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.
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] The key ideas behind Landau's theory are the notion of adiabaticity and the Pauli exclusion principle.
[7] Consider a non-interacting fermion system (a Fermi gas), and suppose we "turn on" the interaction slowly.
As the interaction is turned on, the spin, charge and momentum of the fermions corresponding to the occupied states remain unchanged, while their dynamical properties, such as their mass, magnetic moment etc.
is called the quasiparticle residue or renormalisation constant which is very characteristic of Fermi liquid theory.
The spectral function for the system can be directly observed via angle-resolved photoemission spectroscopy (ARPES), and can be written (in the limit of low-lying excitations) in the form: where
[10] Another important property of Fermi liquids is related to the scattering cross section for electrons.
By Pauli's exclusion principle, both the particles after scattering have to lie above the Fermi surface, with energies
[1] The Fermi liquid is qualitatively analogous to the non-interacting Fermi gas, in the following sense: The system's dynamics and thermodynamics at low excitation energies and temperatures may be described by substituting the non-interacting fermions with interacting quasiparticles, each of which carries the same spin, charge and momentum as the original particles.
The linear contribution corresponds to renormalized single-particle energies, which involve, e.g., a change in the effective mass of particles.
The quadratic terms correspond to a sort of "mean-field" interaction between quasiparticles, which is parametrized by so-called Landau Fermi liquid parameters and determines the behaviour of density oscillations (and spin-density oscillations) in the Fermi liquid.
Still, these mean-field interactions do not lead to a scattering of quasi-particles with a transfer of particles between different momentum states.
The renormalization of the mass of a fluid of interacting fermions can be calculated from first principles using many-body computational techniques.
Specific heat, compressibility, spin-susceptibility and other quantities show the same qualitative behaviour (e.g. dependence on temperature) as in the Fermi gas, but the magnitude is (sometimes strongly) changed.
The remainder of the total weight is in a broad "incoherent background", corresponding to the strong effects of interactions on the fermions at short time scales.
, which is often taken as an experimental check for Fermi liquid behaviour (in addition to the linear temperature-dependence of the specific heat), although it only arises in combination with the lattice.
[15] Fermi liquid theory predicts that the scattering rate, which governs the optical response of metals, not only depends quadratically on temperature (thus causing the
[16][17][18] This is in contrast to the Drude prediction for non-interacting metallic electrons, where the scattering rate is a constant as a function of frequency.
One material in which optical Fermi liquid behavior was experimentally observed is the low-temperature metallic phase of Sr2RuO4.
[19] The experimental observation of exotic phases in strongly correlated systems has triggered an enormous effort from the theoretical community to try to understand their microscopic origin.
One possible route to detect instabilities of a Fermi liquid is precisely the analysis done by Isaak Pomeranchuk.
[4] Although Luttinger liquids are physically similar to Fermi liquids, the restriction to one dimension gives rise to several qualitative differences such as the absence of a quasiparticle peak in the momentum dependent spectral function, and the presence of spin-charge separation and of spin-density waves.
One cannot ignore the existence of interactions in one dimension and has to describe the problem with a non-Fermi theory, where Luttinger liquid is one of them.
At small finite spin temperatures in one dimension the ground state of the system is described by spin-incoherent Luttinger liquid (SILL).
[9] The ground state of such transitions is characterized by the presence of a sharp Fermi surface, although there may not be well-defined quasiparticles.
In optimally doped cuprates and iron-based superconductors, the normal state above the critical temperature shows signs of non-Fermi liquid behaviour, and is often called a strange metal.
[23][24] Understanding the behaviour of non-Fermi liquids is an important problem in condensed matter physics.
Approaches towards explaining these phenomena include the treatment of marginal Fermi liquids; attempts to understand critical points and derive scaling relations; and descriptions using emergent gauge theories with techniques of holographic gauge/gravity duality.