 84, 013708 (2013) .
 22
Qi, X.L. & Zhang, S.C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011) .
 23
Hosur, P., Ghaemi, P., Mong, R. S. K. & Vishwanath, A. Majorana modes at the ends of superconductor vortices in doped topological insulators. Phys. Rev. Lett. 107, 097001 (2011) .
 24
Caroli, C., de Gennes, P. G. & Matricon, J. Bound Fermion states on a vortex line in a type II superconductor. Phys. Lett. 9, 307–309 (1964) .
 25
Hess, H. F., Robinson, R. B., Dynes, R. C., Valles, J. M. & Waszczak, J. V. Scanningtunnelingmicroscope observation of the Abrikosov flux lattice and the density of states near and inside a fluxoid. Phys. Rev. Lett. 62, 214–216 (1989) .
 26
Hess, H., Robinson, R. & Waszczak, J. Vortexcore structure observed with a scanning tunneling microscope. Phys. Rev. Lett. 64, 2711–2714 (1990) .
 27
Schnyder, A. P., Brydon, P. M. R. & Timm, C. Types of topological surface states in nodal noncentrosymmetric superconductors. Phys. Rev. B 85, 024522 (2012) .
 28
Aoyama, K., Savary, L. & Sigrist, M. Signatures of the helical phase in the critical fields at twin boundaries of noncentrosymmetric superconductors. Phys. Rev. B 89, 174518 (2014) .
 29
Samokhin, K. & Mineev, V. Gap structure in noncentrosymmetric superconductors. Phys. Rev. B 77, 104520 (2008) .
 30
Andersen, O. K. Linear methods in band theory. Phys. Rev. B 12, 3060–3083 (1975) .
 31
Antonov, V., Harmon, B. & Yaresko, A. Electronic structure and magnetooptical properties of solids Kluwer Academic Publishers (2004) .
 32
Macdonald, A. H., Pickett, W. E. & Koelling, D. D. A linearized relativistic augmentedplanewave method utilizing approximate pure spin basis functions. J. Phys. C 13, 2675–2683 (1980) .
Acknowledgements
We thank C. Ast and H. Benia for useful discussions, C. Stahl and E. Goering for help with magnetization measurements, and the Crystal Growth and Chemical Service Groups at MPIFKF for assistance. Z.S. acknowledges the financial support from Rubicon grant No. 680.50.1119 (NWO, NL), P.W. and A.M. from EPSRC. P.W. acknowledges the support from MaxPlanckSociety, DCP from IBSR009G1.
Author information
Affiliations
Contributions
D.C.P. grew samples and performed magnetization, specific heat and transport measurements, E.A.Y. and C.L. performed the transport measurements at low currents, Z.S., M.E. and A.M. performed the STM measurements, Z.S., M.E., A.M., A.P.S., and P.W. analysed data, A.Y. performed the DFT calculations, P.W., A.P.S. and D.C.P. wrote the manuscript. All authors discussed the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Figures 15, Supplementary Notes 13 and Supplementary References (PDF 1797 kb)
Rights and permissions
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Sun, Z., Enayat, M., Maldonado, A. et al. Dirac surface states and nature of superconductivity in Noncentrosymmetric BiPd. Nat Commun 6, 6633 (2015). https://doi.org/10.1038/ncomms7633
Received:
Accepted:
Published:
Further reading

Evidence for the coexistence of timereversal symmetry breaking and BardeenCooperSchriefferlike superconductivity in La7Pd3
Physical Review B (2021)

Prediction of superconductivity and topological aspects in singlelayer β−Bi2Pd
Physical Review B (2020)

Unconventional superconducting properties of noncentrosymmetric Re5.5Ta
Physical Review B (2020)

Fermi surface investigation of the noncentrosymmetric superconductor α PdBi
Physical Review B (2020)

RRuB2 (R=Y, Lu) , topological superconductor candidates with hourglasstype Dirac ring
Physical Review B (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.