Eight-Unit-Cell Electronic Modulations in Cuprates Originating from Local Molecular Orbitals

Zhiheng Yao; Sixuan Chen; Jianfa Zhao; Shusen Ye; Weixiang Qu; Ning Xia; Yuling Dai; Luchuan Shi; Hongrui Zhang; Zhenqi Hao; Changqing Jin; Shuo Yang; Yayu Wang

doi:10.1103/lvpn-gblk

Eight-Unit-Cell Electronic Modulations in Cuprates Originating from Local Molecular Orbitals

Zhiheng Yao^1,*, Sixuan Chen^1,*, Jianfa Zhao ^2,*, Shusen Ye¹, Weixiang Qu ¹, Ning Xia ¹, Yuling Dai², Luchuan Shi², Hongrui Zhang¹ et al.

Zhenqi Hao¹, Changqing Jin², Shuo Yang ^1,3,4,†, and Yayu Wang ^1,3,4,‡

¹State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
²Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
³New Cornerstone Science Laboratory, Frontier Science Center for Quantum Information, Beijing 100084, China
⁴Hefei National Laboratory, Hefei 230088, China

^*These authors contributed equally to this work.
^†Contact author: shuoyang@tsinghua.edu.cn
^‡Contact author: yayuwang@tsinghua.edu.cn

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Phys. Rev. Lett. 137, 156001 – Published 5 October, 2026

DOI: https://doi.org/10.1103/lvpn-gblk

Abstract

The pair density wave state with eight-unit-cell ( $8 a_{0}$ ) periodicity has been widely regarded as the primary order in cuprates, yet its existence and origin remain subjects of intense debate. Using spectroscopic imaging scanning tunneling microscopy, we observe spatial modulations of the electronic states with approximately $8 a_{0}$ periodicity in both the superconducting and insulating regimes of hole-doped ${Ca}_{2} {CuO}_{2} {Cl}_{2}$ cuprate. We find that the $8 a_{0}$ spatial patterns are generated by the formation of molecular orbitals by doped holes, which organize into $4 a_{0} \times 4 a_{0}$ plaquettes as the basic unit. Our results identify the $4 a_{0}$ molecular-orbital plaquette as the fundamental electronic building block in cuprates, while the $8 a_{0}$ pair density wave represents a spatial subharmonic that emerges at sufficiently high doping.

Physical Review Letters

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Eight-Unit-Cell Electronic Modulations in Cuprates Originating from Local Molecular Orbitals

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