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The discovery of the hydrogen-rich superconductor H3S with a superconducting transition temperature Tc of about 200 K has spurred the search for room-temperature superconductivity in hydrogen-rich compounds1. Despite the substantial challenges of high-pressure experiments on tiny samples, the macroscopic superconducting properties of hydrides have been well characterized, including electrical resistance1,8,9,10, magnetization6,7,11 and upper critical field5. However, there is limited experimental insight into the superconducting pairing mechanism in these materials. Although strong electron–phonon interactions and high-frequency phonons have been proposed theoretically as critical factors for the formation of Cooper pairs in hydrogen-rich superconductors12, experimental validation has remained elusive. Furthermore, theoretical calculations of the superconducting parameters vary depending on the approach used13,14,15,16,17,18,19. Thus, a quantitative determination of the superconducting gap size and symmetry is essential, as it will provide an experimental basis to complete theoretical understanding and enable further predictions of superconductivity in hydrides.

Experimentally determining the superconducting gap under high pressure, particularly in a diamond anvil cell environment, is extremely challenging. Conventional techniques, such as angle-resolved photoemission spectroscopy and scanning tunnelling microscopy, cannot be used under high-pressure conditions. Although Capitani et al. used infrared reflectance spectroscopy to detect the superconducting gap and phonon frequencies of H3S (ref. 20), further reluctance and absorption contributions from the diamond anvils and the NaCl insulating layer complicate the interpretation of the results. Andreev reflections have been observed in cerium hydrides21, but the weak signal (approximately 2%) is insufficient to reliably extract information about the superconducting gap. Recently, Du et al.22 developed a planar tunnel junction method, allowing for precise measurement of the superconducting gap structure under megabar pressure. Despite this advancement, the in situ chemical synthesis of planar tunnel junctions for hydrogen-rich superconductors with high purity and good homogeneity under high-pressure environment remains challenging.

In this work, we have successfully synthesized planar tunnel junctions of H3S and D3S using S + H2 and S + D2 precursors, respectively. Through tunnelling spectroscopy, we demonstrate that both compounds exhibit fully gapped structure, with gap values 2Δ of approximately 60 meV and 44 meV (obtained by fitting with the Dynes model), respectively. Furthermore, tunnelling spectra in the inhomogeneous sample synthesized using S and ammonia borane (NH3BH3) as an alternative hydrogen source reveal extra gap features from another likely H-depleted HxS superconducting phase.

Synthesis of planar tunnel junctions

The synthesis process of the planar tunnel junction for H3S in a diamond anvil cell is schematically illustrated in Fig. 1a. A small piece of sulfur sample surrounded by hydrogen gas was compressed between two opposing diamond anvils after gas loading and subsequent pressurizing. A roughly 15-nm tantalum thin film was deposited in the centre of the bottom anvil tip and an oxide layer was grown directly over the film to serve as normal metal (N) and insulating barrier (I) components of the N/I/S tunnel junction, respectively (detailed preparation of the electrical leads is provided in Extended Data Fig. 1). The key challenge to overcome in determining the superconducting gap in hydride materials is the synthesis of high-purity samples with only limited amounts of hydrogen available clamped between diamond anvils. Because planar tunnelling spectroscopy is not an atomic-resolution local probe such as a scanning tunnelling microscope and the measured tunnelling conductance is a sum of all components at the contact area, the presence of other phases in a multiphase sample can severely distort the gap feature of the desired phase. To ensure the necessary amount of hydrogen gas for complete chemical reaction, we made a cavity with a depth of about 1 µm and a diameter of about 30 µm on the top anvil with a focused ion beam machine (Extended Data Fig. 1d). Sulfur and hydrogen gas precursors were reacted using in situ laser heating, synthesizing H3S to serve as the superconducting component of the N/I/S junction. Then, the N/I/S junction was synthesized between two anvil tips, marked by the red oval in Fig. 1a. To prevent destruction of the insulating barrier during laser heating, pulsed laser heating was implemented and long exposure times at the junction area were avoided.

