Anharmonic theory of superconductivity and its applications to emerging quantum materials

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

Anharmonic Origin of the Giant Thermal Expansion of NaBr

All phonons in a single crystal of NaBr are measured by inelastic neutron scattering at temperatures of 10, 300, and 700 K. Even at 300 K, the phonons, especially the longitudinal-optical phonons, show large shifts in frequencies and show large broadenings in energy owing to anharmonicity. Ab initio computations are first performed with the quasiharmonic approximation (QHA) in which the phonon frequencies depend only on V and on T only insofar as it alters V by thermal expansion. This QHA is an unqualified failure for predicting the temperature dependence of phonon frequencies, even 300 K, and the thermal expansion is in error by a factor of 4. Ab initio computations that include both anharmonicity and quasiharmonicity successfully predict both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of longitudinal-optical phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anharmonicity originating from the cubic anharmonicity of nearest-neighbor NaBr bonds. Anharmonicity is not a correction to the QHA predictions of thermal expansion and thermal phonon shifts but dominates the behavior.

Dielectric constants of ionic crystals and their variations with temperature and pressure

Measurements of the audio- and radio-frequency dielectric constants of the alkali and thallium halides have been made over the range of temperature 1.5 to 350 K and at pressure up to 4 kbar (400 MN m -2 ), on crystals of high purity. The results are used to separate, for each compound, that part of the variation in dielectric constant which is explicitly dependent on temperature from that part which is explicitly dependent on volume. The observed variations at constant temperature are used to provide measures of the Gruneisen parameters for the long-wave transverse-optic phonons, and the variations at constant volume are discussed in terms of the anharmonic self-energies of these phonons. The materials studied here are all simple highly ionic compounds but, at room temperature, the self-energies of some prove to be positive while for others they are negative. It is shown how this can be interpreted in terms of competing three-phonon and four-phonon decay and scattering processes.