Anomalous softening of phonon dispersion in cuprate superconductors

Saheli Sarkar,Catherine Pépin,Maxence Grandadam

doi:10.1103/physrevresearch.3.013162

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.

Highlights

The “pseudogap” phase [1,2,3,4,5,6,7,8,9,10] of the underdoped hightemperature copper-oxide-based superconductors remains incomprehensible even after decades of research, by and large due to a complex interplay of several symmetrybroken orders [11,12]
In onedimensional metals [28,29,30] and in some transitional-metal dichalcogenides [31], this softening grows towards zero [Fig. 1] and a full phonon softening occurs at the CDW wave vector (Q) below CDW ordering temperature TCDW, reflecting the origin of CDW order in them
In this paper we provide a theoretical explanation to the anomalous phonon softening, revealing an unusual connection between the fluctuations of CDW and superconductivity in underdoped cuprates

Summary

Introduction

The “pseudogap” phase [1,2,3,4,5,6,7,8,9,10] of the underdoped hightemperature copper-oxide-based superconductors (cuprates) remains incomprehensible even after decades of research, by and large due to a complex interplay of several symmetrybroken orders [11,12]. We find that a strong phonon softening occurs only below Tc, due to quench of fluctuations in both CDW and superconductivity arising from a connection between them, as can be found in a fractionalization of a PDW order [52].

Results

Conclusion