Fig. 1: Synthesis of planar tunnel junctions.
Fig. 1: Synthesis of planar tunnel junctions.
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a, Schematic of planar tunnelling junction synthesis between two opposing anvils. Electrical leads are deposited on the bottom anvil and isolated from the metallic Re gasket with CBN/MgO/CaO insulating material. A rectangular sample (green) is loaded above the electrical leads. Detailed views of the region between the anvil tips before and after laser heating are shown from the side perspective. Gold leads are shown as thick orange lines and tantalum lead with Ta oxidized layer are coloured red and grey, respectively. The initial sulfur and synthesized H3S are marked in light green and dark green, respectively, surrounded by H2 (pink). The Ta/Ta2O5/H3S junction areas are indicated by the red oval. b, Schematic description of the differential conductance and resistance measurements from the top view of the region between the anvil tips. c,d, Optical microscope images (reflection and transmission) through the top diamond anvil of H3S-S1 before (c) and after (d) laser heating at 158 GPa. Scale bar, 10 µm.

The optical images of H3S-S1 before and after laser heating are presented in Fig. 1c,d. Notably, we added two more gold leads to form a ‘double’ four-terminal configuration, which allows measurement of both the electrical resistance and the tunnelling spectra of the sample, as illustrated in Fig. 1b. The crystal structure of the synthesized samples was characterized by X-ray powder diffraction. Thus, we have characterized the synthesized samples from three aspects: electrical resistance, crystal structure and tunnelling spectroscopy.

In this work, we synthesized three high-purity H3S samples (H3S-S1 (158 GPa), H3S-S2 (151 GPa) and H3S-S3 (161 GPa) and one high-purity D3S sample (160 GPa)) using elemental sulfur and H2 or D2 gas. We also synthesized one hydrogen sulfide sample (H3S-S4 (172 GPa)) using sulfur and ammonia borane as an alternative hydrogen source, which show multiphase features. Samples H3S-S1 and H3S-S4 were characterized by electrical resistance, X-ray diffraction and tunnelling spectroscopy, H3S-S2 and D3S by X-ray diffraction and tunnelling spectroscopy and H3S-S3 by tunnelling spectroscopy only.

Superconducting gap of H3S

Before exploring the superconducting gap features, we examine the resistance and crystal structure properties of H3S-S1. As shown in Fig. 2a, the temperature dependence of electrical resistance exhibits a sharp drop at Tconset = 197 K and then reaches zero at Tczero = 190 K, indicating the formation of the superconducting phase in H3S. The X-ray powder diffraction patterns (Fig. 2b and Extended Data Fig. 2) show the \(Im\bar{3}m\) crystal structure with no further diffraction peaks through the sample, suggesting a high-purity single-phase sample of H3S.

Fig. 2: Superconducting gap of H3S.
Fig. 2: Superconducting gap of H3S.
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a, Temperature dependence of the electrical resistance of H3S-S1. b, X-ray powder diffraction pattern of H3S-S1 (black data points) and the Rietveld refinement of the \(Im\bar{3}m\) phase (red curve). c, Tunnelling spectra of H3S-S1 measured at 20 K. Black arrows indicate positions of quasiparticle peaks. d, Temperature dependence of the tunnelling spectrum for H3S-S1, measured from 20 K (black curve) to 130 K (olive curve) with 10-K steps and 220 K (grey curve, shifted by −7 MΩ−1 for comparison). a.u., arbitrary units.

Source data

To characterize the superconducting gap features of H3S, we conducted differential conductance measurements across the junctions at 20 K. Figure 2c shows the tunnelling spectra for H3S-S1 at 158 GPa. A pair of coherence peaks emerges in the tunnelling spectra at symmetric positions (ΔpH3S-S1 ≈ ± 32 meV) relative to the Fermi energy, whereas the differential conductance within the energy below ±ΔpH3S-S1 drops to nearly zero, exhibiting a U-shaped structure, characteristic of the nodeless superconducting gap structure. Notably, the intensity of quasiparticle peaks at positive and negative energies in tunnelling spectra shows a particle–hole asymmetry, which may be because of the energy-dependent transmission of tunnel electrons23.

