High temperature superconductivity in sulfur hydride under ultrahigh pressure: A complex superconducting phase beyond conventional BCS

The recent report of superconductivity under high pressure at the record transition temperature of Tc=203K in sulfur hydride has been identified as conventional in view of the observation of an isotope effect upon deuteration. Here it is demonstrated that conventional theories of superconductivity in the sense of BCS or Eliashberg formalisms can neither account for the observed values of Tc nor the pressure dependence of the isotope coefficient. The only way out of the dilemma is a multi-band approach of superconductivity where already small interband coupling suffices to achieve the high values of Tc together with the anomalous pressure dependent isotope effect. In addition, it is shown that anharmonicity of the hydrogen bonds vanishes under pressure whereas anharmonic phonon modes related to sulfur are still active