Spectroscopic Evidence for the Superconductivity of Elemental Metal Y under Pressure

Very high applied pressure induces superconductivity with the transition temperature ($T_c$) exceeding 19 K in elemental yttrium, but relatively little is known about the nature of that superconductivity. From point-contact spectroscopy (PCS) measurements in a diamond anvil cell (DAC), a strong enhancement in the differential conductance is revealed near the zero-biased voltage owing to Andreev reflection, a hallmark of the superconducting (SC) phase. Analysis of the PCS spectra based on the extended Blonder-Tinkham-Klapwijk (BTK) model indicates two SC gaps at 48.6 GPa, where the large gap $\Delta_L$ is 3.63 meV and the small gap $\Delta_S$ is 0.46 meV. When scaled against a reduced temperature, both small and large SC gaps collapse on a single curve that follows the prediction from BCS theory. The SC gap-to-$T_c$ ratio is 8.2 for the larger gap, and the initial slope of the upper critical field is -1.9 T/K, indicating that Y belongs to a family of strongly coupled BCS superconductors. The successful application of PCS to Y in DAC environments demonstrates its utility for future research on other pressure-induced high-$T_c$ superconductors.

superconducting state below 1.2 K 10 . AC magnetic susceptibility and electrical resistivity measurements show that Tc monotonically increases to 20 K at 100 GPa and decreases at higher pressures, showing a peak near 100 GPa, where there is a structural change 5,11 . Although the Tc(P) phase diagram of yttrium and its structural evolution with decreasing volume have been established 12,13 , SC properties such as the upper critical field and SC gap, which are important for understanding the mechanism of its superconductivity, have yet to be studied.
To address these issues, we have carried out point-contact spectroscopy (PCS) measurements of Y metal in a diamond anvil cell (DAC). The PCS measurements, which were performed as a function of both temperature and magnetic field at 48. 6 GPa, reveal that the differential conductance (dI/dV) of Y is best described by an s-wave superconducting order parameter with two SC gaps, i.e., ∆L(0) = 3.63 meV and ∆S(0) = 0.46 meV. The SC gap-to-Tc ratio, 2∆L(0)/kBTc, for the larger gap is 8.2, which is much higher than the 3.53 expected for a weakly coupled Bardeen-Cooper-Schrieffer (BCS) superconductor; instead, it is comparable to that of strongly correlated superconductors such as high-Tc cuprates, heavy fermions, and Fe-based compounds 14 . In support of the unusual superconductivity, the initial slope of the upper critical field at Tc is −1.9 T/K at 48.6 GPa, which is ten times that of the two-gap superconductor MgB2 15 and larger than that of the Fe-based superconductor LiFeAs 16 . The successful development of the PCS technique in a DAC not only reveals the strongly coupled superconductivity of elemental Y but is also expected to provide a much-needed method to guide efforts to understand the SC properties of high-Tc superconductors under extreme environments 7 .
The electrical resistivity of Y under pressure is plotted as a function of temperature in Fig. 1a. The resistivity at 21.1 GPa decreases with decreasing temperature, exhibiting metallic behavior. However, a signature of the SC phase transition is absent at temperatures above 6 K. Increasing the pressure to 35.4 GPa causes the resistivity to drop sharply to zero at 9.9 K owing to the SC transition. A further increase in pressure gradually enhances Tc to 19.1 K at 90.2 GPa, above which Tc decreases slightly with pressure. Figure 1b displays the dependence of Tc on pressure, where the results obtained in this work are represented by star symbols that track data obtained from previous ac magnetic susceptibility  and resistivity measurements (11)(12)(13)(14)(15)(16)(17) 5,10,11,12 . Even though the Tc obtained in this work is slightly higher than that in previous studies, the pressure dependence of Tc and the positions of the peak near 100 GPa are similar.
The change in the pressure-induced SC state of Y in the presence of a magnetic field at 33.4 and 48.6 GPa are displayed in Fig. 2a and 2b, respectively. The resistivity reveals a peak near Tc and decreases to zero for both pressures owing to the SC phase transition. A hump-like feature near Tc is often observed in disordered superconductors, which can be ascribed to the development of SC puddles surrounded by normal state regions near Tc 8,17,18 . At 9 T, which is the strongest magnetic field available in this work, the SC phase at 48.6 GPa is still robust, and the onset of Tc occurs at 3.9 K. The upper critical field (Hc2) observed in Y under pressure is the highest among bulk element superconductors, suggesting that the pressurized Y metal is a type-II superconductor 17,19 .