The temperature variation of tunnelling spectra for H3S-S1 is shown in Fig. 2d. On warming, the height of the coherence peaks is continuously suppressed before fading into the background, and the bottom of the spectrum is elevated, owing to large thermal smearing at high temperatures. To quantitatively clarify the temperature evolution of the superconducting gap, we fitted the tunnelling spectra, which are normalized through division by the parabolic background fitted with Brinkman–Dynes–Rowell (BDR) model24 (Extended Data Fig. 3), with a single s-wave Dynes model25 (Methods). The parabolic background arises from the metal(N)/barrier(I)/metal(N) tunnelling process in the normal state24,26 (Methods). As shown in Fig. 3a, tunnelling spectra at different temperatures are in good agreement with fits to the Dynes model, except the asymmetry of the intensity of quasiparticle peaks at low temperatures. The temperature evolution of the simulated gap values is summarized in Fig. 3b, which is in good agreement with the Bardeen–Cooper–Schrieffer (BCS) theory27 (pink curve), and the gap value ΔH3S-S1 ≈ 29 meV is extracted. Above 130 K, the gap features of H3S-S1 become indistinguishable from the parabolic background owing to large thermal smearing and quasiparticle broadening effects, and no reliable gap value can be extracted (Extended Data Fig. 4).

Fig. 3: Temperature evolution of normalized tunnelling spectra and comparison with the Dynes model.
Fig. 3: Temperature evolution of normalized tunnelling spectra and comparison with the Dynes model.
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a, Normalized tunnelling spectra (blue data points) and comparison with the Dynes model (red curves) at different temperatures. Spectra above 20 K are offset vertically for clarity. To minimize the influence of energy-dependent transmission in determining the gap value, the normalized tunnelling spectra were fitted using data at negative bias. b, Extracted gap and Γ values from the Dynes model at different temperatures. Error bars are from fitting errors of the Dynes model. The pink curve represents the temperature dependence of the gap value from BCS theory, for which Δ0 = 29 meV and Tc = 190 K are used.

Source data

Also, we have measured tunnelling spectra for H3S-S2 (151 GPa) and H3S-S3 (161 GPa) samples at 2 K, as shown in Extended Data Figs. 5 and 6. Both samples also exhibit a fully open gap structure with gap values ΔH3S-S2 ≈ 29 meV and ΔH3S-S3 ≈ 31.5 meV (obtained by fitting with the Dynes model), respectively. Although the magnitude of the normal state conductance differs among the three samples, the gap symmetry and value are well matched, giving ΔH3S ≈ 30(±1.5) meV. The observed superconducting gap is attributed to the random orientation of crystal directions, as evidenced by the well-defined powder rings in the X-ray diffraction patterns (Extended Data Fig. 2), indicating a uniformly oriented powder sample. There is no clear signature of the in-gap states or any further quasiparticle peaks in the three samples, suggesting an isotropic gap feature of H3S. Furthermore, we have studied the magnetic-field-dependent evolution of the tunnelling spectra for H3S-S3, as shown in Extended Data Fig. 6. The effective suppression of coherence peaks under magnetic field confirms the superconducting origin of the gap features. The gap value at 9 T shows only a slight decrease owing to the high upper critical field5. Further measurements are desirable to study the gap evolution under higher magnetic fields.

