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 (k,ω)-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 nonrelativistic Fermi liquids and D-branes of string theory.
- Publication:
-
Physical Review Letters
- Pub Date:
- June 2005
- DOI:
- 10.1103/PhysRevLett.95.016405
- arXiv:
- arXiv:hep-th/0503006
- Bibcode:
- 2005PhRvL..95a6405H
- Keywords:
-
- 71.10.Ay;
- 11.25.Uv;
- 71.18.+y;
- 71.27.+a;
- Fermi-liquid theory and other phenomenological models;
- D branes;
- Fermi surface: calculations and measurements;
- effective mass g factor;
- Strongly correlated electron systems;
- heavy fermions;
- High Energy Physics - Theory;
- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect;
- Condensed Matter - Strongly Correlated Electrons;
- Mathematics - Algebraic Topology
- E-Print:
- 4 pages, revtex