Dense Superconducting Hydrides: Comparison
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Please note this is a comparison between Version 1 by Dong Wang and Version 2 by Jason Zhu.

To date, about twenty hydrides experiments have been reported to exhibit high-Tc superconductivity and their Tc agree well with the predicted values. However, there are still some controversies existing between the predictions and experiments.

  • superconductivity
  • hydrides
  • high pressure

1. Unexplained Anomalous Superconducting Behaviors in Hydrides

According to the established understanding of superconductivity [1], both typical conventional and unconventional superconductors are universally characterized by three parameters: the London penetration depth λL, the Peppard coherence length ξ, and the electron mean free path. Type I superconductors with λL < ξ are a limited set of materials, mostly pure forms of elements, which are all considered as conventional superconductors [2], while most superconducting materials, including both conventional and unconventional, are type II with ξ < λL or strong type II have ξ ≪ λL superconductors. According to Ginzburg–Landau (GL) theory, strong type II superconductors commonly show a broadening of transition temperature as ∆T/Tc ~ 0.02, which increases with increasing applied magnetic field. For instance, in cuprate, it finds ∆T/Tc∝H2/3 [3]. Intriguingly, J. E. Hirsch [4][5][6] points out that the ∆T/Tc of hydrides shows no significant broadening in the increasing magnetic field. Even ∆T/Tc of H3S without magnetic field are regarded to be too small according to GL theory [7][5][6]. Therefore, although the superconducting hydrides have been accepted as typical BCS conventional superconductors, their most notable anomalous superconducting behavior remains unexplained by the classical GL theory.
The contradiction between the successful and accurate prediction of Tc in many high-pressure hydrides, and the fact that they do not follow the classical GL theory, requires further investigations in which the utmost urgent thing is to experimentally prove whether the high-pressure hydrides are superconductors or not by confirming if the key Meissner effect coexists with zero resistance. To date, a total of about seven magnetization measurements have been reported to observe the Meissner effect in CSH [7], LaHx [8][9], and HxS [10][9][11][12] with magnetic susceptibility and nuclear resonant scattering.
This anomalous behavior of hydrides can be caused by several possible reasons: (1) the pressure increases during cooling [13], which suppresses the broadening of Tc. This phenomenon is commonly observed in low-temperature diamond anvil experiments. Solving this problem requires minimizing the variation of the pressure values during the cooling process or accurately determining how the pressure changes with temperature [13]. Then a reliable temperature dependence of resistance curve could be measured to determine the broadening of Tc; (2) the significant resistance drop might be caused by other phase transitions rather than superconducting transition [5], such as metallization phase transitions, structural or magnetic phase transitions. These possibilities can be verified by investigating if the changes in the crystal structure, phonon structure, electronic structure, or magnetic structure concur with the resistance drops. More importantly, the Meissner effects must be conclusively confirmed to concur with the resistance drops; (3) it is a new type of superconductivity. That means not only GL theory but also BCS theory is inapplicable to this type of superconductivity, and new mechanisms need to be explored in the first priority for hydrides.

