Duality and the vibrational modes of a Cooper-pair Wigner crystal

TL;DR

This paper explores the vibrational modes of a Cooper pair Wigner crystal formed in underdoped cuprates, linking these modes to observable thermal properties and recent experimental anomalies.

Contribution

It introduces a continuum duality approach to analyze low-lying vibrational modes in a Cooper pair crystal, connecting theory with experimental thermal conductivity data.

Findings

Calculated the speed of sound in the Cooper pair Wigner crystal.

Linked vibrational modes to the bosonic contribution in thermal conductivity.

Suggested these modes explain recent thermal conductivity observations in underdoped YBCO.

Abstract

When quantum fluctuations in the phase of the superconducting order parameter destroy the off-diagonal long range order, duality arguments predict the formation of a Cooper pair crystal. This effect is thought to be responsible for the static checkerboard patterns observed recently in various underdoped cuprate superconductors by means of scanning tunneling spectroscopy. Breaking of the translational symmetry in such a Cooper pair Wigner crystal may, under certain conditions, lead to the emergence of low lying transverse vibrational modes which could then contribute to thermodynamic and transport properties at low temperatures. We investigate these vibrational modes using a continuum version of the standard vortex-boson duality, calculate the speed of sound in the Cooper pair Wigner crystal and deduce the associated specific heat and thermal conductivity. We then suggest that these modes could be responsible for the mysterious bosonic contribution to the thermal conductivity recently observed in strongly underdoped ultraclean single crystals of YBCO tuned across the superconductor-insulator transition.