Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

Shuqiu Wang,Yi Xue Chong,H Eisaki,Peayush Choubey,Peayush Choubey,Peter J Hirschfeld,S Uchida,Weijiong Chen,Wangping Ren,J C Séamus Davis,J C Séamus Davis,J C Séamus Davis,J C Séamus Davis

doi:10.1038/s41467-021-26028-x

Abstract

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap {Delta }_{{{{{{rm{P}}}}}}}({{{{{boldsymbol{r}}}}}}) in real-space, and a characteristic quasiparticle scattering interference (QPI) signature {Lambda }_{{{{{{rm{P}}}}}}}({{{{{boldsymbol{q}}}}}}) in wavevector space. By studying strongly underdoped Bi2Sr2CaDyCu2O8 at hole-density ~0.08 in the superconductive phase, we detect the 8a0-periodic {Delta }_{{{{{{rm{P}}}}}}}({{{{{boldsymbol{r}}}}}}) modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature Lambda ({{{{{boldsymbol{q}}}}}}) that is predicted specifically for the temperature dependence of an 8a0-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi2Sr2CaDyCu2O8 pseudogap phase.

Highlights

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electrondensity depletion in the CuO2 antiferromagnetic insulator
When p holes per unit-cell are introduced to CuO2, the antiferromagnetic iiennnseturhlgaeytorgerag(pioAnΔF*)pÀsp
We use a quantitative, atomic-scale model for pair density wave (PDW) state based upon CuO2 electronic structure and the t-J Hamiltonian, H

Summary

Introduction

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electrondensity depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs Such a state should exhibit a periodically modulating energy gap ΔPðrÞ in real-space, and a characteristic quasiparticle scattering interference (QPI) signature ΛPðqÞ in wavevector space. By visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature ΛðqÞ that is predicted for the temperature dependence of an 8a0-periodic PDW. A spatially homogeneous d-wave superconductor has an electron-pair potential or order parameter ΔdðrÞ 1⁄4 Δ0eiφ with macroscopic quantum phase φ and critical temperature Tc. By contrast, a PDW state has an order parameter ΔPðrÞ that modulates spatially at wavevectors h

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