Anomalous softening of phonon-dispersion in cuprate superconductors

TL;DR

This paper explains the unusual phonon-softening observed in under-doped cuprate superconductors below T_c by analyzing the interplay of charge-density wave, superconducting orders, and quasiparticle lifetime effects.

Contribution

It introduces a perturbative framework that accounts for the anomalous phonon-softening below T_c and captures material-specific features of this phenomenon.

Findings

Phonon-softening occurs below T_c in cuprates, unlike in metallic systems.

Interplay of CDW, SC, and quasiparticle lifetime explains the softening.

The formalism accounts for material-specific phonon behavior.

Abstract

A softening of phonon-dispersion has been observed experimentally in under-doped cuprate superconductors at the charge-density wave (CDW) ordering wave vector. Interestingly, the softening occurs below the superconducting (SC) transition temperature T$_{c}$, in contrast to the metallic systems, where the softening occurs usually below the CDW onset temperature T$_{\text{CDW}}$. An understanding of the `anomalous' nature of the phonon-softening and its connection to the pseudo-gap phase in under-doped cuprates remain open questions. Within a perturbative approach, we show that a complex interplay among the ubiquitous CDW, SC orders and life-time of quasi-particles associated to thermal fluctuations, can explain the anomalous phonon-softening below T$_{c}$. Furthermore, our formalism captures different characteristics of the low temperature phonon-softening depending on material specificity.