Upper Bounds on Superfluid Stiffness
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Date
2021-04
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Abstract
Below the transition temperature Tc, electric current in a superconducting material flows unimpeded without resistance. It has numerous applications ranging from energy-efficient magnets used in MRI machines to quantum information processing and computation devices. All known superconductors have Tc values well below room temperature at ambient pressures. Hence, understanding the material properties that limit Tc is a problem of immense practical importance. The widely accepted BCS theory posits two-electron bound states inside a superconductor, called Cooper pairs. The pairs are described by a complex order parameter, with an amplitude and a phase. In many novel superconductors, phase fluctuations determine Tc, rather than the collapse of the pairing amplitude. Our work shows that superfluid phase stiffness, Ds, can be bounded from above on very general grounds assuming only linear response and causality. The bound on Ds further leads to an upper bound on Tc in 2D, which holds irrespective of the pairing mechanism, interaction strength, or order-parameter symmetry. These bounds turn out to be particularly useful for strongly interacting systems with a low density of carriers or very narrow electronic bands. For quadratic dispersion in 2D, we show that Tc can never exceed one-eighth of the Fermi temperature, no matter how strong the pairing interaction. There have been recent experiments on 2D quantum materials that have tested our prediction1. Even for a multi-band non-parabolic system like twisted bilayer graphene, our bound is surprisingly easy to compute and comes very close to the highest experimentally observed Tc2,3.
[1] Nakagawa, Y. et al. Gate-controlled BCS-BEC crossover in a two-dimensional superconductor. arXiv 2012.05707, (2020).
[2] Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
[3] Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Description
Poster Division: Math and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)
Keywords
Superconductivity, Superfluid Stiffness, Flat bands, BCS-BEC crossover
Citation
arXiv Preprint: Verma, Nishchhal, Tamaghna Hazra, and Mohit Randeria. "Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors." arXiv preprint arXiv:2103.08540v1 (2021). https://arxiv.org/abs/2103.08540v1