The current status and future development of high-temperature conventional superconductivity

The robust evidence and reproducibility of high-temperature superconductivity in hydrogen-rich materials under challenging experimental conditions of megabar pressures is presented.

The current status and future development of high-temperature conventional superconductivity

Mikhail I. Eremets
This survey highlights key advancements in high-temperature superconductivity in hydrogen-rich materials, emphasizing the robust evidence and reproducibility of superconductivity under challenging experimental conditions of megabar pressures.In the near future, achieving roomtemperature superconductivity is highly probable, and the field is expected to transition towards near-ambient-pressure superconductivity.
A new family of superconductors, hydrogen-rich superconductors, was established following the discovery of superconductiv ity (SC) w ith a critical temperature ( T c ) of 203 K in hydrogen sulphide H 3 S compressed to megabar pressures [1 ].H 3 S is a covalent metal with strong bonds between sulphur and hydrogen atoms.Many others are hydride-rich hydrides or superhydrides with a very different structure, in which hydrogen atoms are weakly covalently bonded to form a cage, while the host metal atom is in the centre of the cage and acts as an electron donor to the hydrogen network.A record T c of ∼250 K has been achieved in LaH 10 [2 ].These hydrides are conventional superconductors, allowing the calculation of superconducting properties in conjunction with crystal structure predictions.The original ideas must be credited to Neil Ashcroft, who first (1968) realized that high-T c conventional SC was theoretically possible in metallic hydrogen [2 ], and 40 years later (2004) also guessed that metallic hydrogen sublattices could be stabilized at a more accessible pressure in H-rich materials [2 ].
The new superconductors such as H 3 S [1 -5 ], YH 9 [6 -8 ] and LaH 10 [2 ] are stable at high pressures, ∼140-200 GPa.Even higher pressures of ∼350-400 GPa are required for the expected roomtemperature SC in MgH 6 , LaH 18 , CeH 18 and several other materials.Despite the limitations imposed by the high-pressure environment, successf ul sy nthesis, structural characterization and experimental evidence of SC at these pressures have been achieved.
Superhydrides are produced at megabar pressures by reacting pure metals with excess hydrogen, often using laser heating.The use of alternative hydrogen sources, such as ammonia borane and hydrocarbons, has greatly simplified the experiments.
The primary tool for the detection and characterization of SC is electrical measurements.Four probe electrical transport measurements provide T c from a sharp change in the temperature dependence of the electrical resistance R ( T ) (Fig. 1 a) and the true zero resistance in the superconducting state.The dependence of T c on the applied magnetic field gives the value of the upper critical field H c2 at which SC is destroyed, and hence the coherence length ξ (Fig. 1 b).
Magnetic susceptibility measurements are equally important (see for example, reference [9 ]) as they provide a wealth of information about a superconductor, including T c , lower critical field H c1 , penetration depth λ L , vortex creep, critical current density and other parameters (Fig. 1 c).These measurements are even more challenging than electrical measurements but are currently possible up to at least 200 GPa using a tiny non-magnetic diamond anvi l cel l (DAC) coupled with a SQUID magnetometer [1 ].The coil technique is also employed [3 ], and a new magnetometry method based on nitrogen vacancy (NV) centres has recently been used [10 ].The latter revealed a pronounced Meissner effect in CeH 9 [10 ] (Fig. 1 d).
However, the Meissner effect is subtle or barely observable in H 3 S and LaH 10 (Fig. 1 c).This is not surprising for superconductors with strong vortex pinning.In the presence of strong pinning, the interesting phenomenon of trapped magnetic flux can be observed [9 ]: after a magnetic field is removed, a remnant magnetization persists up to T c (Fig. 1 e).This phenomenon provides conclusive evidence for SC as such.The trapped flux method is highly effective when combined with a DAC, as the background from the DAC is virtually eliminated since the signal is measured in nominally zero applied magnetic fields.Further evidence for SC in H 3 S is provided by the shielding of [17 ]).(b) The dependence of T c on applied magnetic field in CeH 9 and CeH 10 .In both cerium hydrides, SC is suppressed at magnetic fields exceeding H c2 (data from ref. [14 ]).(c) Magnetic susceptibility measurements in H 3 S at 162-167 GPa (ref.[18 ]).The Meissner effect in superconducting H 3 S at 155 GPa (magnetic field expulsion upon cooling the sample below its T c at an applied magnetic field, field cooling (FC) mode-red circles) is noticeably weaker than the magnetic field screening in zero field cooling (ZFC) mode (black circles).The yellow curve represents smoothed FC data (Fast Fourier Transformation (FFT) filter, 7 points) for clarity.(d) The Meissner effect is rather pronounced in CeH 9 as found using the NV centre technique (red and blue dots), consistent with simultaneous measurements of electrical resistance indicating a transition at T c ≈ 91 K at 137 GPa (grey dots) data from ref. [10 ]).(e) Temperature dependence of a trapped magnetic moment in superconducting H 3 S generated under FC conditions at different magnetic fields μ 0 H M (5-3000 mT) (details are in ref. [9 ]).
applied magnetic fields by the H 3 S sample, monitored by nuclear magnetic resonance scattering of synchrotron radiation with a 119 Sn Mössbauer sensor.Finally, the superconducting gap in H 3 S was estimated by infrared spectroscopy [2 ] and tunnelling spectroscopy (to be published).The isotope effect, i.e. the shift in T c resulting from the replacement of hydrogen by deuterium atoms, prov ides ev idence for the electron-phonon mechanism of SC in hydrides.A significant shift in T c was observed in H 3 S, LaH 10 , YH 6 , YH 9 , CeH 9 and CeH 10 [11 ], as well as in other compounds (Fig 1 a).
Powerful theoretical predictions of crystal structures and calculations of SC have greatly accelerated the experimental search for new superconductors [2 ].There are numerous examples of excellent agreement with experimental observations, such as the prediction of SC in LaH 10 at 280 K at ∼200 GPa [2 ], which closely matches the experimen-tally observed T c of ∼250 K at 170 GPa [2 ].Another recent example is CaH 6 at T c ∼ 215 K, where the remarkable cage structure was predicted long before it was realized in other hydrides ( [13 ] and references therein).These and other successes may create the i l lusion that experiments merely confirm predictions, and that the main challenge is to select suitable materials from a large number of candidates.However, the importance of experimental research should not be underestimated.First, it is the ultimate judge of the validity of new superconductors.Secondly, even when driven by theoretical predictions, experiments often reveal unexpected phenomena.
For example, in the case of H 2 S, SC at 70 K was predicted and confirmed, but it was serendipitously discovered that H 2 S can be transformed into H 3 S, which has T c = 203 K. Independently, SC with T c = 200 K was predicted in H 3 S at high pressure in another system (H 2 S) 2 H 2 .Experiments often reveal stable and metastable phases that have been overlooked in theoretical calculations (as observed in LaH 10 ).Deviations from the predictions also highlight the importance of anharmonic and other corrections.In a number of cases, the predicted phases have not been found yet (H 3 Se, YH 10 , MgH 6 , LuH 6 , Hf H 10 , etc).
All these discrepancies do not necessarily mean that the predictions are wrong; rather, the calculations can be refined based on these experimental results.However, publishing negative results is a challenge.It is clear that the synergy between theory and experiment needs to be strengthened through direct contacts and discussions, especially as the field moves from binary to ternary systems in the search for new superconductors, not only at high, but also at low and ambient pressures.The numerous predictions of superconductors with T c > 80 K ( [15 ,16 ] and references therein) hold great promise for practical applications.
Finally, the tantalizing goal of achieving room-temperature SC appears to be within reach, given the predictions of numerous phases in the currently accessible pressure range of 3 00-400 GPa.

