High-TC Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions Between Hydrogen and Central-Atom Electrons 1 2 Dale R. Harshman Anthony T. Fiory 27 May 2020† Abstract The uniquely characteristic macrostructures of binary hydrogen-clathrate compounds MHn formed at high pressure, a cage of hydrogens surrounding a central-atom host, is theoretically predicted in various studies to include structurally stable phonon-mediated superconductors. High superconductive transition temperatures TC have thus far been measured for syntheses with M = La, Y, and Th. In compressed LaH10, independent studies report TC of 250 K and over 260 K, a maximum in TC with pressure P, and normal-state resistance scaling with temperature (suggesting unconventional pairing). According to reported band structure calculations of Fm m-phase LaH10, the La is anionic, with the chemical valence electrons appearing evenly split between La and H10. Thus, compressed LaH10 contains the combination of structure, charge separation and optimal balanced allocation of valence electrons for supporting unconventional high-TC superconductivity mediated by Coulomb interactions between electronic charges associated with La and H10. A general expression for the optimal superconducting transition 1 1/2 2 temperature for MHn clathrates is derived as TC0 = kB [(n + v)/2A] e /ζ, where is a universal constant, (n + v) is the chemical valence sum per formula unit, taking unity for H and v for atom M, A is the surface area of the H-polyhedron cage, and is the mean distance between the M site and the centroids of the polyhedron faces. Applied to Fm m LaH10, TC0 values of 249.8(1.3) K and 260.7(2.0) K are found for the two experiments. Associated attributes of charge allocation, structure, effective Coulomb potential, and H-D isotope effect in TC of Fm m LaH10 and Im m H3S are discussed, along with a generalized prospective for Coulomb-mediated superconductivity in MHn. Keywords LaH10 Superhydrides Superconductivity TC Coulomb mediation Dale R. Harshman [email protected] 1 Department of Physics, The College of William and Mary, Williamsburg, VA 23187, USA 2 Department of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA † Harshman D. R. and Fiory A. T., J. Supercond. Nov. Magn. (2019) http://dx.doi.org/10.1007/s10948-020-05557-4 public share: https://rdcu.be/b411V 1 Introduction dependence reported in [29]. Negative pressure shifts in TC calculated in [5, 23-26] Binary hydride clathrates MHn are a class of evidently do not capture these experimental compounds comprising a central atom findings. In the normal state, the electrical surrounded by a polyhedron hydrogen cage resistance of LaH10 and YH9 samples is found and have been designated as superhydrides. to be nearly proportional to temperature [12- Following earlier theoretical results [1], 14, 30], exhibiting the characteristic absence superconductivity at high temperatures has of resistance saturation of unconventional been predicted in dozens of such (and other) high-TC superconductors [31]. hydride compounds under compression, assuming strong-coupled electron-phonon A review of conventional electron-phonon theory [2-4]. Notably, the superconductors coupling theory in [4] includes a listing of LaH10 [5, 6], YHn (n = 4, 6, 9) [5-9], and ThHn numerous computational flaws that remain to (n = 9, 10) [6, 10] have been experimentally be addressed.1 As independent corroboration verified in [11-13], [14, 15], and [16], of phonon mediation has yet to be respectively. The LaH10 clathrate, exhibiting convincingly established [36], alternative superconductivity at temperatures of about considerations of electronic mechanisms are 250 K [12] and above 260 K [13] for applied being developed, particularly in view of the pressures P ~ 137 – 218 GPa, currently holds high pressures [37], correspondences to high- the record for the highest transition TC cuprates [38] and limitations on the Fermi temperature, TC. Electron-phonon interaction temperatures [39]. theory rooted in strong-coupling Migdal- Éliashberg methodology [17-19], density An unconventional Coulomb-mediated functional theory, or ab initio methods [4, 20], high-TC mechanism, wherein super- predicts TC for LaH10 spanning a broad range conductivity originates locally within the of 199 – 288 K [4-6, 21-26] and monotonic- metal-clathrate structure, is proposed herein ally decreasing with increasing pressure [5, which is independent of conventional 24-26]. The Fm m phase of LaH10 is phononic pairing involving the extended theoretically stable at P = 129 – 264 GPa [25]. crystalline lattice. The proposed model is a novel adaptation of the inter-reservoir Although electrical resistance meas- Coulomb-mediated superconducting pairing urements are generally employed as the theory, first introduced in [40], and principal indicator of superconductivity, the successfully applied to compressed Im m H3S reported data already indicate unconventional [41],2 which asserts that quasiparticle pairing behavior, particularly for LaH10 and YH9. For arises from Coulomb interactions between each compound, a maximum TC is observed in charges in two adjacent, spatially-separated its pressure dependence, referred to as a reservoirs, designated as type I and type II. In “dome” in T -vs.