Magnesium diboride differs from ordinary metallic superconductors in several important ways, including the failure of conventional models to predict accurately its unusually high transition temperature, the effects of isotope substitution on the critical transition temperature, and its anomalous specific heat. A detailed examination of the energy associated with the formation of charge-carrying pairs, referred to as the 'superconducting energy gap', should clarify why MgB2 is different. Some early experimental studies have indicated that MgB2 has multiple gaps, but past theoretical studies have not explained from first principles the origin of these gaps and their effects. Here we report an ab initio calculation of the superconducting gaps in MgB2 and their effects on measurable quantities. An important feature is that the electronic states dominated by orbitals in the boron plane couple strongly to specific phonon modes, making pair formation favourable. This explains the high transition temperature, the anomalous structure in the specific heat, and the existence of multiple gaps in this material. Our analysis suggests comparable or higher transition temperatures may result in layered materials based on B, C and N with partially filled planar orbitals.
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