Figure 1 .
Figure1.Characterization of superconducting state in hydrogen-rich compounds using different methods.(a) Four-probe electrical transport measurements demonstrate a sharp resistance drop to zero Ohm in both H 3 S (at 141 GPa) and its deuterated counterpart D 3 S (at 154 GPa) (details are in ref.[17 ]).(b) The dependence of T c on applied magnetic field in CeH 9 and CeH 10 .In both cerium hydrides, SC is suppressed at magnetic fields exceeding H c2 (data from ref.[14 ]).(c) Magnetic susceptibility measurements in H 3 S at 162-167 GPa (ref.[18 ]).The Meissner effect in superconducting H 3 S at 155 GPa (magnetic field expulsion upon cooling the sample below its T c at an applied magnetic field, field cooling (FC) mode-red circles) is noticeably weaker than the magnetic field screening in zero field cooling (ZFC) mode (black circles).The yellow curve represents smoothed FC data (Fast Fourier Transformation (FFT) filter, 7 points) for clarity.(d) The Meissner effect is rather pronounced in CeH 9 as found using the NV centre technique (red and blue dots), consistent with simultaneous measurements of electrical resistance indicating a transition at T c ≈ 91 K at 137 GPa (grey dots) data from ref.[10 ]).(e) Temperature dependence of a trapped magnetic moment in superconducting H 3 S generated under FC conditions at different magnetic fields μ 0 H M (5-3000 mT) (details are in ref.[9 ]).