Enhanced Anharmonicity Under Pressure

Contradicting common sense, pressure does not monotonically harden the phonons in many systems but makes some specific modes soften at given points of the first Brilloiun zone, even inducing dynamical instabilities that drive structural phase transitions. As the harmonic part of the ionic potential becomes smaller, higher order terms turn out to be more and more important. In AlH₃, for instance, anharmonicity suppresses the predicted high superconducting transition temperature at 110 GPa in agreement with experiments. Furthermore, anharmonicity stabilizes the high-pressure simple cubic phase of calcium even at zero temperature, explaining its mechanical stability. We will review the calculations performed in these two systems and show that anharmonicity can be tackled making use of perturbation theory or the so called self-consistent harmonic approximation.