Two No-Go Theorems on Superconductivity

Abstract

We study lattice superconductors such as attractive Hubbard models. As is well known, Bloch's theorem asserts absence of persistent current in ground states and equilibrium states for general fermion systems. While the statement of the theorem is true, we can show that the theorem cannot exclude possibility of a surface persistent current. Such a current can be stabilized by boundary magnetic fields which do not penetrate into the bulk region of a superconductor, provided emergence of massive photons, i.e., Meissner effect. Therefore, we can expect that a surface persistent current is realized for a ground/equilibrium state in the sense of stability against local perturbations. We also apply Elitzur's theorem to superconductors at finite temperatures. As a result, we prove absence of symmetry breaking of the global $U(1)$ phase of electrons for almost all gauge fields. These observations suggest that the nature of superconductivity is the emergence of massive photons rather than the symmetry breaking of the $U(1)$ phase of electrons.

18 pages, v2: minor corrections

References in corpus (4)

• Generalized Bloch theorem and chiral transport phenomena
• Equilibrium Surface Current and Role of U(1) Symmetry: sum rule and surface perturbations
• On the Higgs-Confinement Complementarity
• Topological Current in Fractional Chern Insulators

Cited by in corpus (13)

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• Lieb-Schultz-Mattis theorem in higher dimensions from approximate magnetic translation symmetry
• Spin texture and spin current in excitonic phases of the two-band Hubbard model
• Chern-Simons-Matter Theories at Large Baryon Number
• Fulde-Ferrell state in ferromagnetic chiral superconductor with magnetic domain wall
• Decay of Superconducting Correlations for Gauged Electrons in Dimensions $D\le 4$
• The Bloch theorem in the presence of an additional conserved charge
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension
• Revisiting Anderson-Higgs mechanism: application of Lieb-Schultz-Mattis theorem