Glassy heat capacity from overdamped phasons and hypothetical phason-induced superconductivity in incommensurate structures

Phasons are collective low-energy modes that appear in disparate condensed matter systems such as quasicrystals, incommensurate structures, fluctuating charge density waves, and moiré superlattices. They share several similarities with acoustic phonon modes, but they are not protected by any exact translational symmetry. As a consequence, they are subject to a wave-vector-independent damping, and they develop a finite pinning frequency, which destroy their acoustic linearly propagating dispersion. Under a few simple, well-motivated assumptions, we compute the phason density of states, and we derive the phason heat capacity as a function of the temperature. Finally, imagining a hypothetical s-wave pairing channel with electrons, we compute the critical temperature Tc of the corresponding superconducting state as a function of phason damping using the Eliashberg formalism. We find that for large phason damping, the heat capacity is linear in temperature, showing a distinctive glasslike behavior. Additionally, we observe that the phason damping can strongly enhance the effective Eliashberg coupling, and we reveal a sharp nonmonotonic dependence of the superconducting temperature Tc on the phason damping, with a maximum located at the underdamped-to-overdamped-crossover scale. Our simple computations confirm the potential role of overdamped modes not only in explaining the glassy properties of incommensurate structures but also in possibly inducing strongly coupled superconductivity therein and enhancing the corresponding Tc.