Origin of the simple modulated structures and the pressure induced superconductivity

We have studied origins of the simple modulations of structures using first-principles calculations for group V, VI, and VII elements which have simple modulated structures. For the approximate structures which are defined by removing the modulations, we calculated phonon frequencies along the direction of the wave vectors of the modulation, and searched for possible phonon modes which may relate with the structural modulations. In phosphorus the Madelung energy works to destabilize the approximate monoclinic structure as well as the simple cubic and simple hexagonal structures, while it works to stabilize the approximate structures in other elements. Observing that the SC phase of phosphorus is stabilized by the band energies, we estimated the superconducting Tc in the SC phase. The calculated Tc remains at nearly same values in the SC phase. The electron phonon coupling increases with increasing pressure but the averaged phonon frequency decreases with increasing pressure, which is due to the increasing destabilizing effect of the Madelung energy.

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