The magnetic field dependence of Tc determined as the onset of the SC phase transition is plotted in Establishing point-contact junctions that could provide appropriate energy-resolved spectroscopic information, i.e., negligible energy dissipation at the junction, in the presence of external pressure is essential for unveiling the SC gap structure of Y. Even though there has been a plethora of efforts in the implementation of the PCS technique under pressure, they are limited to low-pressure ranges below ~3 GPa in clamp-type cells 22,23 . Here, we successfully applied the PCS technique in a DAC environment up to 48.6 GPa, providing an essential breakthrough in probing low-energy physics under extreme conditions surpassing the existing pressure limit. Figure 3  GPa, which is obtained from the PCS. The signature of the Andreev reflection owing to the presence of an SC gap is representatively shown in Fig. 3b, where the broad peak in dI/dV is overlaid with a small peak near zero-bias voltage 24,25 . The solid and dashed lines are best fits based on the Blonder-Tinkham-Klapwijk (BTK) model for single and two s-wave SC gaps, respectively, showing that two-gap superconductivity is realized in elemental metallic Y. To take into account the dip feature observed near 10 mV, an intergrain Josephson effect (IGJE) that could lead to a dip feature at the edge of the Andreev reflection is introduced to the modified BTK model 26,27 : where G0 is the differential conductance in the normal state and wI is the IGJE weight. The first term of Equation (1) corresponds to the modified BTK formula for the two-band s-wave SC pairing symmetry (denoted as bands L and S), which is expressed as follows: Here, the contribution from each band is evaluated using the modified BTK formula 25 . The second term of Equation (1) is a contribution from the IGJE, which is the solution of the Fokker-Planck partial differential equation for a resistively shunted junction model with current fluctuations caused by thermal noise in the small capacitance limit 26 . The detailed numerical calculation procedures of Equations 1 and 2 are provided in section A in the SI.
The dependence on temperature of dI/dV divided by its normal-state value at 10.5 K, (dI/dV)/(dI/dV)10.5 K, is selectively displayed in Fig. 3c with an offset for clarity. With increasing temperature, the broad peak from the Andreev reflection is gradually suppressed and disappears at temperatures above Tc of 10.3 K (see Fig. S6 for details). Figure 3e is a color contour plot of the normalized conductance on the T-V axes, where green (red) represents larger (smaller) values. The suppressed IGJE regime in dark yellow surrounds the SC phase. The dependence on the magnetic field of the spectroscopic feature of Y, (dI/dV)/(dI/dV)8.5 T, at 5.0 K is summarized in Fig. 3d. The Andreev reflection is gradually suppressed with the magnetic field as in temperature and suppresses entirely above the critical field of 7 Tesla. As shown in the color contour plot on the H-V axes in Fig. 3f, however, the magnetic field suppresses the SC energy gap faster than the temperature because it suppresses not only the size of the SC energy gap but also Tc.
The dashed lines in Fig. 3c and 3d are least-squares fits of data to the modified BTK+IGJE model with contributions from the two SC gaps and IGJE terms, where contributions from the larger band wL and IGJE term wI are fixed to 0.75 and 0.7 over the whole temperature and field range, respectively (see Fig. S10 for other parameters obtained from the best fits). We note that the local heating effect of a nonballistic junction may develop a dip feature at the edge of the Andreev reflection. However, a systematic comparison between the anomalous dip structure in dI/dV at a high biased voltage and the bulk critical current defined from the I−V characteristic curve suggests that the dip feature near the SC gap is less likely from the local heating effect (see Fig. S4 and S5 in SI for details).
