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Decay of superconducting correlations for gauged electrons in dimensions D ≤ 4

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Tada,  Yasuhiro
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Tada, Y., & Koma, T. (2018). Decay of superconducting correlations for gauged electrons in dimensions D ≤ 4. Journal of Mathematical Physics, 59(3): 031905. doi:10.1063/1.5029282.


Cite as: http://hdl.handle.net/21.11116/0000-0001-4220-0
Abstract
We study lattice superconductors coupled to gauge fields, such as an attractive Hubbard model in electromagnetic fields, with a standard gauge fixing. We prove upper bounds for a two-point Cooper pair correlation at finite temperatures in spatial dimensions D <= 4. The upper bounds decay exponentially in three dimensions and by power lawin four dimensions. These imply the absence of the superconducting long-range order for the Cooper pair amplitude as a consequence of fluctuations of the gauge fields. Since our results hold for the gauge fixing Hamiltonian, they cannot be obtained as a corollary of Elitzur's theorem. Published by AIP Publishing.