scholarly journals Landau Fermi Liquid Theory

1996 ◽  
Vol 49 (1) ◽  
pp. 79
Author(s):  
D Neilson
Keyword(s):  
Fermi Surface ◽  
Landau Theory ◽  
Collective Modes ◽  
Fermi Liquids ◽  
Original Formulation ◽  
Zero Sound ◽  
Liquid Theory ◽  
Recent Modification ◽  
High Transition ◽  
Helium 3

This article reviews the Landau theory of interacting Fermi liquids such as mobile electrons in solids or helium-3. It starts with Landau's original formulation which takes advantage of the existence of a Fermi surface to map the strongly interacting single-particle excitations near the Fermi surface into a system of weakly interacting quasiparticle excitations. The theory relates microscopic parameters for the quasiparticle energies and scattering strengths to experimental observables. The resulting low lying collective modes of the system, such as zero sound in helium-3, are then discussed. Next the rigorous microscopic basis of the theory is presented. Finally there is an outline of a recent modification of the theory which may resolve some of the puzzles about the nature of the electron states in materials exhibiting high transition temperature superconductivity.

Landau theory of Fermi liquids and the integration-over-the-coupling-constant algorithm

1994 ◽  
Vol 49 (20) ◽  
pp. 14172-14178 ◽  
Author(s):  
Sudhakar Yarlagadda ◽  
Gabriele F. Giuliani
Keyword(s):  
Landau Theory ◽  
Fermi Liquids ◽  
Coupling Constant

Landau theory of Fermi liquids reformulated

1986 ◽  
Vol 138 (3) ◽  
pp. 404-414 ◽  
Author(s):  
Ch.G. van Weert ◽  
M.C.J. Leermakers ◽  
A.M.J. Schakel
Keyword(s):  
Landau Theory ◽  
Fermi Liquids

Umklapp Scattering in Fermi Liquids: A Renormalisation Group Approach

1997 ◽  
Vol 11 (15) ◽  
pp. 1813-1828 ◽  
Author(s):  
Deepak Kumar ◽  
R. Rajaraman
Keyword(s):  
Renormalisation Group ◽  
Three Dimensions ◽  
Fermi Liquids ◽  
Electronic Systems ◽  
Group Approach ◽  
Liquid Theory ◽  
Group Methods ◽  
Almost All ◽  
Umklapp Scattering

The role of Umklapp scattering for electrons on a lattice is studied. Using renormalisation group methods it is shown that the effective low energy interaction involves not only forward scattering, but also non-forward Umklapp scattering. We show that the latter can happen to almost all of the electrons even when they have a filling of around one-half. The bahavior of these Umklapp couplings is studied in the loop expansion. It is shown that they remain marginal to all loop orders. The discussion is given in the context of two-dimensional lattices, but generalisation to three-dimensions is mentioned. We also briefly discuss the possible consequences of this on Fermi liquid theory and on physical properties of such electronic systems.

Theories of High Tc Superconductors

1987 ◽  
Vol 99 ◽  
Author(s):  
John Bardeen
Keyword(s):  
Low Temperatures ◽  
Landau Theory ◽  
3D Models ◽  
Oxide Superconductors ◽  
High Tc Superconductors ◽  
Pairing Interaction ◽  
Ginzburg Landau ◽  
High Tc ◽  
Wide Range ◽  
High Transition

ABSTRACTMany theories have been given to account for the high transition temperatures in the oxide superconductors. While most are based on pairing, they differ as to the origin of the attractive interaction that gives rise to the pairs and whether the pairing is weak or strong. If weak(λ < ∼ 0.5), the energy range of the pairing interaction must be wider than is consistent with one mediated solely by phonons. With measurements on single crystals becoming available, giving data covering a wide range of frequencies and temperatures, it is possible to narrow down the possible options. The data show that anisotropie 3D models are required. Observed isotope shifts indicate that phonons must play a role, but additional mechanisms are likely necessary to account for the high T's. Thermal, magnetic and transport data are consistent with anisotropie Ginzburg-Landau theory near T, with expected departures at low temperatures.

The acoustic impedance of liquid helium-3

1965 ◽  
Vol 284 (1396) ◽  
pp. 125-136 ◽  
Keyword(s):  
Acoustic Impedance ◽  
Fermi Liquid ◽  
Quartz Crystal ◽  
Zero Sound ◽  
Saturated Vapour Pressure ◽  
Saturated Vapour ◽  
A Value ◽  
Reflexion Coefficient ◽  
Helium 3 ◽  
Good Agreement

Measurements have been made of the acoustic impedance ( Z ) of liquid 3 He under its saturated vapour pressure in the temperature range 0·035 to 0·6°K. A 1000 Mc/s sound wave is propagated along the axis of an X -cut quartz crystal, and undergoes many reflexions from each end of the crystal. Values are obtained for the reflexion coefficient at an interface between quartz and liquid 3 He by comparing the rate at which the signal decays in the crystal, with and without liquid 3 He present on the ends. These values then lead directly to the acoustic impedance ( Z ) of the liquid. Usually, Z / ρ (where ρ is the density) should be equal to the velocity of sound, and above 0·1°K this is found to be so. However, at about 0·1°K the value of Z / ρ increases abruptly, and at lower temperatures has a value about 10% greater. This result is in good agreement with Landau’s theory of a Fermi liquid, which relates the change in impedance with the propagation of a new mode of sound, the so-called 'zero-sound’.

scholarly journals Atypical behavior of collective modes in two-dimensional Fermi liquids

2020 ◽  
Vol 32 (34) ◽  
pp. 345602 ◽  
Author(s):  
M P Gochan ◽  
J T Heath ◽  
K S Bedell
Keyword(s):  
Collective Modes ◽  
Fermi Liquids ◽  
Two Dimensional

The heat capacity of liquid 3He beyond T3 log T

1987 ◽  
Vol 65 (11) ◽  
pp. 1549-1551
Author(s):  
A. M. J. Schakel ◽  
Ch. J. Calkoen ◽  
Ch. G. van Weert
Keyword(s):  
Heat Capacity ◽  
Magnetic Susceptibility ◽  
Temperature Dependence ◽  
Analytic Functions ◽  
Spin Fluctuation ◽  
Landau Theory ◽  
Particle Mass ◽  
Fermi Liquids ◽  
Quasi Particle ◽  
Fluctuation Model

The heat capacity of liquid 3He up to 2.5 K is calculated on the basis of a spin-fluctuation model in the context of the Landau theory of Fermi liquids. A good fit of the data is achieved by including the temperature dependence of the magnetic susceptibility and by using a different, smaller, quasi-particle mass. It is also shown that the magnetic susceptibility and the compressibility are analytic functions of the temperature.

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