Superconducting gap of D3S

After the characterization of the superconducting gap of H3S, we turn to its deuterium counterpart D3S to investigate the isotope effect. As shown in Fig. 4a, the synthesized D3S sample exhibits the same \(Im\bar{3}m\) crystal structure as H3S. The tunnelling spectrum of D3S at 20 K is shown in Fig. 4b. There are two kinks at the energy position ΔpD3S ≈ ±25 meV, corresponding to coherence peaks, whereas the gap structure shows the same U-shape as for H3S. To extract the gap value of D3S, we normalized the tunnelling spectrum through division by the parabolic background fitted with BDR model24 (dashed pink curve) and fitted it with the Dynes model, which gives ΔD3S ≈ 22 meV. The smaller gap value in D3S, together with the same fully gapped feature, confirms the phonon-mediated pairing mechanism in the H3S superconductor. Notably, at high bias around ±60 mV, there is a clear step-like structural feature, as indicated by the green arrows in Fig. 4b, which may correspond to inelastic scattering from a bosonic phonon mode of D3S with energy difference ΩD3S = E (60 meV) − ΔD3S (22 meV) around 38 meV.

Fig. 4: Superconducting gap of D3S.
Fig. 4: Superconducting gap of D3S.
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a, X-ray powder diffraction pattern of D3S (black data points) and the Rietveld refinement of the \(Im\bar{3}m\) phase (red curve). The inset is an optical image of the D3S sample. b, Tunnelling spectra of D3S (blue curve). Black and green arrows indicate the positions of quasiparticle peaks and step-like structures of D3S, respectively. The dashed pink curve represents the parabolic background and the inset is the comparison between the normalized tunnelling spectra (data points) and the Dynes model (curve). a.u., arbitrary units.

Source data

Superconducting gap features of multiphase hydrogen sulfide

As mentioned above, phase inhomogeneity is a common phenomenon in hydrogen-rich compounds. For instance, several new phases of hydrogen sulfide have been observed in X-ray diffraction experiments, in which crystal structures of some concomitant phases differ greatly from the \(Im\bar{3}m\) phase, identified as H4S3, H2.85±0.35S2 and H6±0.4S5 (refs. 28,29). We find that some of the planar tunnelling spectra features can be attributed to different phases present in multiphase samples.

A representative example is shown in Fig. 5. The sample H3S-S4 (172 GPa) shows a two-gap feature in the spectra at 2 K. Except for the coherence peak at about 30 meV, which corresponds to the superconducting gap of H3S (Fig. 5a,b), there is a kink at around 8 meV (Fig. 5a). The kink is suppressed with increasing temperature and disappears above 40 K, suggesting that it corresponds to a second concomitant superconducting phase, which we denote HxS. Indeed, electrical resistance measurements reveal a second superconducting transition with Tc (HxS) around 40 K (Fig. 5c). The X-ray powder diffraction data show that the sample contains several different phases. As shown in Fig. 5d, as well as the regions characterized predominantly by \(Im\bar{3}m\) H3S (red region) and β-Po sulfur (yellow region) phases, there is another blue region with unique X-ray powder diffraction patterns that cannot be described by either of these two phases (Fig. 5e,f). Given that the superconducting gap features of the junction area (dashed rectangle in Fig. 5d) consist of contributions from both \(Im\bar{3}m\) H3S and HxS phases, it is likely that the X-ray powder pattern in this blue region is related to the HxS superconducting phase. The limited X-ray diffraction data do not allow us to resolve the crystal structure of the HxS phase. Further investigations into the crystal structure of HxS are desirable.

Fig. 5: Superconducting gap features of multiphase hydrogen sulfide sample.
Fig. 5: Superconducting gap features of multiphase hydrogen sulfide sample.
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a, Tunnelling spectra of H3S-S4 measured at 2 K (blue curve), 20 K (orange curve) and 40 K (green curve). Arrows indicate positions of quasiparticle peaks of H3S (red) and HxS (cyan). b, Temperature dependence of tunnelling spectra for H3S-S4, measured from 40 K (black curve) to 180 K (grey curve) with 20-K steps. The distortion of the fully gapped structure in the tunnelling spectrum of H3S-S4 is the result of the relatively poor barrier quality and phase inhomogeneity, as analysed in Extended Data Fig. 7. c, Temperature dependence of electrical resistance for H3S-S4. Arrows indicate Tc of H3S and HxS. The inset is an optical image of the H3S-S4 sample. d, Phase distribution in the multiphase sample H3S-S4, reconstructed on the basis of X-ray powder diffraction data. Contacts are indicated by the green area, with the sulfur, HxS and H3S regions shown in yellow, blue and red, respectively. The colour brightness indicates the relative phase content, with brighter colours corresponding to higher concentrations, as determined from the peak intensities at characteristic diffraction angles across different X-ray powder diffraction patterns. Grey points represent the points at which the experimental data were collected. The tunnel junction area is marked with a dashed rectangle. e, X-ray powder diffraction pattern of H3S-S4 (black data points) and the Rietveld refinement of the \(Im\bar{3}m\) H3S phase (red curve). f, X-ray powder diffraction pattern of concomitant HxS phase in H3S-S4. a.u., arbitrary units.

