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Misaki Sasaki, Masahiro Ohkuma, [Ryo Matsumoto](https://orcid.org/0000-0001-6294-5403), Toru Shinmei, Tetsuo Irifune, [Yoshihiko Takano](https://orcid.org/0000-0002-1541-6928), Katsuya Shimizu

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Enhancement of superconductivity on thin film of Sn under high pressureMisaki Sasaki1, Masahiro Ohkuma2,∗ Ryo Matsumoto2, ToruShinmei3, Tetsuo Irifune3, Yoshihiko Takano2, and Katsuya Shimizu11KYOKUGEN, Graduate School of Engineering Science,Osaka University, Toyonaka, Osaka, 560-8531, Japan2Research Center for Materials Nanoarchitectonics (MANA),National Institute for Materials Science, Tsukuba 305-0047, Ibaraki, Japan and3Geodynamics Research Center, Ehime University, Matsuyama, 790-8577, Ehime, Japan(Dated: January 30, 2025)We investigated the pressure effects of a superconductivity on thin films of Sn. Elemental su-perconductor Sn with a body-centered tetragonal structure, β-Sn, exhibits superconductivity belowthe superconducting transition temperature (Tc = 3.72 K) at ambient pressure. Tc of Sn increaseswith lowering dimension such as in thin film and nanowire growth, or by high-pressure application.For thin films, Tc exhibits a slight increase up to approximately 4 K compared to the bulk value,attributable to the crystalline size and lattice disorder. By applying pressure on a bulk Sn, Tc de-creases with increasing pressure from 3.72 K to 5.3 K with the structural transformation into γ-Snaround 10 GPa. However, the combination of these effects on thin films of Sn, namely, thin-filmgrowth and pressure effects, remains underexplored. In this study, we combined film-growth andpressure-application techniques to further increase Tc using a diamond anvil cell with boron-dopeddiamond electrodes. The drop of the electrical resistance suggesting the onset of Tc on the thinfilm reached above 6 K in γ-Sn phase. Further, the upper critical magnetic field was drasticallyenhanced. Atomic force microscopy suggests that the refinement of the grain size of the thin filmunder the non-hydrostatic pressure conditions contributes to stabilizing the higher Tc of γ-Sn.I. INTRODUCTIONApplying high pressures to directly compress a mate-rial is a useful approach to investigate intriguing physicalproperties and search for new materials [1, 2]. For in-stance, oxygen—a gas at ambient conditions— exhibitsmetallic behaviors and superconductivity at high pres-sures [3, 4]. Recently, high-temperature superconductorssuch as hydrogen-rich materials and nickelates under highpressure have attracted considerable attention [5–18]. Inaddition, recent discoveries of the high-temperature su-perconducting states in elemental solid Ti and Sc at ex-treme pressures imply the potential of high-temperaturesuperconductivity in high-pressure phases of other ele-ments [19–21].Some elemental superconductors with thin-film dimen-sions show an increase in superconducting transition tem-perature (Tc) compared to the bulk value, attributableto the crystalline size and lattice disorder [22–25]. Inthe case of Sn, Tc for thin films and nano-wires variesslightly depending on the size and surface morphology[26–29]. The mechanism of Tc enhancement is not thor-oughly clear although it has been proposed to arise fromchanges in the phonon density of states, the electron den-sity of states, and the electron-phonon coupling [30–32].Sn exhibits various crystal structures at high pressures[33–35]. Half a century ago, Wittig investigated the elec-trical transport properties of bulk Sn at high pressuresof up to 16 GPa and revealed the highest Tc is 5.3 K∗ Present address: School of Engineering, Institute of ScienceTokyo, Yokohama, Kanagawa 226-8501, Japanat 11.3 GPa on the pressure induced phase, γ-Sn, whereβ-Sn shows superconductivity below 3.72 K at ambientpressure [36]. However, research on combination of pres-sure application and thin-film growth on elemental su-perconductors is inadequate. Here, we hypothesize thatchanging the crystalline size of a thin film via pressureapplication could stabilize the higher Tc.In this study, we combined thin film growth andpressure-application techniques to increase Tc using adiamond anvil cell (DAC) with boron-doped diamond(BDD) electrodes [37–39]. We