Point contact Andreev reflection studies of a non-centro symmetric superconductor Re6Zr

Re6Zr, a non-centrosymmetric superconductor is an interesting system as recent experimental evidence suggests that the superconducting state breaks time reversal symmetry. This implies a mixing of spin singlet-triplet states leading to a complex order parameter in this system. Here, we report point contact Andreev Reflection (PCAR) measurements on a single crystal of Re6Zr (superconducting transition temperature (Tc) = 6.78 K). We observe multiple gap features in the PCAR spectra which depends on the type of tip and contact. Spectral features appear at voltages 1.0 ± 0.1 mV, 0.75 ± 0.05 mV and 0.45 ± 0.1 mV suggesting that there are at least more than one band contributing to superconductivity. However, strong surface inter-band scattering is possibly responsible for the uncertainty in observing them together distinctly in a single contact in the PCAR measurements. Interestingly, the bulk gap (Δ  = 1.95kBTc = 1.1 meV) is occasionally observed in PCAR spectra, mostly with ferromagnetic tips. The gap features associated with the other two smaller gaps disappear at the bulk Tc. In addition, no anisotropy in the upper critical field was observed. Our results suggest an unconventional superconducting order in this compound: Multiband singlet states dominated by inter-band pairing which break the time reversal symmetry or singlet mixed with triplet states.

suggested as evidence for strong spin singlet-spin triplet mixing 19 . Since singlet triplet mixing is expected to give a rise to a strongly anisotropic gap function, it is important to obtain detailed information of the superconducting gap symmetry on high quality single crystals.
Point contact Andreev reflection (PCAR) spectroscopy 20 is a powerful tool to investigate the superconducting gap structure in superconductors. In this technique, a ballistic contact is established by bringing a sharp normal metal tip in contact with the surface of the superconductor. The dependence of the differential conductance (G(V) = dI/dV) as a function bias voltage (V) of such a contact is sensitive to the magnitude and symmetry of the superconducting gap function. Consequently, G(V)-V spectra provides valuable insight on the gap symmetry and its temperature evolution in unconventional superconductors.

Results
Sample Characterization. The Laue diffraction measurement performed on the single crystal used for the present study reveals sharp Bragg spots consistent with growth along the principal axis of the crystal ( Fig. 1(b)). XRD data (see Fig. S1 of Supplementary Information) along with the Rietveld refinement indicates the crystal was single phase, forming the α-Mn cubic structure. Besides, EDAX confirmed the atomic ratio to be approximately 6:1. Figure 1(a) shows resistivity versus temperature (ρ − T) measurements at zero magnetic field. We observe a sharp superconducting transition with T c ~ 6.78 K and a normal state resistivity ~200 μΩ-cm at 10 K (See Inset of Fig. 1(a)). The mean free path was estimated to be low 21 . Since Re 6 Zr is a very hard material it is difficult to reduce the intrinsic defects such as vacancies, dislocations by annealing. Scattering from these defects is the likely cause of the low mean free paths. The temperature variation of upper critical field (H c2 ) is determined from the temperature at which the resistance is 90% of the normal state resistance in fixed magnetic fields (Inset of Fig. 1(c) shows the R-T scans in different magnetic fields). At 1.4 K, H c2 ~ 11 T (see Fig. 1(c)) consistent with earlier reports on polycrystalline samples 19 as well as single crystals 21 . Point Contact Andreev Reflection (PCAR) studies. PCAR studies were carried out on the Re 6 Zr single crystal with different normal metal and ferromagnetic tips. To obtain spectroscopic information from PCAR measurements one has to ensure that the point contact diameter (d) is in the ballistic or the diffusive regime, i.e. d < l in , where l in is the inelastic mean free path 22 . The size of the point contact is often estimated from the contact resistance using the Sharvin formula. However, this method can be misleading since the microscopic structure of the contacts (such as the existence of multiple parallel contacts) is difficult to know. On the other hand, it has been shown that diagnostics of the spectra can be used to determine if the contacts are in the ballistic or diffusive regime. When the contact is in the thermal regime (d >> l in ) it has been shown that the spectra exhibit pronounced dips at high bias related to the critical current of the superconductor 23 . Spectra showing pronounced www.nature.com/scientificreports www.nature.com/scientificreports/ dips at high bias were thus discarded for quantitative analysis ( Fig. 2(b) shows some representative spectra analyzed in this work upto high bias showing no features related to heating). For most contacts, the contact resistance, R c was in the range of 0.5 to 5 ohm which would give the contact diameter from the Sharvin resistance formula as 10-50 