Source data

Discussion and summary

As the order parameter, the superconducting gap is fundamentally related to the origin and nature of the superconducting coupling mechanism. Our observation of the superconducting gap by tunnelling spectroscopy provides unambiguous evidence for superconductivity in H3S and D3S. The observed isotope effect and the inferred s-wave gap symmetry suggest that phonon-mediated Cooper-pair pairing is the dominant mechanism in H3S. Unexpectedly, the observed superconducting gap value of H3S 30(±1.5) meV together with the 2Δ/kBTc(H3S-S1) ratio of 3.54 are smaller than that calculated by different theoretical approaches18,30,31,32. The discrepancies between experimental results and theoretical calculations require further detailed investigations on the origin of superconductivity in H3S.

On the other hand, the observation of multigap features in inhomogeneous hydrogen sulfide sample reveals the existence of concomitant superconducting phases and call for a more comprehensive study of hydrides in which several superconducting phases are present. Finally, it would be insightful to apply this tunnelling technique to study superconducting gap structures in other hydride systems, such as metal superhydrides, as it would be helpful to explain the origins of high Tc and to identify the pathways to new materials with higher Tc and at lower pressure.

Methods

Sample preparation inside the diamond anvil cell

Diamond anvil cells with culets of about 50 µm in diameter, bevelled to about 160 µm, were used in our experiments. 200-µm-thick rhenium gaskets were pre-indented to a thickness of 20 µm and then covered with an insulating film, prepared from a mixture of cBN and MgO/CaO/epoxy powder. A hole with a diameter of about the culet size was drilled using a laser before electronic leads were deposited on the diamond anvil in an ion beam sputtering machine. Ta2O5 barriers were created by oxidation of the Ta layer in a plasma machine under pure O2 atmosphere under pressures of 10−1 mbar for 5 min at 350 W power. Polycrystalline sulfur samples were prepared from sulfur powder (purity of 99.999%, Alfa), which was first pre-compressed to thin plates with thickness about 1 µm and then cut into a rectangle shape with dimensions of about 10 µm × 5 µm. H2, D2 or NH3BH3 were used as sources of hydrogen or deuterium for the chemical reaction and pressure transmitting medium. Note that there may be imperfect contact between the sulfur and the electrodes in samples loaded with H2 or D2 before laser heating because a small amount of H2 or D2 may penetrate between them after the gas loading procedure. However, sufficient contact is made between the hydrogenated sample and the electrodes after laser heating owing to the expansion after hydrogenation of the sulfur sample. Using tunnelling spectroscopy for H3S and D3S samples at high pressures, we spent dozens of diamond anvil pairs exploring the best conditions for Ta oxidation, sample shape and thickness, gas loading and sample synthesis at high pressure.

X-ray diffraction and pressure estimation

X-ray powder diffraction data were collected at beamline ID27 at the European Synchrotron Radiation Facility (ESRF) (λ = 0.3738 Å), with a beam spot size of 0.6 × 0.6 µm2 (EIGER2 X CdTe 9M detector). CeO2 powder was used as a reference sample for the calibration. Primary processing and integration of the data were carried out using DIOPTAS software and XDI software33,34. The indexing of X-ray powder diffraction patterns and refinement of the crystal structures were carried out using the GSAS35 and EXPGUI36 packages. The pressure was estimated using the Raman shift of stressed diamond anvils37.

