Fermi liquid theory

For other uses, see Fermi (disambiguation).
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Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures.[1] The theory describes the behavior of many-body systems of particles in which the interactions between particles may be strong. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956,[2] and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory.[3] The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas (collection of non-interacting fermions), and why other properties differ.

Fermi liquid theory applies most notably to conduction electrons in normal (non-superconducting) metals, and to liquid helium-3.[4] Liquid helium-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase). An atom of helium-3 has two protons, one neutron and two electrons, giving an odd number of fermions, so the atom itself is a fermion. Fermi liquid theory also describes the low-temperature behavior of electrons in heavy fermion materials, which are metallic rare-earth alloys having partially filled f orbitals. The effective mass of electrons in these materials is much larger than the free-electron mass because of interactions with other electrons, so these systems are known as heavy Fermi liquids. Strontium ruthenate displays some key properties of Fermi liquids, despite being a strongly correlated material that is similar to high temperature superconductors such as the cuprates.[5] The low-momentum interactions of nucleons (protons and neutrons) in atomic nuclei are also described by Fermi liquid theory.[6]

  1. ^ Phillips, Philip (2008). Advanced Solid State Physics. Perseus Books. p. 224. ISBN 978-81-89938-16-1.
  2. ^ Landau, L. D. (1957). "The Theory of a Fermi Liquid" (PDF). Sov. Phys. JETP. 3 (6): 920–925.
  3. ^ Abrikosov, A.A.; Khalatnikov, I.M. (1959). "The theory of a Fermi liquid (the properties of liquid 3He at low temperatures)". Reports on Progress in Physics. 22 (329): 329–367. doi:10.1088/0034-4885/22/1/310.
  4. ^ Schulz, H. J. (March 1995). "Fermi liquids and non–Fermi liquids". In "proceedings of les Houches Summer School Lxi", ed. E. Akkermans, G. Montambaux, J. Pichard, et J. Zinn-Justin (Elsevier, Amsterdam. 1995 (533). arXiv:cond-mat/9503150. Bibcode:1995cond.mat..3150S.
  5. ^ Wysokiński, Carol; et al. (2003). "Spin triplet superconductivity in Sr2RuO4" (PDF). Physica Status Solidi. 236 (2): 325–331. arXiv:cond-mat/0211199. Bibcode:2003PSSBR.236..325W. doi:10.1002/pssb.200301672. S2CID 119378907. Retrieved 8 April 2012.
  6. ^ Schwenk, Achim; Brown, Gerald E.; Friman, Bengt (2002). "Low-momentum nucleon–nucleon interaction and Fermi liquid theory". Nuclear Physics A. 703 (3–4): 745–769. arXiv:nucl-th/0109059. Bibcode:2002NuPhA.703..745S. doi:10.1016/s0375-9474(01)01673-6. ISSN 0375-9474.