2. How to Understand the Origin of the Highest Tc in Hydrides

The BCS theory accounts for why hydrides could have high-Tc values but is unable to describe material-related properties, such as why LaH10 and CSH have the highest Tc values but other hydrides do not. Is there any other hydride having even higher Tc values? The answers to these questions are still unclear but fundamentally important for searching the higher Tc superconductors.
Marvin Cohen has long believed that the secret for increasing superconducting temperatures resides in covalent bonds; he asserts that these new compounds allow for testing of this idea [14]. Actually, in 1971, J. Gilman already predicted the possibility of making a new form of hydrogen in a metallic state through the preparation of a covalent compound LiH2F under pressure [15]. Quan and Pickett proposed the metallization of the covalent bond is the key driving force for high-Tc in MgB2 [16]. Covalent metals such as MgB2 are rare at ambient pressure but may be formed and become stabilized at high pressures. Indeed, it is noteworthy that so far all systems with Tc > 200 K under pressure are hydrogen-rich compounds, typically the covalent H3S [10], LaH10 [17], and CSH [18][19] systems. Besides, covalent hydrogen-rich organic-derived materials are another class of high-Tc materials that combine the advantages of covalent metals and metal super-hydrides. A common feature for all these classes of materials is the existence of covalent bonds, which probably implies that strong-covalent bonding is the key to driving the high-Tc superconductivity in hydrides. In addition, van Hove singularity around the Fermi level is also observed in H3S [20][16][21] and LaH10 [22][23] from calculations, which shows remarkable effects on Tc and thus is regarded as a possible origin for high Tc. Recently, Coulomb effects [24], Lifshitz transition [25], multiband pairing [26], and anharmonicity [27][28][29][30][31][32] are also proposed to account for the high-Tc superconductivity in the dense hydrides. Therefore, more efforts are demanded on investigating the origin of material-dependent high-Tc in hydrides, especially identifying and confirming the role of metallic covalent bonds in the high-Tc superconducting hydrides.

3. The Limits of the BCS-Eliashberg Theory

It is shown that electron-phonon coupling constant λ for many hydrides is typically predicted to be above 2 and some even reaches 5.8 in CaH6 [33]. Provided BCS–Eliashberg-Migdal theory usually accounts for the universal behavior of conventional superconductors with λ < 1.5–2, the validity of the theory for strongly coupling hydrides is still under debate [34][35][36]. In addition, anharmonic effects and energy-dependent electronic structure also play significant roles in the high-Tc superconductivity, which are neglected in the theory and require particular attention in future predictions.
(1) The Migdal-Eliashberg (ME) theory [37][38], in which vertex corrections are neglected for simplification, usually describes electron-phonon coupling effects accurately for conventional superconductors. As the electron-electron repulsion in the theory is usually approximated by an empirical parameter μ* (mostly considered to be ~0.1) to reproduce the experimental Tc [39], this approach becomes less accurate in the limit of sizeable electron-phonon coupling or in the case of systems with strongly anisotropic electronic properties [23][34][35][36]. It is more appropriate to use other methods based on a perturbative Green’s function approach such as the full ab-initio Migdal–Eliashberg approach or SCDFT method [40][41][23]. The latter recently has been applied to reproduce the Tc of H3S, in good agreement with the experiment [40].
 (2) Neglecting the energy dependence of density of states (DOS) around the Fermi level in the Migdal–Eliashberg theory for simplification may overlook some peculiar energy-dependent electronic structures occurring in hydrides (i.e van Hove singularity in H3S [16][21][42][43] and LaH10 [23], Fermiology due to Lifshitz transitions [25]) around Fermi level, which may suppress the Tc. For instance, predictions beyond the constant DOS approximation, by explicitly considering the electronic structure around the Fermi level in H3S, show the constant DOS approximation employed, to date, overestimates Tc by ∼60 K, or underestimates by ∼10 K when the energy dependence of DOS are present or absent near the Fermi level [21], respectively.
 (3) Because of the low mass of hydrogen and its large quantum fluctuations from equilibrium, substantial anharmonic corrections to Tc have been predicted in some superconducting hydrides and phases of hydrogen [27][28][29][30][31][32]. For instance, PtH at 100 GPa shows a strong anharmonic hardening of the phonon energies, which suppresses the Tc by over an order of magnitude [29]. Anharmonic effects are also predicted to lead to an inverse isotope effect in superconducting palladium hydride [30] and cause the value of Tc to fall 22% from 250 K to 194 K in H3S [27]. Thus, it becomes urgent to extensively develop an understanding of the anharmonic effects on Tc of the superconducting dense hydrides.
In addition, the BCS theory also faces some other unexplained experimental phenomena, such as the reversible phase transition between the normal and superconducting phases in the H-T plane (for type I superconductors); the electron mass in the London magnetic field should be twice of the free electron mass (2m) rather than twice of an effective mass (2m*) as predicted.

