A Dynamical Approach to the Explanation of the Upper Critical Field Data of Compressed H<sub>3</sub>S

Abstract

Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H c2 (T)) data of H 3 S reported by Mozaffari et al. [Nature Communications 10, 2522] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S 1 = {T c , gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of H c2 (T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μand m*-dependent equation for H c2 (T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model.For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of H c2 (0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S 2 = {μ, m*, interaction parameter λ m , Landau index N L }, which is altogether different from S 1 .

Compressed H<sub>3</sub>S: Fits to the Empirical <i>H<sub>c2</sub>(T)</i> Data and a Discussion of the Meissner Effect

“…For the variation of μ(t) = μ 1 q(t) (μ 1 = ρkθ), the model we employed for q(t) was specified in (17iii). The work in [20] and this paper shows that while almost equally good fits to the same data can be obtained by numerous values of ρ, the values of v F , ξ and λ L , etc., that they lead to are different.…”

“…However, these fits came with the caveat that μ(0) = q(0)ρkθ > 250 eV for all these models, in stark contrast with its value < 1 eV noted in (9). Because any value of ρ < 1 causes the limit z − in (13) to become pure imaginary and leads to complex roots, the fits in [20] were obtained by employing ρ = 1. In order to seek fits that also lead to μ(0) of the desired order, we stipulated that ( ) ( )…”

“…The μ-, Tand H-dependent core equations via which the H c2 (T) and J c (T) of any SC can be dealt with are given in Section 2. The procedural details of our approach are given in Section 3 where we follow up on [20], in which we gave fits using our approach to two data-sets reported in [6], for the purpose of shedding light on several features associated with a) H&M's result ( )…”

“…Substitution of ( 15) into (13) determines how λ m1 , μ 1 and h 1 change with t. It has been shown [20] that each of the following models for q(t) provides an excellent fit to the data of Mozaffari, et al:…”

“…A salient feature of our approach is that all the results it leads to via a chain of calculations depend only on three parameters, viz., ρ (which determines the chemical potential at t = 1), η and sf. Among these, by far the most important parameter is ρ [20]. For this reason, while seeking to obtain H&M's value of J c1 (0), we kept the values of η and the sf fixed at 2.76 and 0.03 T, respectively, and varied only ρ.…”