investigated the pressureeffects on superconductivity of thin films of Sn comparedto the bulk sample. We observed a higher Tc for thethin film comapred to previous studies on high-pressurephase. Further, we observed a drastically enhanced crit-ical magnetic field on the thin film under high pressure.II. EXPERIMENTAL PROCEDUREThin films of Sn were deposited on a diamond anvil bya resistance heating evaporation. The target metal was ahigh-purity Sn, purchased from Kojundo Chemical Lab.Co. Ltd. Comparing with the high pressure measure-ments, we also prepared Sn thin film on a diamond sub-strate for electrical transport measurements at ambientpressure. The film deposition on two diamonds was per-formed simultaneously. The optical images of the thinfilms on the diamond anvil and the diamond substrateare shown in Fig. 1(a) and the inset of Fig. 1(c), respec-tively. The film thickness and surface morphology of thefilms were evaluated via atomic force microscopy (AFM;Nanocute, SII NanoTechnology Inc.) at room tempera-arXiv:2501.17451v1  [cond-mat.supr-con]  29 Jan 20252ture. For the magnetic measurements of the bulk Sn, awire of high-purity Sn (Nilaco Corp.) was used.High-pressure generation was performed using DAC.The pressure value at room temperature was evaluatedusing ruby fluorescence and Raman shift of diamond[40, 41]. In the electrical transport measurements, di-amond anvil with BDD electrodes with a culet size of300 µm was used [37–39]. The BDD electrodes weredeposited homoepitaxially on the diamond anvil by mi-crowave plasma chemical vapor deposition [42]. Thiselectrode exhibits high durability and can be reused un-til the diamond anvil itself fractures. Further, thin filmscould be deposited directly on the diamond anvil withBDD electrodes, eliminating the need for an electrodefabrication process after thin film deposition [37, 43, 44].The pressure-transmitting media in the solid, liquid, andgaseous states are compatible with this system. A gas-ket of a stainless steel was pre-indented and a 200 µmdiameter hole was drilled. The insulating layer was pre-pared using a MgO–epoxy mixture. We termed thissetup as non-hydrostatic. We also performed the high-pressure generation with better hydrostatic pressure con-dition than non-hydrostatic measurement using a liquidpressure-transmitting medium, glycerol. A 150 µm diam-eter hole was drilled in the insulating layer of MgO–epoxymixture to prepare the sample space, which was filledwith glycerol. We termed this setup as quasi-hydrostatic.In quasi-hydrostatic pressure measurements, the pres-sure value was evaluated using Raman shift of diamond[41]. The electrical transports under a magnetic field(H) perpendicular to the surface were measured by afour-terminal method by physical properties measure-ment system (Quantum Design).For magnetic measurements, we used a miniature DACin combination with a superconducting quantum inter-ference device magnetometer (MPMS, Quantum Design)[45–50]. A nano-polycrystalline diamond with culet sizeof 600 µm and a pre-indented tungsten gasket with ahole size of 200 µm were used [51]. Bulk Sn pieces andruby powders were loaded into the sample space withouta pressure-transmitting medium. The in-phase compo-nent of the AC magnetic response (m′) was measured.The frequency and amplitude of the AC field were 3 Hzand 0.2 mT, respectively.III. EXPERIMENTAL RESULTSA. Ambient pressureFigure 1(b) shows the temperature (T ) dependence ofm′ for the bulk Sn under H, where no background signalfrom DAC is subtracted. Below 3.7 K, the diamagneticsignal suggesting the superconducting state was observedat H = 0. The Tc onset was decreased by applying H.Figure 1(c) shows the T dependence of the electrical re-sistance (R) under H perpendicular to the film surface.The residual resistance ratio (RRR) was estimated to be11. At H = 0, an R drop suggesting the onset of thesuperconducting transition was observed at 3.75 K. Tcslightly increased compared to the bulk value and wassimilar to values from the previous studies on thin films[27, 28]. By applying H, the onset of Tc decreased withincreasing H. However, the critical magnetic field wasthree times higher than that of the bulk Sn (Fig. 1(d)).Hc of 100 mT estimated using Hc(T ) = Hc(1− (T/Tc)2)was similar to that of a previous study [28]. Consider-ing to the Hc, the thin film transformed into a type IIsuperconductor, as previously reported [28, 52, 53].0 1 2 3 4020406080100H [mT]T [K] Thin film Bulk3.0 3.5 4.0 4.5 5.00.00.10.20.3Resistance [Ω]T [K] 0 mT  7 mT  13 mT 19 mT  23 mT  25 mT(a) (c)(d)Bulk sample(b)BDDSnHFIG. 