Interplay among superconductivity, charge density waves, and magnetism in EuMo₆S₈

Abstract In a one-dimensional metal, the energy of the electrons can always be lowered by opening an energy gap around the Fermi energy (the Peierls instability): all occupied states are then in the lower-energy band, while the higher-energy band is empty. The opening of such a gap requires a structural distortion, resulting in the formation of a charge density wave. In a three-dimensional system, the gapping takes place in the region where the Fermi surface is nested (i.e., large parallel areas of the Fermi surface are spanned by a certain wave vector), giving rise to partial gapping of the Fermi surface, accompanied by a structural distortion. In this case, a charge density wave can coexist with superconductivity. Both charge-density-wave and superconducting transitions involve the formation of an energy gap at the Fermi energy. A charge-density-wave gap is formed at a region of the Fermi surface where there is a high density of electronic states. In such a material, there is also a strong electronphonon interaction. A region with high density of states and a high electron-phonon interaction is just the portion of the Fermi surface that will enhance the superconducting transition temperature, according to the BCS (Bardeen-Cooper-Schrieffer) theory. When a charge-density-wave gap opens up at the Fermi surface these electronic states are no longer available to form Cooper pairs and to enhance the superconducting transition temperature. The opposite is also true; if a superconducting gap opens, the states involved in forming this gap are no longer available to take part in a charge-density-wave transition. It appears that charge density waves and superconductivity compete for the same portion of the Fermi surface and thus inhibit each other. In this paper, we will review a unique situation with respect to the competition between these two ground states and will also discuss how this competition affects the anomalous behavior of critical field in EuMo6S, at high pressure.