Fermi liquid theory 1
Concept of Landau's Fermi liquid theory elementary excitations of interacting Fermions are described by almost independent fermionic quasiparticles state of Fermi liquid described simply by quasiparticle distribution
Phenomenological Theory by Landau energy functional:
deviation from ground state ground state distribution
spin index filled Fermi sea Fermi liquid theory 2
effective quasiparticle spectrum:
bare quasiparticle spectrum: Fermi velocity:
effective mass
density of states at : Fermi volume conserved Fermi liquid theory 3
couplings: symmetric antisymmetric (charge) (spin)
spherical symmetry: Legendre Polynomials
Landau parameters:
charge
spin Fermi liquid theory - physical properties 4 specific heat:
T thermal softening of Fermi surface compressibility:
change of Fermi volume spin susceptibility:
spin splitting of Fermi sea Fermi liquid theory - Gallilei invariance 5 momentum shift for all particles
current density
shifted Fermi sea
''bare particle'' view quasiparticle view quasiparticle induced motion motion
intrinsic consistency Fermi liquid theory - 3He Fermi liquid 6
strong short-range repulsion
Fermi liquid
longer-ranged attraction
superfluid
enhanced diminished enhanced Fermi liquid theory Microscopic considerations 7
Hamiltonian
kinetic energy contact interaction „perturbation“
Rayleigh-Schrödinger Fermi liquid theory perturbation theory Landau parameters Fermi liquid theory Microscopic considerations 8
Rayleigh-Schrödinger
energy:
Distribution function characterizes unperturbed state Fermi liquid theory Microscopic considerations 9
Rayleigh-Schrödinger Fermi liquid theory Microscopic considerations 10
Rayleigh-Schrödinger
Fermi sea Fermi liquid theory Microscopic considerations 11
Rayleigh-Schrödinger
„screening“
cutoff
interaction range
Fermi sea
weak K-dependence Fermi liquid theory Microscopic considerations 12
Rayleigh-Schrödinger
cancels
relabeling Fermi liquid theory Microscopic considerations 13
Rayleigh-Schrödinger Fermi liquid theory Microscopic considerations 14
Rayleigh-Schrödinger
variation: Fermi liquid theory Microscopic considerations 15 Fermi liquid theory Microscopic considerations 16
Lindhard function Fermi liquid theory Microscopic considerations 17
Lindhard function Fermi liquid theory Microscopic considerations 18 Fermi liquid theory Microscopic considerations 19 Fermi liquid theory Microscopic considerations 20 Fermi liquid theory Microscopic considerations 21
Landau parameters: Fermi liquid theory Microscopic considerations 22
Landau parameters:
repulsive interaction Fermi liquid theory Microscopic considerations 23
repulsive interaction
more spin higher less compressible polarizable effective mass
ferromagnetism Fermi liquid theory Microscopic considerations 24 distribution function
ground state Fermi liquid theory Microscopic considerations 25 distribution function
3-dimensional Fermigas Fermi liquid theory Microscopic considerations 26 distribution function
quasiparticle Z weight Fermi liquid theory one-dimensional systems 27
Landau parameters
breakdown of perturbation approach ! Fermi liquid theory one-dimensional systems 28 distribution function
1-dimensional Fermigas non-perturbative Fermi liquid theory one-dimensional systems 29 distribution function
non-perturbative
1-dimensional Fermigas
no quasiparticle weight Tomonaga
Z=0 not a Fermi liquid Luttinger liquid Fermi liquid theory one-dimensional systems 30
Tomonaga-Luttinger liquid no quasiparticles
Fermi liquid behavior disappears Z=0 excitations: collective modes (bosonization of Fermions)
separation of charge and spin excitations
charge spin