nm 22,24 . Though we can completely rule out the contacts reported in this work to be in thermal regime based on the spectra obtained, there could be some contacts in the diffusive regime as well (a consequence of the low mean free paths in the sample which results in broadened PCAR spectra) from which we can still get energy resolved information 25 . In Fig. 2(c-e) we show representative G(V)-V spectra for three different contacts recorded at temperatures below 2 K. All the spectra display multiple gap features. For the spectrum shown in Fig. 2(c) prominent gap features are seen at bias voltage ±0.72 mV (referred to V 2 ) and ±1.07 mV(referred to V 3 ). In addition symmetric very small humps are seen at voltages ± 0.47 mV (referred to V 1 ). Similarly, for the spectrum shown in Fig. 2(d) symmetric peaks are observed at voltages ±0.80 mV and ±0.49 mV and for the spectrum in Fig. 2(e) at voltages ±1.05 mV and ±0.45 mV. This clearly indicates that multiple gaps contribute to superconductivity. To probe this further, more statistics was obtained by repeating the measurements with different contacts and also different tips. (Some of the spectra are shown in Fig. S2 of the Supplementary Information). Interestingly, www.nature.com/scientificreports www.nature.com/scientificreports/ for some contacts only the gap feature at V 1 ∼ 0.40 mV was seen distinctly ( Fig. S2(a,b)). For some only the gap feature at V 2 ∼ 0.7 mV was seen ( Fig. S2(c,d)) while for some other contacts features at both V 1 = ±0.4 mV and V 2 = ±0.7 mV were seen together ( Fig. S2(e,f)). The gap feature at V 3 = ±1.05 mV was observed very rarely ( Fig. S2(g,h)) and mostly with ferromagnetic tips like Ni and Fe indicating it to be direction dependent and spin sensitive. This feature corresponds to the bulk gap (Δ = 1.95k B T c = 1.1 meV) in Re 6 Zr 19 . The observation of the multiple gap features in Re 6 Zr indicates that more than one energy band contributes to superconductivity, a situation similar to multi-band superconductivity observed in MgB 2 20 or other NCS systems like LaNiC 2 26 , BiPd 7 , Nb 0.18 Re 0.82 7 etc. To obtain quantitative information we fit the spectra showing distinctly a single gap feature with the Blonder-Tinkham-Kalpwijk 27 (BTK) model with an isotropic gap according to which the current versus voltage characteristics of a N/S point contact is given by: is the density of states of the normal metal at Fermi level and v F is the Fermi velocity of the normal metal. A(E) is the Andreev reflection probability and B(E) is the normal reflection probability. From Eq. 1, G(V) (dI/dV) versus voltage (V) or the PCAR spectra can be simulated. The broadening arising from the finite lifetime (τ) of the superconducting quasi-particle can be incorporated in the BTK model by replacing Ε → Ε + iΓ which modifies the expression of A(E) and B(E) 28 which now become a function of Γ also. The parameter, Γ = τ h phenomenologically accounts for the finite lifetime of the superconducting quasiparticle 29 , provided Γ is much smaller than the characteristic superconducting energy scale (Δ). Γ in practice incorporates all non-thermal sources of broadening, e.g. distribution of superconducting energy gaps, instrumental broadening etc. We use Δ, the dimensionless barrier potential at the interface (z) and Γ as fitting parameters to fit the experimental data with the BTK model. We observe that the fits broadly capture the shape of the spectra giving a value of the gaps as Δ 1 = 0.53 meV, corresponding to V 1 (see Fig. 3(a)) and Δ 2 = 0.74 meV corresponding to V 2 ( Fig. 3(b)). For the spectrum shown in Fig. 3(b) we observe that the fit deviates significantly at bias voltages above the coherence peak. In order to fit the spectra in Fig. 3(c) and (d) showing two distinct gap features we use a two-band BTK model 30 , where, current (I), and hence G is a weighted sum from two transport channels [G 1 (V) and G 2 (V)], arising from two bands in the superconductor. In this model the normalized 2N are calculated using the generalized BTK formalism using the relative weight factors of the two gaps (w), superconducting energy gaps (Δ 1 and Δ 2 ), the barrier potentials (z 1 and z 2 ), and the broadening parameters (Γ 1 and Γ 2 ) as fitting parameters. We observe that the two-gap model with two isotropic gaps provide a good fit for the spectra shown in Fig. 3(c) and (d). Interestingly, the spectra shown in Fig. 3(a,b) show a marginally better fit with the two band model especially at high bias. From the two gap fits we obtain the two gaps as Δ 1 ~ 0.40 ± 0.1 meV, and Δ 2 ~ 0.76 ± 0.10 meV and the weightage (w) of the dominant gap being greater than 0.52. Γ1, Γ2 < 0.15 meV which depends on the contact. We believe that the primary source of spectral broadening here is from interfacial defects which varies from contact to contact. It is also important to note that in none of the spectra we observe any evidence of any zero bias conductance peak which is a characteristic feature associated with the presence of the Andreev bound state expected to be observed for NCS superconductors 1,31 .