1. (Color online) (a) Optical image of the thin film of Snon the diamond anvil with BDD electrodes. The dotted areaindicates one of the BDD electrodes. (b) T dependence of thein-phase component of m′ on the bulk Sn. (c) T dependenceof R on the thin film of Sn on the diamond substrate. Themagnetic field was applied perpendicularly to film. The insetshows the optical image of the thin film of Sn on the diamondsubstrate (d) T dependence of the critical magnetic field onthin film and bulk Sn.B. Non-hydrostatic pressure on bulk SnFigure 2(a) shows the T dependence of m′ on the bulkSn under high pressures. On applying pressure, Tc de-creased, as previously reported. Figure 2(b) shows theT dependence of m′ at 2.7 GPa under varying H. Thedecrease of Tc was observed by applying H = 2 mT. AtH = 10 mT, Tc was below 2 K. Hc was evaluated to be13 mT, as shown in the inset of Fig. 2(b).C. Non-hydrostatic pressure on thin filmFigure 3(a) shows the T dependence of R on the thinfilm of Sn under high pressures on pressurization. Asshown in the inset of Fig. 4(a), RRR was estimated to be1.4 at 2.5 GPa, which was much lower than that underambient pressure. We speculate that the crystallographic32.7 GPaBulk sample(a)(b)0 1 2051015H [mT]T [K]FIG. 2. (Color online) (a) T dependence of m′ on bulk Snunder high pressures. (b) T dependence of m′ at 2.7 GPaunder varying magnetic fields. The inset shows the T depen-dence of the critical magnetic field.defect was introduced because of the non-hydrostaticpressure condition. The R drop suggesting the super-conducting transition was observed around 4 K, whereasTc was 3.75 K under ambient pressure. Tc decreased onfurther increasing the pressure, as previously reported.R showed peak behavior just above Tc at 5.5 GPa, pos-sibly due to the granularity or disorder on the thin films.Above 9.5 GPa, R slightly tended to decrease around 6K, suggesting the superconducting transition, where γ-Snphase could emerge. With further pressure application,the R drop became significant, and Tc slightly decreased.After applying 20 GPa, the pressure was decreased to10.5 GPa. Figure 3(b) shows the T dependence of R forthe thin film of Sn under high pressures with depressur-ization. The onset of Tc increased to 6.3 K at 10.5 GPa,and γ-Sn remained at 8.5 GPa. γ-Sn vanished when thepressure was decreased to 3.5 GPa.Figures 4(a) and (b) show the T dependence of R forthe thin film of Sn under various H at 2.5 and 10.5GPa under non-hydrostatic pressure condition. Tc wasobserved at 1 T, whereas the upper critical magneticfield (Hc2) was approximately 0.1 T under ambient pres-sure. Drastic Hc2 enhancement was also observed in theγ phase at 10.5 GPa. As shown in Fig. 4(c), Hc2 es-timated using Werthamer–Helfand–Hohenberg (WHH)model reached several teslas at high pressures [54–56]. Notably, the Hc2 enhancement of β-Sn under thenon-hydrostatic pressure condition was observed repro-ducibly. Figure 5(b) shows the T dependence of R forthe thin film of Sn with the other setup at 5 GPa. Theoptical image of the thin film of Sn is shown in Fig. 5(a).The R decrease suggesting the superconducting transi-tion was observed even at H = 1.0 T. The enhancementof Hc2 is thought to originate from the shortening in themean free path of the electrons and the resulting shorten-ing in the coherence length. The RRR was estimated tobe 11 under ambient pressure; however, it decreased to1.4 under non-hydrostatic pressure condition, indicatingthat the mean free path of the electrons shortened.(a)(b) Depressurizing processFIG. 