Visualizing the Cuprate Pair Density Wave State
Kazuhiro Fujita, Brookhaven National Lab
The defining characteristic i , ii of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in cupratesiii , iv. Although Cooper-pair tunnelingv has detected an indirect evidence of a cuprate PDW and electronic structures of the underdoped cuprates can be explained very well by a coexisting d-wave superconductivity and PDW modelvi, the definitive signature in single-electron tunneling of a periodic Δ(r) modulation has never been observed. Here, using a new approach, we discover strong Δ(r) modulations in Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q~2π/a0(1/8,0); 2π/a0(0,1/8). Simultaneous imaging of the localdensity-of-states N(r,E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r,E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW statevii , viii . Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi2Sr2CaCu2O8+δ. In this talk, I will present the recent development of the cuprate PDW studies as described above and discuss a possible role of the PDW in the cuprate.
This work was done in collaboration with Zengyi Du, Hui Li Sanghyun Joo, Elizabeth P. Donoway, Jinho Lee, J. C. Séamus Davis, Genda Gu, Peter D. Johnson, and has been published in Nature 580 65-70 (2020).
i Flude, P. and Ferrel, R. A. Superconductivity in a Strong Spin-Exchange Field. Phys. Rev. 135, A550 (1965).
ii Larkin, A. I. and Ovchinnikov, Yu. N. Inhomogeneous State of Superconductors. Sov. Phys. JETP 20, 762 (1965).
iii Fradkin, E., Kivelson, S. A., Tranquada, J. M., Colloquium: Theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457 (2015).
iv Agterberg, D. F. et al., The Physics of Pair Density Waves: Cuprate Superconductors and Beyond. Annual Review of Condensed Matter Physics 11 231-270 (2020).
v Hamidian, M. H. et al., Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+δ. Nature 532, 343-347 (2016).
vi Choubey, P. et al., Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity. Proc. Natl’ Acad. Sci. 117, 14805–14811 (2020).
vii Agterberg, D. F. and Tsunetsugu, H. Dislocations and vortices in pair-density-wave superconductors. Nature Phys. 4, 639-642 (2008).
viii Berg, E., Fradkin, E., Kivelson, S. A., Charge-4e superconductivity from pair-densitywave order in certain high-temperature superconductors. Nature Phys. 5, 830-833 (2009).