Landau theory of Fermi liquids
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| Landau theory of Fermi liquids | |
|---|---|
| Name | Landau theory of Fermi liquids |
| Field | Lev Landau; Condensed matter physics |
| Introduced | 1956 |
| Key people | Lev Landau; Lev Pitaevskii; Gabriele F. Giuliani; Alexei Abrikosov; John Bardeen; Lev D. Landau |
| Related | Fermi–Dirac statistics; Fermi surface; Quasiparticle |
Landau theory of Fermi liquids Landau theory of Fermi liquids is a phenomenological framework, developed by Lev Landau in the 1950s, that describes low-temperature properties of interacting fermion systems in terms of long-lived quasiparticle excitations near a Fermi surface. It connects microscopic models such as the Fermi gas and the Hubbard model with observable collective behavior measured in experiments on systems like helium-3, metals, and nuclear matter. The theory introduces interaction parameters and kinetic equations that have guided later developments in BCS superconductivity, quantum many-body theory, and renormalization group analyses.
Introduction
Landau proposed that a strongly interacting fermionic system at low temperature can be adiabatically connected to a noninteracting Fermi gas state described by Fermi–Dirac occupation, yielding long-lived quasiparticles with a one-to-one correspondence to the excitations of the Fermi surface. This idea influenced work by Feynman, Dyson, Hubbard, and P. W. Anderson and underpins treatments in quantum field theory and many-body physics. Landau's formulation employs phenomenological parameters fit to experiments on systems including He-3, metals, and neutron stars studied in nuclear physics.
Landau quasiparticles and basic assumptions
The central object is the quasiparticle: a fermionic excitation with renormalized energy ε_p and effective mass m* defined at the Fermi momentum p_F. Landau assumed conservation laws associated with symmetry and adiabatic continuity from a noninteracting Fermi gas to the interacting system, paralleling concepts used by Lev P. Pitaevskii and Elliott Lieb in mathematical studies. Quasiparticles obey a semiclassical kinetic equation analogous to the Boltzmann equation as developed in kinetic theory by Boltzmann and refined in quantum contexts by Lev Landau and Peierls. The lifetime τ(ε) of quasiparticles scales as (ε − ε_F)^{-2}, consistent with calculations by Luttinger and Luttinger in perturbation theory.
Landau parameters and phenomenology
Interactions among quasiparticles are encoded in dimensionless Landau parameters F_l^s and F_l^a for spin-symmetric and spin-antisymmetric channels labeled by angular momentum l, introduced by Lev Landau and employed by Abrikosov and Khalatnikov in transport studies. These parameters determine collective modes such as zero sound, first analyzed in Pitaevskii's extensions and observed in helium-3 experiments interpreted by Pines and Nozières. Relations link F_0^s to compressibility, F_1^s to effective mass m*/m via Galilean invariance arguments used in Fermi-related theory, and F_0^a to magnetic susceptibility in works by Abrikosov and Pitaevskii.
Thermodynamic and transport properties
Landau theory yields explicit formulas for low-temperature specific heat C_V ∝ m* T derived using Fermi-surface integrals employed in Sommerfeld analyses and for spin susceptibility χ ∝ (1 + F_0^a)^{-1} connected to Pauli and Stoner theory developed by Stoner. Transport coefficients—electrical resistivity, thermal conductivity, and shear viscosity—are obtained from the kinetic equation with quasiparticle scattering amplitudes related to Landau parameters, drawing on methods from Sommerfeld and Peierls and compared to predictions of Boltzmann transport. Collective excitations such as zero sound and first sound were treated by Lev Landau and later measured in ultrasonic experiments on He-3 and metals investigated by Anderson and Bardeen.
Extensions and microscopic derivations
Microscopic foundations arise from diagrammatic perturbation theory in QED-like fermion systems and from renormalization group derivations by Wilson, Michael Fisher, and Shankar. The theory connects to BCS theory of superconductivity by identifying instabilities in particular Landau channels, as shown in work by Bardeen, Cooper, and Schrieffer. Extensions include multiband Fermi-liquid theories used in studies of heavy fermion compounds analyzed by Gegenwart and Si, non-Fermi-liquid behavior near quantum critical points treated by Sachdev and Patrick Lee, and Fermi-liquid generalizations in nuclear matter applied to neutron stars by Baym and Pethick.
Applications and experimental tests
Landau Fermi-liquid predictions have been tested in He-3 experiments by Osheroff and collaborators, in electronic measurements of metals and semiconductors examined by Kadanoff and Mahan, and in nuclear physics experiments probing nuclear matter parameters by Bethe and Negele. Modern tests employ angle-resolved photoemission spectroscopy (ARPES) developed by Shen and Damascelli, quantum oscillation experiments pioneered by Lifshitz and Lifshitz, and transport studies in graphene and twisted bilayer graphene explored by Geim and Jarillo-Herrero. Deviations from Landau behavior guide searches for exotic states such as non-Fermi liquid metals, spin liquids, and unconventional superconductors investigated in laboratories at CERN, MIT, and Max Planck Institute.