Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

• Published in: Nature physics 2015-10, Vol.12 (2), p.150-156
• Main Authors: Hamidian, M. H., Edkins, S. D., Kim, Chung Koo, Davis, J. C., Mackenzie, A. P., Eisaki, H., Uchida, S., Lawler, M. J., Kim, E.-A., Sachdev, S., Fujita, K.
• Format: Article
• Language: English
• Subjects: 136/138; 639/301/119/1003; 639/301/119/995; Atomic; Classical and Continuum Physics; Complex Systems; Condensed Matter Physics; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; COPPER OXIDE; Cuprates; Density; electronic properties and materials; Electronic structure; Energy use; Fermi surfaces; Form factors; High temperature; letter; Mathematical and Computational Physics; Modulation; Molecular; Optical and Plasma Physics; Physics; Spectra; superconducting properties and materials; Superconductors; Temperature; Theoretical
• ISSN: 1745-2473; 1745-2481
• DOI: 10.1038/nphys3519

A detailed scanning tunnelling microscopy study of the cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+ x reveals the microscopic origin of the d -symmetry form factor density wave that exists in the pseudogap phase of this material. Research on high-temperature superconducting cuprates is at present focused on identifying the relationship between the classic ‘pseudogap’ phenomenon 1 , 2 and the more recently investigated density wave state 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 . This state is generally characterized by a wavevector Q parallel to the planar Cu–O–Cu bonds 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 along with a predominantly d -symmetry form factor 14 , 15 , 16 (dFF-DW). To identify the microscopic mechanism giving rise to this state 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , one must identify the momentum-space states contributing to the dFF-DW spectral weight, determine their particle–hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization 14 of electronic structure and reveal that the characteristic energy of the dFF-DW modulations is actually the ‘pseudogap’ energy Δ 1 . Moreover, we demonstrate that the dFF-DW modulations at E = − Δ 1 (filled states) occur with relative phase π compared to those at E = Δ 1 (empty states). Finally, we show that the conventionally defined dFF-DW Q corresponds to scattering between the ‘hot frontier’ regions of momentum-space beyond which Bogoliubov quasiparticles cease to exist 30 , 31 , 32 . These data indicate that the cuprate dFF-DW state involves particle–hole interactions focused at the pseudogap energy scale and between the four pairs of ‘hot frontier’ regions in momentum space where the pseudogap opens.