3. (Color online) T dependence of electrical R undernon-hydrostatic pressure with (a) pressurizing process (b) de-pressurizing process. The number in (b) indicates the orderof measurements.D. Quasi-hydrostatic pressure on thin filmWe performed high-pressure generation with better hy-drostatic pressure condition using a liquid pressure trans-4(a)(b)(c)2 3 4 5 6 7 8 9 10050100150    0 T  0.2 T  0.4 T 0.6 T  0.8 T  1.0 T 1.5 T  2.0 T  2.5 T 3.0 TR [Ω]T [K]2.5 GPa0 100 200 300050100150200FIG. 4. (Color online) (a) and (b) T dependence of R underthe magnetic field at (a) 2.5 and (b) 10.5 GPa. The insetof (a) shows T dependence of R between 2 and 300 K at 2.5GPa without the external magnetic field. (c) T dependenceof the upper critical magnetic field at 2.5 and 10.5 GPa. Thesolid lines represent the fitting curves estimated by the WHHmodel.mitted medium, glycerol. Figure 6(a) shows the R–Tof the thin film at 9 GPa under quasi-hydrostatic pres-sure conditions. The optical image of the thin film in-100 μm(a) (b)5 GPaRun 2FIG. 5. (Color online) (a) Optical image of the thin film ofSn at 5 GPa and (b) T dependence of R at 5 GPa.(a)(b)0 50 100 150 200 250 3000246810R [Ω]T [K]2 3 4 5 6 7 80.00.20.40.60.81.0R/R(T = 8 K)T [K] (1) 9 GPa (2) 12 GPa (3) 8 GPa (4) 2 GPa9 GPa50 μmFIG. 6. (Color online) (a) T dependence of R at 9 GPa.The inset shows the optical image of the thin film. (b) Tdependence of R under high pressures between 2 and 8 K.side the DAC is shown in the inset of Fig. 6(a). TheRRR was with in 2—3 in quasi-hydrostatic pressure mea-surements, which was slightly higher than those for thenon-hydrostatic pressure condition. The R drop suggest-ing superconducting transition was observed around 5K. Figure 6(b) shows R–T under quasi-hydrostatic pres-sure condition between 2 and 8 K with warming process.5The R value was normalized using the value at 8 K. At9 GPa, R slightly decreased with decreasing T around5.3 K, suggesting the superconducting transition on γ-Sn. The R drop was also observed around 3 K. The γ-Snphase became significant on further pressure application.The onset of Tc slightly increased at 12 GPa. We also de-creased the pressure from 12 to 8 GPa. The R decreasesuggesting the superconducting transition of γ-Sn wasslightly observed, whereas the γ-Sn was clearly observedat 8.5 GPa under the non-hydrostatic pressure condition.With further pressure decrease, γ-Sn vanished at 2 GPa.IV. DISCUSSIONA. Pressure dependence of TcFigure 7 shows the pressure dependence of Tc for thethin film and bulk samples compared with results froma previous study [36]. For the bulk Sn, the behavior ofTc with respect to pressure was good agreement with theprevious study. A similar tendency was observed for thethin film in β-Sn phas;, however, its Tc was higher com-pared to bulk Sn. One possible reason is the geometryof the thin film. As shown in Fig 1(a), the thin film areaoccupies approximately 70% of the culet of the diamondanvil, which produces the pressure distribution. In theγ-Sn phase, Tc with quasi-hydrostatic pressure measure-ments showed a trend similar to the previous results [36].Meanwhile, Tc with non-hydrostatic pressure showed ahigher value. We observed the highest Tc of 6.3 K at10.5 GPa, which was approximately 10% higher thanthat reported in a previous study [36]. The highest Tc isnot fully explained by the pressure gradient. Assumingthat the Tc of bulk γ-Sn continues to change at a rateof −0.11 K/GPa, it is necessary to decrease the pressureto 4 GPa from the γ phase above 10 GPa. However, theγ phase cannot exist metastably under this pressure aswas observed during the γ to β phase transition on thedecompression process (Fig. 3(b)). We emphasize thatwe observed the mid point of Tc to be greater than 6.0K (Fig. 4(b)).B. Atomic force microscopyTo investigate the morphology on the thin films, weperformed AFM measurements before and after apply-ing pressure under the non-hydrostatic pressure condi-tion. Figures 8(a) and (b) show the optical and AFMimages of the thin film before pressurization. The thinfilm of Sn was deposited on a diamond anvil withoutBDD electrodes. The average film thickness was evalu-ated to be 70 nm. A magnified AFM image is shown inFig. 