We now investigate the temperature dependence of gaps Δ 1 , Δ 2 and Δ 3 by tracking the temperature dependence of the point contact spectra (Fig. 4(a),(c) and (d)). All PCAR spectra become featureless around T = 6.8 K indicating that the largest gap (Δ 3 ) closes at the bulk T c . The G(V)-V spectra of Fig. 3(b) showing distinctly the feature corresponding to the gap Δ 2 was fitted with the single gap BTK model at all temperatures (See Fig. 4(a)). As seen from Fig. 3(b), the fit with two gaps does not improve the quality of fit substantially at the lowest temperature and besides the value of Δ 2 obtained from both fits remains unchanged. The temperature variation of Δ 2 obtained from the fits is shown in Fig. 4(b). (We also plot the temperature variation of Γ obtained from the fits and observe that it is much lower than Δ 2 ). Δ 2 follows the temperature dependence from Bardeen-Cooper-Schriffer (BCS) theory and this gap also closes at T c . (We confirmed this by analyzing another contact showing predominantly the Δ 2 gap feature distinctly, see Fig. S3 of Supplementary Information). The G(V)-V spectra showing distinctly the feature corresponding to the gap Δ 1 for different temperatures are shown in Fig. 4(c). They could not be fitted with the single gap BTK model for all temperatures. Figure 4(e) shows the fit with one gap (Δ 1 ) and two gaps (Δ 1 and Δ 2 ) of the spectra at the lowest temperature. No substantial improvement is visible between the two fits. At higher temperatures, we believe that the small feature at V 3 corresponding to Δ 3 starts to dominate making it increasingly difficult to fit the spectra. Figure 4(d) shows the temperature dependence of the PCAR spectra where all the three gap features are distinctly resolved at the lowest temperature. We tried fitting the spectra at T = 1.6 K with two and three band BTK models where each gap is expected to be isotropic. However, neither gave a reasonable fit and the gap feature at V 3 = 1.05 mV was difficult to reproduce (see Fig. 4(f)). Thus, any spectra showing features corresponding to Δ 3 was difficult to fit at all temperatures using the isotropic BTK model.
To reconcile with the observation of different gaps from the PCAR spectra, it is important to check if there is any anisotropy in the superconducting properties for the NCS superconductor Re 6 Zr. We studied the angular dependence of the upper critical field (H c2 ) though resistivity (ρ) measurements in magnetic field (H) for different temperatures below T c . The ρ vs H plot at 3 K for different angles of the sample transport current to the magnetic field is shown in the inset of Fig. 5(a). The sample was rotated with respect to the axis of the magnetic field. H c2 was taken as the field at which the resistivity is 90% of the normal state value (shown by the dashed line in the inset). The phase diagram for angles between 0° to 90° are obtained from this measurement and is shown in Fig. 5(a). No substantial anisotropy was observed in H c2 . Furthermore, magnetic field dependence of Andreev spectroscopy was carried out for a few contacts at T = 2 K upto 11 Tesla (Representative spectra are shown in Fig. 5(b) and (d)). PCAR spectra became featureless at 11 T consistent with the measured H c2 value for Re 6 Zr from resistivity measurements. For spectra showing only one gap feature distinctly, the spectra could be fitted with the BTK model and Δ could be extracted from the fits. Δ decreased with H and appear to close at H c2 (See Fig. 5(c)) (Note: The voltage of the coherence peaks of the PCAR spectra show the same variation with H as Δ (see blue triangles in Fig. 5(c)). For spectra which showed two or three gap features at H = 0, on applying magnetic field, the features smeared out (See Fig. 5(d)) making it difficult to resolve the peaks associated with the individual gaps at higher fields. To see how the two coherence peaks associated with the two gaps, Δ 1 and Δ 2 shown in Fig. 5(d) vary with magnetic field, we plot the voltage corresponding to the coherence peaks in the spectra as a function of H in Fig. 5(e). Due to the broadening caused by the strong pair breaking effect of the magnetic field, it is difficult to make out from the spectra if magnetic field causes any collapse of the double-gap state.

