Exact solution for finite center-of-mass momentum Cooper pairing
| Autor: | Setty, Chandan, Zhao, Jinchao, Fanfarillo, Laura, Huang, Edwin W., Hirschfeld, Peter J., Phillips, Philip W., Yang, Kun |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 108, 174506 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.108.174506 |
| Popis: | Pair density waves (PDWs) are superconducting states formed by ``Cooper pairs" of electrons containing a non-zero 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 generic and robust mechanism that favors a modulated solution of the superconducting order parameter in the presence of time reversal symmetry. Here, we study the problem of two electrons subject to an anisotropic ($d$-wave) attractive potential. We solve the two-body Schrodinger 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 interaction. Using this insight from the exact two-body solution, we construct a BCS-like variational many-body wave function and calculate the free energy and superconducting gap as a function of the center-of-mass momentum. A zero temperature analysis of the energy shows that the conclusions of the two-body problem are robust in the many-body limit. Our results lay the theoretical and microscopic foundation for the existence of PDWs. Comment: 24 pages, 6 figures |
| Databáze: | arXiv |
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