Sulfur hydride and superconductivity theory

In his comments in “Unmasking the record-setting sulfur hydride superconductor” (Physics Today, July 2016, page 21 ) Sung Chang quotes Mari Einaga, who explains that the Bardeen-Cooper-Schrieffer (BCS) theory “was largely abandoned because of the discovery of cuprates and other unconventional superconductors.” We believe that is true, and it has curtailed development of the BCS theory. Indeed, Jorge Hirsch, in a dramatic review, ¹ has called the whole theory into question.

Hirsch listed metallic hydrogen and metal hydrides as examples of the failure of the BCS theory’s predictive power: The predicted high transition temperature, T_c, in those two cases has not materialized. ¹ However, in an ironic twist, Mikhail Eremets and colleagues have recently found T_c = 203 K in sulfur hydride. ² Their finding appears to vindicate the BCS theory because Tian Cui and his team had used the theory ³ to predict the record-breaking high T_c before the experiment by Eremets and colleagues, and Ion Errea and coworkers later verified Cui and coworkers’ results theoretically. ⁴ Both groups used the McMillan formula (derived from a generalized version of BCS theory), which relates T_c to the electron–phonon coupling strength and the Coulomb pseudopotential, a measure of the Coulomb repulsion between electrons.

Despite that twist, Hirsch does have other points that need serious consideration. He argues that in the BCS theory, the Coulomb pseudopotential acts as a wild card that can be freely adjusted to fit the theory with any experimental result. ¹ The Coulomb pseudopotential, 0.16 from a private communication with Errea, is unusually large compared with its typical value of approximately 0.12. The discrepancy needs to be explained.

We note, too, that the electrical resistivity of sulfur hydride under pressure in the normal state is experimentally measured in reference but is not theoretically evaluated in references and . The theoretical evaluation should be consistent with the experimental measurement because, according to BCS theory, both resistivity and superconductivity arise from the same electron–phonon interaction. Historically, a considerable number of researchers attempted but were unable to find consistent resistivity and superconductivity theoretically, even in simple metals. ⁵ The significance of those failures should not be underestimated. A similar evaluation should be made on sulfur hydride, and an understanding sought of the unusually large Coulomb pseudopotential there.

In his article, Chang states that “the BCS theory has a deceptively simple recipe for achieving high T_c: Create a high density of conduction-electron states and couple the conduction electrons to high-frequency phonons.” But he voices caution. Perhaps understanding normal-state electrical resistivity and Coulomb pseudopotential in sulfur hydride can be of some help in getting to the bottom of the problem.