Stability of Fermi Surfaces and K-Theory

Abstract

Nonrelativistic Fermi liquids in d+1 dimensions exhibit generalized Fermi surfaces: (d-p)-dimensional submanifolds in the momentum-frequency space supporting gapless excitations. We show that the universality classes of stable Fermi surfaces are classified by K-theory, with the pattern of stability determined by Bott periodicity. The Atiyah-Bott-Shapiro construction implies that the low-energy modes near a Fermi surface exhibit relativistic invariance in the transverse p+1 dimensions. This suggests an intriguing parallel between norelativistic Fermi liquids and D-branes of string theory.

arXiv comment4 pages, revtex

References in corpus (10)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Dirichlet-Branes and Ramond-Ramond Charges
• Renormalization Group Approach to Interacting Fermions
• D-Branes And K-Theory
• K-theory and Ramond-Ramond charge
• Superfluid analogies of cosmological phenomena
• Self-Duality, Ramond-Ramond Fields, and K-Theory
• Duality Relations Among Topological Effects In String Theory
• On Ramond-Ramond fields and K-theory
• Gapless Fermions and Quantum Order

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