ARTICLE https://doi.org/10.1038/s41467-019-10552-y OPEN Superconducting phase diagram of H3S under high magnetic fields Shirin Mozaffari1, Dan Sun2, Vasily S. Minkov3, Alexander P. Drozdov3, Dmitry Knyazev3, Jonathan B. Betts2, Mari Einaga4, Katsuya Shimizu 4, Mikhail I. Eremets3, Luis Balicas 1 & Fedor F. Balakirev 2 The discovery of superconductivity at 260 K in hydrogen-rich compounds like LaH10 re- invigorated the quest for room temperature superconductivity. Here, we report the tem- 1234567890():,; perature dependence of the upper critical fields μ0Hc2(T) of superconducting H3S under a record-high combination of applied pressures up to 160 GPa and fields up to 65 T. We find that Hc2(T) displays a linear dependence on temperature over an extended range as found in multigap or in strongly-coupled superconductors, thus deviating from conventional Werthamer, Helfand, and Hohenberg (WHH) formalism. The best fitofHc2(T) to the WHH formalism yields negligible values for the Maki parameter α and the spin–orbit scattering constant λSO. However, Hc2(T) is well-described by a model based on strong coupling superconductivity with a coupling constant λ ~ 2. We conclude that H3S behaves as a strong- coupled orbital-limited superconductor over the entire range of temperatures and fields used for our measurements. 1 National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310, USA. 2 Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 3 Max-Planck-Institut fuer Chemie, Hahn-Meitner Weg 1, 55128 Mainz, Germany. 4 KYOKUGEN, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka, Osaka 560-8531, Japan. Correspondence and requests for materials should be addressed to F.F.B. (email: [email protected]) NATURE COMMUNICATIONS | (2019) 10:2522 | https://doi.org/10.1038/s41467-019-10552-y | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10552-y he ongoing scientific endeavor to stabilize super- mechanisms for a given type-II superconductor. The WHH the- Tconductivity at room temperature led to the discovery ory24 includes both pair-breaking effects through the Maki of superconductivity, with a very high critical temperature parameter and the spin–orbit constant. = fi Tc 203 K, in sulfur hydride H3S under high pressures of Here, we report measurements of the upper critical eld in H3S 1 2,3 p = 155 GPa .H3S along with other hydrides seems to be the samples under extremely high pressures and high magnetic fields. closest compound, so far, to metallic hydrogen, which is predicted The ultrahigh pressures can only be obtained through the use of a 4–6 to be a high temperature superconductor .H3S forms as the diamond anvil cell (DAC), however, measurements on samples result of the chemical instability of H2S under high pressures, contained by a DAC are quite challenging, particularly in pulsed 7–10 where H2S decomposes into elemental sulfur S and H3S . fields due to the narrow magnet bore and the large magnetic-field The structure of H3S is believed to be body-centered cubic with induced currents which heat the cell. The small diameter of the Im-3m symmetry above 150 GPa10, and characterized by H atoms DAC1 employed in our study allows us to perform transport symmetrically situated midway between two body-centered S measurements up to 65 T without heating the sample sig- atoms. Tc shows a sharp increase from 95 K to 203 K in the nificantly. Our pulsed field measurements under p > 150 GPa pressure range of 110–155 GPa, but decreases with further represent a significant pressure increase over a previous pulsed 25 increasing the pressure due to the pressure-induced phase tran- field study under 10 GPa .Wefind that H3S is an orbital-limited 1,10 sition from the R-3m to the Im-3m phase of H3S . superconductor over the entire temperature range and likely a The superconductivity in H3S is believed to be conventional, or multigap or strongly coupled superconductor. whose pairing is mediated by phonons characterized by high- frequency optical modes due to the motion of hydrogen1,11–14. The high Tc arises from both the metallization of the strongly Results 15 covalent bonds in H3S and the high phonon frequencies dis- Temperature dependence of the resistance. Figure 1 displays the 16 played by its light elements . Band structure calculations indicate resistance as a function of the temperature T for H3S samples 17 fi that H3S is a multiband metal having a large Fermi surface pressurized up to 155 GPa and 160 GPa. The onset, i.e., the rst (broad energy dispersive bands) as the result of the hybridization deviation from the normal state resistivity, of the super- 8,9,13,16,18,19 = between the H 1s and the 3p orbitals of sulfur . Band conducting transitions are estimated to be Tc 201 K for the = structure calculations