4. More Experiments Are Demanded

Due to the complexity and challenges of high-pressure experiments, the high-pressure measurements of hydrides is only limited to <20 groups, which stays far behind theoretical predictions (more than 5000), and the experiment results are largely outnumbered by those theoretical predictions [23]. The experiments are not only performed to confirm and the benchmark of theoretical predictions, but it is more important to reveal breakthrough discoveries that may be overlooked by theories. Thus, in addition to routine resistance measurements, more experimental efforts should be devoted to developing new high-pressure techniques facilitating the following measurements on the superconducting hydrides.
(1) Crystal structure determination of hydrides. The crystal structure is the most fundamental information, however, to date, the positions of H atoms in hydrides remain undetermined with conventional X-ray methods due to their weak scattering power. Consequently, all hydrogen networks and the nature of bonding predicted from the theory have never been confirmed. However, owing to the new technology developments of high-pressure X-ray diffraction beamline for diamond anvil cell [44], recently a successful unit cell parameters determination of phase IV of hydrogen at 200 GPa with synchrotron X-ray by Ji et al. [45][46] shows promise for conquering the problems in the future. Powder neutron diffraction has been applied at high-pressure study up to 90 GPa and could be an ideal probe to study the H structures [47].
(2) The magnetic responses of superconducting hydrides. To date, only seven magnetization measurements have been reported: AC magnetic susceptibility measurements for CSH [7], three for HxS [10][9][12], LaHx [8][9], the nuclear resonant scattering measurements for H3S [11]. However, the magnetic signal from samples are commonly complicated by the noise from backgrounds [48][49][50], which leaves the reported Meissner effects in debate [48][49][50]. To increase the required signal-to-background ratio required the development of a new high-pressure technique, such as specially designed miniature nonmagnetic DAC cells made of Cu-Ti alloy is needed to accommodate in a SQUID magnetometer [51].
 (3) Electronic and vibrational properties of hydrides. The electron pairing in hydrides are mediated by electron-phonon coupling, which is essentially associated with interactions between the electronic states near the Fermi level and the high frequencies phonons of H atoms. The information on the electronic and vibrational properties of H is crucial for understanding the mechanisms underlying the material-dependent high Tc in hydrides. Experimentally, the electronic structure of H atoms (and host atoms) can be probed with X-ray Raman [52] and nuclear magnetic resonance spectroscopy [53]. The vibrational properties of hydrides can be obtained from the phonon dispersion, which can be measured with the high resolution (meV)-energy resolution inelastic X-ray scattering. The zone-center vibrational optical modes and the superconducting gap can be also studied with or Raman and Infrared spectroscopes [54].
Combing the results from (1)–(3), it is also possible to determine (a) if the anomalous resistive behavior hydrides is originated from superconducting transition or other phase transitions or errors from experiments; and (b) the anharmonic effects on the Tc.

5. Perspective

The exploration of room temperature superconductors has been a coveted goal of many scientists. The progress in the last 30 years has been tremendous. The discovery of new superconductors, including cuprates, heavy fermion superconductors, organic superconductors, iron-based superconductors, two-dimensional superconductors, topological superconductors, nickelates, and now dense superhydrides, has not only provided important topics for physics and materials science but also opened up new research fields. The research of superconductivity has gone through the London equation [55], Landau-Ginzberg theory [56], and BCS theory [57]. The Meissner effect, as a result of spontaneous symmetry breaking, is a manifestation of the Anderson–Higgs mechanism [58][59][60]. The BCS theory is one of the most important theoretical advances after the establishment of quantum mechanics and has been successfully applied to conventional superconductors. However, the mechanism of high-temperature superconductivity remains a grand challenge in physics and a unified theory remains elusive. To date, the existence of d-wave symmetry and pseudo-energy gaps in copper-oxygen is well established [61][62][63]. Studies of iron-based superconductors, organic superconductors, heavy fermion superconductors, two-dimensional superconductors, nickelates, and topological superconductors have also shown the existence of multiple cooperative and competing orders is a universal phenomenon [64][65][66][67][68][69]. These results provide a base for developing ultimate theories in the future.

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