-P [12, 14], setting bounds on C pressure for maximum T as found in C 1 The layered FeH , synthesized with no demonstration unconventional high-TC superconductors, such 5 of superconductivity [32], is predicted to be as in the compressed phases of Cs3C60 [27]. superconducting in [33, 34] and non-superconducting in Differences between the LaH10 samples [35]. reported in [12] and [13] indicate a 10-K 2 Note that here is a typographical error at the end of increase in T related to increased pressure, C Section 3 (p. 5) of [41] which should read, “ℓ = (A/)1/2 similar to the influence of higher synthesis = 2.88 Å,” with the reported TC0 remaining unchanged. pressure noted in [28] and the pressure the case of compressed LaH10, the hydrogen 2 Coulomb-Mediated Superconductivity polyhedron cage is identified as type I in MHn (superconducting) and the central La as type II (mediating). These charge reservoirs are Experimental bases for unconventional high- separated by an interaction distance TC superconductivity and optimal TC are the determined as the mean distance between the non-monotonic “dome”-shaped pressure polyhedron center and the centroids of its dependence in TC reported for Fm m LaH10 faces. The requisite balance between type I [12] and P63/mmc YH9 [14]. This signature and type II charges for optimal high-TC feature of high-TC materials defines optimal P superconductivity posited in [40] appears and TC at the top of the dome where TC is satisfied by the anionic nature of the La charge highest [31]. As shown by the samples as revealed by theoretical band structure of numbered 1 – 6 in [12], TC systematically LaH10 at high pressure [5, 22]. As shown in increases with increasing P at sub-optimal Section 2, each reservoir contains a number of pressures. Conventional electron-phonon charges per formula unit equal to one-half of interaction theory predicts a fundamentally the total number of chemical valence charges, different monotonic decrease in TC with which is optimally 13 for LaH10. increasing pressure above a structural stability threshold [24-26], and resembling the behavior of depressed TC at pressures above In Section 2, a general expression for TC0 optimal [12, 13]. Values of optimal TC and is derived for MHn clathrates and applied to corresponding pressures are determined from calculate TC0 of LaH10. Section 2 also data for LaH10 [12, 13] and YH9 [14] (Section considers the question of superconductivity A1). and charge equilibrium between the two reservoirs in LaH , YH , and ThH , express- 10 n n Unconventional high-TC superconductivity ing TC0 as a function of the average H-H bond in the hydrogen clathrates is further length in the binary clathrates. Section 3 demonstrated in the temperature dependence considers potential superconducting clathrates of the normal-state resistance, RN(T). As is in terms of inter-reservoir charge equilibrium discussed in Section A2, RN(T) for both Fm m and phase purity. Also, data for the isotope LaH10 [12, 13] and P63/mmc YH9 [14] is effect in TC reported in [12] are analyzed from linear, exhibiting an absence of saturation at the perspective of sample-quality variations, high temperature, indicative of an absence of similar to that done for Im m H3S [42]. strong electron-phonon coupling, and a near- Finally, implications of the Coulomb potential zero intercept extrapolation to zero signature in optical reflectivity data and temperature, RN(T0) ~ 0. Given that both relevant electron-phonon coupling in LaH10, materials exhibit this unconventional are considered. Results are summarized and behavior, it is unlikely coincidental. Recall conclusions drawn in Section 4. The that the lack of saturation and R (T) T are Appendix contains theoretical and N well-recognized features of optimal high-TC experimental TC-vs-P results for LaH10, YH9, materials [31, 43], strongly suggesting a and YH6 (Section A1), normal-state resistance pairing mechanism akin to that of other (Section A2), pressure dependence of the (unconventional) high-TC superconductors. In LaH10 lattice parameter (Section A3), and optimally- and over-doped high-T cuprates, accuracy and systematic errors of the C R (T) T is generally attributable to interlayer Coulombic pairing model (Section N “Planckian” dissipation [44, 45]. Analysis of A4). RN in Section A2 indicates Planckian 3 1 2 dissipation in LaH10 comparable to the high- TC0 = kB (/ℓ) e /ζ , (1) TC cuprates [46-48]. where ζ is the perpendicular distance between Superconductive pairing in high-T the two interacting charge reservoirs, and the C 1/2 superconductors is successfully modeled by length ℓ = (/A) is the linear interaction Coulomb interactions between charges in charge spacing defined by the participating spatially separated charge reservoirs [40, 41, charge (a dimensionless fraction) per unit 49-55].