also yield small Fermi surface pockets for sample under 155 GPa, and Tc 174 K for the other sample 17 the high-Tc phase of H3S . under 160 GPa. The drop in Tc for the higher pressure sample is 1 Despite the very high Tcs reported for H3S, the studies of consistent with the results in ref. The width of these transitions Δ = Hc2(T) are limited to a narrow range of temperatures close to Tc are Tc 5.5 K and 26 K for the samples under 155 GPa and 160 due to the inherent experimental difficulties in performing GPa, respectively, indicating that the latter sample is less homo- ultrahigh pressure measurements under very high magnetic fields. geneous, or that it is subjected to stronger pressure gradients. The The behavior of Hc2(T) provides valuable information such as an value of Tc for the sample under 155 GPa increases slightly over estimation of the Cooper pair coherence length, the strength of time, indicating an evolution towards a more homogeneous the electron–phonon coupling, the role of the spin–orbit cou- sample or weaker pressure gradients. Notice that the super- pling, and the dominant mechanism breaking the Copper pairs. conducting transition displayed by this sample shows a step In type-II superconductors, the orbital and the spin- around 195 K indicating that its superconducting state indeed is paramagnetic pair-breaking effects are the two main mechan- inhomogeneous. For samples synthesized within the confines of isms depairing electrons under high magnetic fields. The orbital the DAC a certain degree of inhomogeneity is inevitable. The pair-breaking effect explains the suppression of superconductivity multiple SC transition steps merge into a single one above a via the formation of Abrikosov vortices20 in the presence of a field. The superconductivity is suppressed when the kinetic 70 energy associated with vortex currents exceeds the condensation fi energy of the paired electrons. When the magnetic eld approa- 60 orb ¼ ϕ = πξ2 ches a critical value Hc2 0 2 , referred to as the orbital limiting field, the vortex cores overlap and the system returns 155 GPa: 07/2018 50 to the normal state. Here, ϕ0 is the flux quantum and ξ is the coherence length. The spin-paramagnetic effect explains 155 GPa: 09/2018 the effect of the magnetic field on the spin of the electron ) 40 based on the work by Clogston21 and Chandrasekhar22. When Ω (m the magnetic energy exceeds the superconducting gap, i.e. R 30 155 GPa: 11/2018 = χ 2 ¼ = ð ÞΔ2 1 2 pHp 1 2N EF , superconductivity will be suppressed, χ Δ where p, N(EF), and are the normal state paramagnetic sus- 20 ceptibility, the density of states at the Fermi level, and the superconducting gap, respectively. If we only consider the spin- 160 GPa: 07/2018 paramagnetic effect, the zero-temperature Pauli limiting field 10 (Chandrasekhar-Clogston limit) for a weakly coupled super- μ = Δð ¼ conductor is approximately 0Hp(0) 1.86 Tc, where 2 T 0 Þ : 120 140 160 180 200 220 240 260 280 300 0 3 52 kBTc (for a conventional Bardeen-Cooper-Schrieffer χ ¼ μ2 ð Þ T (K) (BCS) superconductor) and p g BN EF (g is the Landé g μ factor and B is the Bohr magneton). Hp can be renormalized Fig. 1 Resistive transition towards the superconducting state. Resistance R – by the strength of the electron phonon coupling or by as a function of the temperature T for two DACs containing H3S samples 2 electronic correlations. In many superconductors Hc2(T)is under pressures p = 155 GPa and 160 GPa. Red line is a fittoR = R0 + AT . 23 affected byp bothffiffiffi pair-breaking mechanisms. The Maki para- Notice that the Tc for the 155 GPa sample shifts slightly to higher values α ¼ orbð Þ= ð Þ meter 2Hc2 0 Hp 0 is a measure of the relative strength while its resistance decreases between July and September 2018. Source between the orbital and the paramagnetic pair-breaking data are provided as a Source Data file 2 NATURE COMMUNICATIONS | (2019) 10:2522 | https://doi.org/10.1038/s41467-019-10552-y | www.nature.com/naturecommunications NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-10552-y ARTICLE moderate field of 3 T in the 155 GPa sample (Supplementary temperatures. The temperature dependence of the Hall coefficient Fig. 1). RH is shown in Fig. 2b, obtained by multiplying the slope of fi μ fi We nd that R(T) exhibits supralinear behavior in both Rxy( 0H) at high elds by the sample thickness, estimated to ∝ 2 = μ samples, which is well described by a R T leading term. A be t (2 ± 1) m. We observed a noticeable decrease in RH(T) quadratic temperature dependence for the resistivity is usually by as much as 20% as the temperature is decreased, corre- – = ascribed to the inelastic electron electron scattering in Fermi sponding to an increase in the effective carrier density n 1/eRH.