Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

Peayush Choubey; Sang Hyun Joo; K Fujita; Zengyi Du; S D Edkins; M H Hamidian; H Eisaki; S Uchida; A P Mackenzie; Jinho Lee; J C Séamus Davis; P J Hirschfeld

doi:10.1073/pnas.2002429117

Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity

Proc Natl Acad Sci U S A. 2020 Jun 30;117(26):14805-14811. doi: 10.1073/pnas.2002429117. Epub 2020 Jun 16.

Authors

Peayush Choubey^{1

2}, Sang Hyun Joo³, K Fujita⁴, Zengyi Du⁴, S D Edkins⁵, M H Hamidian⁶, H Eisaki⁷, S Uchida⁷, A P Mackenzie⁸, Jinho Lee³, J C Séamus Davis^{9

10

11}, P J Hirschfeld¹²

Affiliations

¹ Institut für Theoretische Physik III, Ruhr-Universität Bochum, D-44801 Bochum, Germany.
² Department of Physics, Indian Institute of Science, 560012 Bengaluru, India.
³ Department of Physics and Astronomy, Seoul National University, 08826 Seoul, Korea.
⁴ Condensed Matter Physics and Materials Science (CMPMS) Department, Brookhaven National Laboratory, Upton, NY 11973.
⁵ Department of Applied Physics, Stanford University, Stanford, CA 94305.
⁶ Department of Physics, Harvard University, Cambridge, MA 02138.
⁷ Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan.
⁸ Max-Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany.
⁹ Laboratory of Atomic and Solid State Physics (LASSP), Department of Physics, Cornell University, Ithaca, NY 14850; jcseamusdavis@gmail.com.
¹⁰ Clarendon Laboratory, University of Oxford, OX1 3PU Oxford, United Kingdom.
¹¹ Department of Physics, University College Cork, T12 R5C Cork, Ireland.
¹² Department of Physics, University of Florida, Gainesville, FL 32611.

Abstract

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi₂Sr₂CaCu₂O₈ and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi₂Sr₂CaCu₂O₈ does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

Keywords: cuprate pseudogap; pair density wave state; quasiparticle interference.