@article{c87de665de394499a594dda46a6dc815,
title = "Exact solution for finite center-of-mass momentum Cooper pairing",
abstract = "Pair density waves (PDWs) are superconducting states formed by Cooper pairs of electrons containing a nonzero center-of-mass momentum. They are characterized by a spatially modulated order parameter and may occur in a variety of emerging quantum materials such as cuprates, transition-metal dichalcogenides (TMDs), and Kagome metals. Despite extensive theoretical and numerical studies seeking PDWs in a variety of lattices and interacting settings, there is currently no exact mechanism that spontaneously favors a modulated solution of the superconducting order parameter. Here, we study the problem of two electrons subject to an anisotropic attractive potential. We solve the two-body Schr{\"o}dinger wave equation exactly to determine the pair binding energy as a function of the center-of-mass momentum. We find that a modulated (finite momentum) pair is favored over a homogeneous (zero momentum) solution above a critical, intermediate interaction strength. Hence our exact result justifies previous mean-field approximations that obtain modulated ground states at finite but large interactions. Using this insight from the exact two-body solution, we construct a variational many-body wave function and show that the conclusions of the two-body problem are robust in the many-body limit. Our results thus lay the theoretical and microscopic foundation for the existence of PDWs.",
author = "Chandan Setty and Jinchao Zhao and Laura Fanfarillo and Huang, {Edwin W.} and Hirschfeld, {Peter J.} and Phillips, {Philip W.} and Kun Yang",
note = "C.S. was primarily supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0018197 and additionally supported by the Robert A. Welch Foundation Grant No. C-1411. K.Y. was supported by the National Science Foundation Grants No. DMR-1932796 and No. DMR-2315954, and performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-1644779, and the State of Florida. P.W.P. thanks DMR-2111379 for partial funding of this project. P.J.H. is supported by the Department of Energy under Grant No. DE-FG02-05ER46236. L.F. acknowledges support by the European Union's Horizon 2020 research and innovation programme through the Marie Sklodowska-Curie grant SuperCoop (Grant No. 838526). E.W.H. was supported by the Gordon and Betty Moore Foundation EPiQS Initiative through the Grants No. GBMF 4305 and No. GBMF 8691. The authors thank Kavli Institute for Theoretical Physics and University of California, Santa Barbara for hospitality and the associated financial support from National Science Foundation under Grant No. NSF PHY-1748958. We benefited from discussions with Qimiao Si, and the organizers and attendees of the workshop \u201CRecent Progress in the Experimental and Theoretical Search for Pair-Density-Wave Order\u201D where this work was conceived and initially presented.",
year = "2023",
month = nov,
day = "1",
doi = "10.1103/PhysRevB.108.174506",
language = "English (US)",
volume = "108",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "17",
}