Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting
fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...
s that describes the normal state of most
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typi ...
s at sufficiently low temperatures.
The interactions among the particles of the many-body system do not need to be small. The
phenomenological
Phenomenology may refer to:
Art
* Phenomenology (architecture), based on the experience of building materials and their sensory properties
Philosophy
* Phenomenology (philosophy), a branch of philosophy which studies subjective experiences and a ...
theory of Fermi liquids was introduced by the Soviet physicist
Lev Davidovich Landau in 1956, and later developed by
Alexei Abrikosov and
Isaak Khalatnikov
Isaak Markovych Khalatnykov ( uk, Ісаа́к Ма́ркович Хала́тников; 17 October 1919 – 9 January 2021) was a leading Soviet theoretical physicist who has made significant contributions to many areas of theoretical physics, ...
using
diagrammatic perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...
.
The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal
Fermi gas
An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer s ...
(i.e. non-interacting fermions), and why other properties differ.
Important examples of where Fermi liquid theory has been successfully applied are most notably electrons in most metals and
liquid helium
Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.
At standard pressure, the chemical element helium exists in a liquid form only at the extremely low t ...
-3.
Liquid
helium-3
Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is th ...
is a Fermi liquid at low temperatures (but not low enough to be in its
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
phase). Helium-3 is an
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers ( mass number ...
of
helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
, with 2
protons, 1
neutron
The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
and 2 electrons per atom. Because there is an odd number of fermions inside the nucleus, the atom itself is also a fermion. The
electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary partic ...
s in a normal (non-
superconducting
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
) metal also form a Fermi liquid, as do the
nucleons
In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number).
Until the 1960s, nucleons w ...
(protons and neutrons) in an
atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden experiments, Geiger–Marsden gold foil experiment. After th ...
.
Strontium ruthenate displays some key properties of Fermi liquids, despite being a
strongly correlated material
Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermi ...
, and is compared with
high temperature superconductors like
cuprates.
Description
The key ideas behind Landau's theory are the notion of ''adiabaticity'' and the
Pauli exclusion principle
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle was formulated ...
.
[ (draft copy)] Consider a non-interacting fermion system (a
Fermi gas
An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with half-integer s ...
), and suppose we "turn on" the interaction slowly. Landau argued that in this situation, the ground state of the Fermi gas would adiabatically transform into the ground state of the interacting system.
By Pauli's exclusion principle, the ground state
of a Fermi gas consists of fermions occupying all momentum states corresponding to momentum