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

Abstract

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 wavevector independent damping, and they develop a finite pinning frequency, which destroy their acoustic linearly propagating dispersion. Under a few and 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 $T_c$ 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 glass-like behavior. Additionally, we observe that the phason damping can strongly enhance the effective Eliashberg coupling, and we reveal a sharp non-monotonic dependence of the superconducting temperature $T_c$ 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 in explaining the glassy properties of incommensurate structures, but also in possibly inducing strongly-coupled superconductivity therein, and enhancing the corresponding $T_c$.

arXiv commentv2: appendices added, references added

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Cited by in corpus (8)

• Josephson effect in a Fibonacci quasicrystal
• Stringlet Excitation Model of the Boson Peak
• Extended linear-in-$T$ resistivity due to electron-phason scattering in moiré superlattices
• Quasiperiodic pairing in graphene quasicrystals
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Atomistic mechanisms of dynamics in a two-dimensional dodecagonal quasicrystal
• The Josephson effect in Fibonacci superconductors
• Superconducting order parameter in aperiodic binary systems