8(c). The average grain size was estimated to be ap-proximately 300 nm. Figure 8(d) shows the optical imageof the thin film after applying pressure up to 4.2 GPa.The pressure was evaluated by the diamond Raman shift.FIG. 7. (Color online) Pressure dependence of the supercon-ducting transition temperature. The green triangles indicatethe results by Wittig [36]. The dotted line indicates a guidefor the eyes.Most of the thin film peeled off and was transferred to theMgO–epoxy mixture. We measured the small remainingthin-film area. Figure 8(e) shows the AFM image of thethin film after pressurization. The average film thicknesswas evaluated to be 60 nm. A magnified view is shownin Fig. 8(f). The grain size was reduced to several tensof nanometers on pressure application.Next, we performed AFM measurements under quasi-hydrostatic pressure condition for comparison with thenon-hydrostatic pressure measurements. The thin filmwas the same as that used in the R–T measurement. Fig-ures 9(a) and (b) show the AFM images of the thin filmbefore applying pressure. The average thickness and av-erage grain size were evaluated to be 82 and 600 nm,respectively. Figures 9(c) and (d) show the AFM imageson the thin film after applying pressure up to 12 GPa.The pressure-transmitting medium was removed usingethanol and nitrogen gas. The average thickness wasevaluated to be 91 nm. Unlike the non-hydrostatic pres-sure measurements, grain refinement was not observed.The AFM results revealed that the grain refinementwas observed only under the non-hydrostatic pressurecondition. In the R–T results, the maximum Tc value un-der the non-hydrostatic condition was 10% higher thanthat under the quasi-hydrostatic condition, suggestingthat the grain refinement plays a pivotal role in stabi-lizing the higher Tc. Smaller grain sizes tend to havehigher Tc, because of phonon softening under ambientpressure [32]. Houben et al. performed nuclear resonantinelastic x-ray scattering on nano-structured films andbulk Sn to investigate the phonon density of states andobserved a decrease in the high-energy phonon modesand a slight increase in the low-energy phonon modes6in nano-structured films [31, 32]. Using the obtainedphonon spectra, calculations based on the Allen–Dynes–McMillan formalism yielded Tc values in good agreementwith the experimental data. In nano-structured films, theelectron–phonon coupling increased by up to 10%, sug-gesting that phonon softening and the associated changein electron–phonon coupling play a major role in the Tcincrease. We consider that the Tc increase under thenon-hydrostatic pressure condition is related to the grainsize and that grain refinement could induce to changes inelectron-phonon coupling.10 μm 5 μm0.2 μm10 μm0.2 μm(a)(b)(c) (f)(e)(d)156 nm0 nm0 nm 0 nm172 nm0 nm33 nm18 nm50 μmMasked areaSnFIG. 8. (Color online) (a) Optical image of the thin filmof Sn on a diamond anvil before pressurization. (b) and (c)AFM image on the thin film before pressurization. (d) Opti-cal images of the thin film of Sn on the diamond anvil afterpressurization. (e) and (f) AFM image of the thin film afterpressurization.C. Possible higher Tc on SnRecently, anomalies in magnetization, resistance, andheat capacity suggesting the superconducting transitionwere observed around 5.5 K in nano-wires of Sn [57]. Fur-ther, based on scanning tunneling microscopy, the thinfilm of Sn deposited on SrTiO3 substrate exhibited su-perconductivity around 8 K [58]. Indeed, in our thin film,the decrease of R was observed at 11 K under 9.5 GPa,suggesting the signature of the superconducting transi-tion, and the anomaly shifted to lower T by applying the2 μm1 μm2 μm1 μm0 nm0 nm 0 nm133 nm0 nm85 nm209 nm160 nm(a)(b)(c)(d)FIG. 9. (Color online) AFM under quasi-hydrostatic pres-sure condition. (a) and (b) AFM image of the thin film beforepressurization. (c) and (d) AFM image of the thin film afterpressurization.magnetic field (Fig 10). On the other hand, some granu-lar or amorphous thin films exhibit a resistance decreaseat higher T than Tc due to the effects of fluctuations[59–62]. Further investigations such as magnetic mea-surements [63, 64], heat capacity measurements [65], andscanning tunneling microscopy [66] under high pressuremay offer insights for the possible stabilization of higherTc.5 10 15 20 25 3093.093.293.493.6R [Ω]T [K]0 T1 T0 5 10 15 20 25 300501009.5 GPaFIG. 10. (Color online) Temperature dependence of the elec-trical resistance at 9.5 GPa. The downward arrows indicatethe onset of the anomalies in the resistance.V. CONCLUSIONIn conclusion, we demonstrated the pressure effect onthe superconductivity of thin films of Sn. We observed7the superconductivity below 6.3 K in the γ-phase of Sn,which was approximately 10% higher than previous bulkresults. 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