Discussions
We now discuss the implication of these results. First, we explore the possibility of singlet-triplet mixing as conjectured from the observation of TRS breaking in μSR measurements in Re 6 Zr 19 . For a NCS, ASOC leads to a term of the form αg(k)·σ in the Hamiltonian, where α is the spin-orbit coupling constant, σ is the Pauli matrices, and the vector g(k), representing the orbital direction, obeys the antisymmetric property such that g(k) = −g(−k). The ASOC breaks the spin degeneracy, which leads to two bands characterized by ± helicities for which the spin eigen states are either parallel or antiparallel to g(k). The superconducting energy gap on both these bands will have singlet and triplet components. The system will therefore have two gaps defined on each of ASOC split bands, where Δ s and Δ t (k) are the spin singlet and spin triplet component of the gap function. Since Δ t (k) is strongly anisotropic and changes sign depending on k direction, a significant Δ t (k) component implies that both Δ ± k ( ) would be strongly anisotropic with a large distribution of gap amplitude over the Fermi surface. Re 6 Zr has a cubic symmetry and the crystal on which measurements were done was oriented along [100] direction. Since the sample does not cleave easily along any other plane, it was not possible to do directional www.nature.com/scientificreports www.nature.com/scientificreports/ PCAR on Re 6 Zr to check any anisotropy effect. However, by changing contacts through pressure it was possible to microscopically probe different k directions. In our experiments, we have observed that the gap feature at V 3 = 1.05 ± 0.05 meV was very sensitive to the contact as well as tip. It was observed more frequently with ferromagnetic tips indicating the presence of spin polarization. Moreover, in the spectra it was visible, its weight seemed to be low (a small feature) and it could not be fitted with the isotropic gap BTK model (see Fig. 4(e)). These observations could indicate that this gap feature is associated with the triplet gap and we conclude that in this scenario spin-singlet spin-triplet mixing if at all present is very small. This is also consistent with our  Fig. 3(b). The solid lines are the fit to the one-gap BTK model. (b) Temperature variation of Δ 2 (Red circles) and Γ (green diamonds) obtained from the fits of data in (a). The dashed black lines show the expected BCS temperature variation for the gap (c) Temperature evolution of the PCAR spectra for the contact shown in Fig. 3(a). The gap feature disappears at the bulk T c = 6.8 K. (d) Temperature dependence of the PCAR spectra for the contact shown in Fig. 2(c). Gap features disappear at the bulk T c = 6.8 K.(e) Fit of the data shown in (c) at the lowest temperature using the one band BTK fit (blue line, with best fit parameters Δ = 0.60 meV, z = 0.18, Γ = 1e-5 meV) and two band BTK fit (Red line, with best fit parameters of Δ 1 = 0.60 meV, z 1 = 0.18, Γ 1 = 0.025 meV, Δ 2 = 0.79 meV, z 2 = 0.18, Γ 2 = 0.025 meV). (f) Fit of the data shown in Fig. 2(c) using the two band BTK fit (blue line, with best fit parameters of Δ 1 = 0.33 meV, z 1 = 0.48, Γ 1 = 0.05 meV, Δ 2 = 0.76 meV, z 2 = 0.58, Γ 2 = 0.048 meV) and three band BTK fit (Red line, with best fit parameters of Δ 1 = 0.33 meV, z 1 = 0.48, Γ 1 = 0.05 meV, Δ 2 = 0.76 meV, z 2 = 0.58, Γ 2 = 0.048 meV, Δ 3 = 1.0 meV, z 3 = 0.25, Γ 3 = 0.6 meV).
www.nature.com/scientificreports www.nature.com/scientificreports/ observation of almost no anisotropy in H c2 . The small spin singlet-triplet mixing is also expected from the small band splitting due to ASOC (~30 meV) 16 calculated for this compound which is comparable to the ASOC spin splitting in Li 2 Pd 3 B where a fully gapped isotropic order parameter has been inferred from penetration depth measurements 32 . (In the isostructural NSC Li 2 Pt 3 B where penetration depth measurements provide evidence of large anisotropy and possible nodes in the gap function, the ASOC band splitting is ~200 meV). On the other hand, the spin singlet component of the gap function has contribution from two isotropic energy gaps (Δ 1 and Δ 2 ) which are present on two different Fermi surface pockets. The uncertainty in their observations in different spectra with different tips and contacts implies that there is strong inter-band scattering. It is also possible that these two gaps are surface sensitive and hence do not show up in bulk measurements like specific heat. Thus, the www.nature.com/scientificreports www.nature.com/scientificreports/ possible scenario which emerges is that there is unconventional superconductivity in Re 6 Zr with very weak spin singlet and spin triplet mixing and presence of multiband superconductivity.
