Unconventional superconductivity in highly-compressed unannealed H3S

While great scientific efforts focus on the synthesis and studies of near-room-temperature (NRT) superconductors exhibited record superconducting transition temperatures (for instance, laser annealed H3S, LaH10 and YHn (n = 4,6,7,9) with Tc > 200 K), unannealed lowTc counterparts of NRT superconductors stay in the background. However, unannealed highly-compressed hydrides are part of hydrogen-rich superconductors family and the success in understanding of NRT superconductivity depends on the study of these materials too. In this paper we analyse experimental temperature dependent upper critical field data, Bc2(T), reported by Drozdov et al (Nature 525, 73 (2015)) for unannealed highly-compressed (P = 155 GPa) H3S with Tc = 46 K and show that this material is unconventional superconductor which exhibits the ratio of Tc to the Fermi temperature, TF, in the range of 0.02 ≤ Tc/TF ≤ 0.05.


I. Introduction
The discovery of near-room-temperature (NRT) superconductivity in highly compressed sulphur hydride, H3S, by Drozdov et al. [1] and in lanthanum decahydride, LaH10, by Somayazulu et al. [2], raises a wide public interest and great scientific efforts to study pressure-induced superconductivity in hydrogen-rich materials [3][4][5][6][7]. It should be noted, that the discovery of the effect of pressure-induced superconductivity in non-superconducting materials is attributed to Jörg Wittig [8] who converted elemental cerium into superconductor at pressure of P = 5 GPa. During this, more than fifty years, long research journey, pressureinduced superconductivity was found in dozens of non-superconducting elements and compounds (details can be found in recent reviews [3,[9][10][11]).
At the same time, some unannealed phases, and particularly H3S [1], are also superconductors with, however, much lower Tc. The latter is this reason why these superconducting phases are in the background of its NRT counterparts. Independent of its lower Tc's, these low-Tc unannealed phases are highly-compressed hydrogen-rich superconductors and there is an interest to understand the superconductivity in these compounds too.
In this paper we analyse temperature dependent upper critical field data, Bc2(T), for unannealed H3S phase (P = 155 GPa) reported by Drozdov et al. in their first milestone paper [1]. In the result, it is found that unannealed H3S phase has the ratio of Tc to the Fermi temperature, TF, in the range of 0.02 ≤ Tc/TF ≤ 0.05, and, thus, this superconductor falls in the unconventional superconductor band of the Uemura plot [16][17][18] together with heavy fermions, fullerens, cuprates, pnictides and NRT superconductors.

II. Extrapolative models for ground state upper critical field
Ground state upper critical field, Bc2(0), is given in the Ginzburg-Landau theory [19] by following expression: where 0 = 2.068 • 10 −15 Wb is magnetic flux quantum, and (0) is the ground state coherence length. To deduce (0) value from real world measurements (which very often perform at high reduced temperatures) several models were proposed. In this paper, to deduce (0) value for unannealed H3S phase we will use classical two-fluid Gorter-Casimir model (GC model) [20]: as well as model proposed by Gor'kov [21] (Gor'kov model): and modified Werthamer, Helfand, and Hohenberg (WHH) [22,23]
Examination of obtained values for Tfluc,phase and Tfluc,amp (Table I) leaded us to an important conclusion that thermodynamic fluctuations are not make influence on the observed Tc in this compound, which is different from the case of annealed H3S phase where the ratio of Tc/Tfluc,amp in some scenarios can be as high as Tc/Tfluc,amp = 0.7 [39].

V. Conclusions
In summary, in this paper we analyse experimental Bc2(T) data of unannealed highlycompressed H3S compound and find that this superconductor exhibits unconventional superconductivity. In addition, we show that thermodynamic fluctuations do not affect the observed critical temperature Tc = 46 K in this superconductor.