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Stability of Fermi surfaces and K theory.
1Berkeley Center for Theoretical Physics and Department of Physics, University of California, Berkeley, California 94720-7300, USA.
Physical Review Letters
|August 11, 2005
Summary
Nonrelativistic Fermi liquids possess generalized Fermi surfaces, classified by K theory and Bott periodicity. This reveals relativistic invariance in low-energy modes, paralleling string theory D-branes.
Area of Science:
- Condensed matter physics
- Quantum field theory
- String theory
Background:
- Nonrelativistic Fermi liquids exhibit generalized Fermi surfaces in d+1 dimensions.
- These surfaces are (d-p)-dimensional submanifolds in (k,omega)-space supporting gapless excitations.
Purpose of the Study:
- To classify the universality classes of stable Fermi surfaces.
- To explore the implications of Fermi surface stability for low-energy excitations.
Main Methods:
- Utilizing K theory for classification.
- Applying the Atiyah-Bott-Shapiro construction.
Main Results:
- Universality classes of stable Fermi surfaces are classified by K theory.
- Bott periodicity governs the pattern of stability.
- Low-energy modes near Fermi surfaces exhibit relativistic invariance in transverse dimensions.
Conclusions:
- A parallel exists between nonrelativistic Fermi liquids and D-branes in string theory.
- The study provides a new framework for understanding Fermi liquid properties.