Abstract
The recent report of superconductivity under high pressure at the record transition temperature of Tc =203 K in pressurized H2S 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 cannot account for 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 coefficient. In addition, it is shown that anharmonicity of the hydrogen bonds vanishes under pressure whereas anharmonic phonon modes related to sulfur are still active.
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