Electrical resistance and differential conductance measurements

Electrical resistance measurements were performed in a four-probe configuration using a Keithley 6221 d.c. current source and a Keithley 2182A nanovoltmeter in delta mode. Differential conductance (dI/dV)(V) measurements were performed in a current-biased four-probe configuration using the Keithley 6221 current source and the Keithley 2182A nanovoltmeter in differential conductance mode. A d.c. current superimposed with a small delta current from a Keithley 6221 was applied across the junctions in the measurements, whereas the delta current was set to be as small as possible but also large enough to obtain an acceptable signal-to-noise ratio (10 nA for H3S-S1, 5 nA for H3S-S2, 4 nA for H3S-S3, 100 nA for H3S-S4, 100 nA for D3S). The bias voltage and differential conductance were measured and calculated by a Keithley 6221. The two-wire electrical resistances of gold electrodes and tantalum strip are around 100 Ω and 30 KΩ, respectively. Further details on the operation of the differential conductance can be found in the Keithley manuals. All electrical measurements were performed in a Quantum Design Physical Property Measurement System.

Data noise and temperature dependence of the background in tunnelling spectrum

There are three main sources of noise in the measurement of differential conductance. One is Johnson–Nyquist noise38,39, which arises owing to thermal fluctuations and is proportional to temperature. The other two sources are flicker noise40 and shot noise41,42, which are the result of resistance fluctuations that generate a fluctuating voltage in the presence of a constant current and the discreteness of charge carriers, respectively. Because we use the same modulation delta current over the entire temperature and bias range for the same sample, flicker noise does not have a notable temperature and bias dependence. However, the Johnson noise increases with increasing temperature and the shot noise increases with increasing tunnel current in the circuit at high bias, which accounts for the reduced signal-to-noise ratio at elevated temperatures and high bias conditions.

The temperature dependence of the background arises from the temperature-dependent tunnelling conductance in the normal state, that is, metal/insulator/metal tunnelling. This phenomenon has been observed experimentally in normal metal tunnel junctions, such as Al/AlOx/Al (refs. 43,44). Simmons45 theoretically analysed the thermal influence on electron tunnelling by considering the smearing of the Fermi–Dirac distribution, which results in an increase of tunnelling conductance with temperature. Other theoretical models have been proposed to discuss the thermal influence on the tunnelling conductance, such as thermal-fluctuation-induced tunnelling46. Furthermore, such factors as the temperature dependence of the dielectric constant of the barrier, the thermal expansion of the barrier and the thermal activation across the barrier can also influence the tunnelling conductance at high temperatures.

Dynes model

The Dynes model25 describes the tunnelling density of states through an N/I/S tunnel junction, in which S is a BCS superconductor. The tunnelling density of states is given by the formula:

$${N}_{{\rm{S}}}(E)={N}_{0}{\rm{R}}{\rm{e}}\,\left[\frac{E+{\rm{i}}\varGamma }{\sqrt{{(E+{\rm{i}}\varGamma )}^{2}-{\varDelta }^{2}}}\right]$$

where Δ is the gap value, Γ is the broadening parameter of the quasiparticle peaks, which includes contributions from both intrinsic quasiparticle recombination and extrinsic inelastic scattering, and N0 is the density of states at the normal state. For fitting the data measured under magnetic fields, the Dynes model is modified by including the Zeeman splitting energy ±μBB, added to E. At zero temperature, the differential conductance (dI/dV)(V) is directly proportional to the tunnelling density of states NS(E), whereas at finite temperatures, the thermal smearing effect should be considered, as follows

$$\frac{{\rm{d}}I}{{\rm{d}}V}(V)\propto \underset{-\infty }{\overset{\infty }{\int }}{N}_{{\rm{S}}}(E)\left[-\frac{\partial f(E+eV,T)}{\partial (eV)}\right]{\rm{d}}E$$

in which f is the Fermi–Dirac distribution.