A second possibility of the interpretation of our data could be that all the three gaps are completely isotropic (as evidenced from specific heat measurements of a fully gapped state) and Re 6 Zr behaves as a conventional multiband superconductor. It is worthwhile to note that the band structure of Re 6 Zr reveals there are multiple bands crossing the Fermi level and that some of these bands are strongly split by spin-orbit coupling 16 . This is consistent with our observation of having multiple bands contributing to superconductivity. The pertinent question which follows is, how can one reconcile these results with the observation of TRS breaking in μSR measurements? To answer this question two possible scenarios have been suggested where a multiband superconductor can break TRS. The first scenario has been proposed for a multiband superconductor with high symmetry 33 such as the cubic structure of Re 6 Zr. In such a system, TRS can get broken even with conventional s-wave singlet pairing. Under certain conditions, when the Coulomb repulsion between two Fermi surface pockets dominate, the relative phase between one pocket and another will be non-zero. Such a superconducting state will break TRS, allowing antiferromagnetic domains and fractional vortices to appear. A second scenario has been proposed in the context of TRS breaking in LaNiC 2 and LaNiGa 2 34 . Here pairing occurs between electrons of the same spin but on different orbitals. This gives rise to a novel non-unitary triplet state, where the gap symmetry continues to have even parity. In this case, TRS breaking triplet superconductivity can be realized even when the Fermi surface remains fully gapped. This model of a fully-gapped triplet pairing has also been used to explain the behavior of iron pnictides 35 . Distinguishing between these two scenarios would require a detailed knowledge of the Fermi surface structure properties in this compound.

Conclusions
In summary, PCAR spectra on a Re 6 Zr single crystal shows three gap features. One of these gap features at a voltage of 1.0 ± 0.1 mV corresponding to the bulk gap (Δ(0) = 1.95k B T c ) as observed in specific heat measurements appear to be tip sensitive and has a low spectral weight. Our results conclusively show that one of the gaps (0.75 ± 0.05 meV) is isotropic. Our measurements suggest that the superconducting state has unconventional pairing. Two possible scenarios can be invoked to understand the results. (1) the bulk gap is spin triplet with a very small spin-singlet-triplet mixing and the isotropic spin singlet gaps are surface sensitive and are associated with different Fermi surface sheets. (2) Re 6 Zr is a multiband superconductor with strong inter-band scattering and a fully gapped isotropic superconducting state. In this model, the TRS is broken at the superconducting transition, due to the presence of non-unitary triplet pairing where pairing occurs between electrons with same spin but on different orbitals. Thus, our experiments reiterate an unusual superconducting state in Re 6 Zr which breaks the time reversal symmetry: Spin singlet-triplet mixing or multiband singlet states driven by inter-band pairing. Validation of these scenario will require further theoretical and experimental studies.

Methods
In this article, we report PCAR measurements on a high quality single crystal of Re 6 Zr. The single crystal was grown using Czochralski crystal pulling method using a tetra-arc furnace under argon atmosphere, starting from a polycrystalline Re 6 Zr button. Polycrystalline sample of Re 6 Zr was prepared by arc melting stoichiometric quantities of Re (99.99%, Alfa Aesar) and Zr (99.99%, Alfa Aesar) on a water-cooled copper hearth in a high-purity Ar atmosphere also in a tetra-arc furnace. The button was melted several times to ensure phase homogeneity. The observed weight loss during the melting was negligible. The phase purity of the polycrystalline button was checked by powder X-ray diffraction. In the Czochralski growth, a tungsten rod was used as the seed, and the crystal was pulled at the rate of 30-50 mm/h. For PCAR measurements we establish contacts by mechanically engaging a fine normal metal or ferromagnetic tip on [100] surface of the Re 6 Zr single crystal inside a conventional 4 He cryostat ( Fig. 2(a)). The differential conductance, G(V), is obtained by numerically differentiating the current versus voltage (I-V) characteristics recorded at fixed temperatures and magnetic fields to give the PCAR spectra.

Data Availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.