Multiple SC gaps have often been reported in novel SC compounds with short coherence lengths, such as high-Tc cuprates, heavy fermion compounds, and other strongly correlated systems 28 36 . We note that the Andreev reflection signature of the small SC gap ∆S is smeared out and merged into the broad peak at high temperatures and high magnetic fields. Taken together with the reasonable description by BCS theory, however, the scaling of the small and large reduced gaps (∆(T)/∆(0)) against the reduced temperature (T/Tc) as well as the reduced magnetic field (H/Hc2) supports that the two SC gaps are coupled.
The ratio of the SC gap-to-Tc, 2∆(0)/kBTc, serves as a criterion for the strength of the SC coupling constant relative to the BCS value of 3.53 for weak-coupling conventional superconductors. This ratio is higher for unconventional superconductors such as high-Tc cuprates, heavy-fermion superconductors, and Fe-based superconductors 14 . In general, the gap ratio in multigap superconductors also deviates from the BCS value, with the ratio being above and below the weak-coupling limit for large and small SC gaps, respectively 37 In conclusion, we presented spectroscopic evidence for the pressure-induced superconductivity of elemental metallic Y in a diamond anvil cell environment for the first time.  Fig. 1(a), indicates that the pressure is close to the quasihydrostatic conditions. The sample was loaded in an argon-filled glove box, where four Pt slices adhered to a small piece of polycrystalline Y (Kojundo, 99.9%, thickness 2-3 µm) by mechanical pressure. The tip of the Pt was flattened to less than 1 µm in advance to avoid further broadening under pressure (see the inset of Fig. 1b). The pressure was measured by the position of the high-frequency diamond Raman signal in the symmetric DAC and the spectral shift of the fluorescence R1 peak of ruby in the Be-Cu DAC at room temperature after each measurement.
Transport and spectroscopy measurements. The van der Pauw configuration was used to measure the electrical resistance in a helium-4 closed-cycle refrigerator with a Lakeshore cryotronics 370 AC resistance bridge. The measurements of the upper critical field and point-contact spectroscopy under pressure were performed using a commercial cryostat PPMS model-6000 (9 T, Quantum Design).
With careful treatment of the Pt slices, the point-contact radius at the Pt/Y interface in the DAC can be reduced to below 5 µm, which is smaller than the extremity of the tip in the traditional method. The voltage responses to the DC current were measured at three small current steps (∆I), and the slope (∆I/∆V) was calculated to obtain the differential conductance value. The corresponding biased voltage in the junction is determined as an average measured voltage of three values, which is the x-axis value in the spectrum. The ∆I/∆V can be approximated to dI/dV when the ∆I(∆V) is small enough, where all our measurements were performed with ∆I less than 0.5% of the whole curve. All values of differential conductance were obtained from the 3-point moving average to minimize the effects of the electromotive force in the circuit. The validity of the junction and its mathematical model for analysis are discussed in the Supplementary Information.

Data availability
All data that support the findings of this study are available from the corresponding author on reasonable request. represented as navy and olive circles, respectively. Tc collected from ac susceptibility measurements is indicated by square symbols 5,11 . The dashed lines indicate the structural phase boundaries measured at room temperature 13 . As the pressure increases, the phase transition sequence for the crystal structure is hcp -α-Sm type -dhcp -dfcc -oF16. The inset shows a photograph of the van der Pauw configuration at 109.4 GPa.  a, Schematic diagram of point-contact spectroscopy on Y inside the diamond anvil cell. b, Normalized differential conductance, (dI/dV)/(dI/dV)10.5 K, at 2.0 K as a function of the bias voltage. The solid and dashed-dotted lines are the best fits to the two-band s-wave and single-band s-wave models, respectively.

Figure Captions
c, Temperature evolution of (dI/dV)/(dI/dV)10.5 K from 2.0 to 10.4 K. The dotted lines are the best fits of data to the modified BTK model with two gaps plus intergrain Josephson effects (see the main text for details). d, Magnetic field evolution of (dI/dV)/(dI/dV)8.5 T from 0.0 to 7.5 T at a fixed temperature of 5.0 K. All the curves are displayed with an offset for clarity. e, Contour plot of (dI/dV)/(dI/dV)10.5 K of temperature (T) vs. bias voltage (V), where green (red) represents larger (smaller) differential conductance. f, Contour plot of (dI/dV)/(dI/dV)8.5 T of field (µ0H) vs. bias voltage (V) at 5.0 K.