U(1) Gauge Theory as a Collective Field Theory for Hubbard Model

1988 ◽  
Vol 02 (05) ◽  
pp. 613-623 ◽  
Author(s):  
Tetsuo Matsui
Keyword(s):  
Field Theory ◽  
Hubbard Model ◽  
Gauge Field ◽  
Landau Theory ◽  
Ginzburg Landau ◽  
Gauge Invariant ◽  
High Tc ◽  
Invariant Order ◽  
Path Integral Method ◽  
Higgs Scalar

I construct a collective field theory for Hubbard model of high Tc superconductivity, using a path-integral method in the third quantized (slave boson) form. It is a U(1) gauge invariant theory consisting of a U(1) gauge field and a Higgs scalar. The gauge field stands for resonating valence bonds and describes a (short range) antiferro-paramagnet phase transition by a condensation machanism. The Higgs scalar represents spinless holes carrying electric charges. Through the confining gauge force, there formed bounded hole pairs on each link, which correspond to the vector mesons in lattice QCD. A superconducting phase is to be described by a condensation of a gauge invariant order parameter for these hole pairs, and to be compared with the color confining chirally broken phase in QCD. A Ginzburg-Landau theory for the vector hole-pair field is proposed.

scholarly journals Possible Alterations of Local Gravitational Field Inside a Superconductor

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 193 ◽  
Author(s):  
Giovanni Alberto Ummarino ◽  
Antonio Gallerati
Keyword(s):  
Gravitational Field ◽  
Landau Theory ◽  
Time Dependent ◽  
Qualitative Comparison ◽  
Ginzburg Landau ◽  
High Tc ◽  
Gravitational Fields ◽  
Favorable Conditions

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.

SUPERFLUID FIELD THEORY

1993 ◽  
Vol 08 (28) ◽  
pp. 5005-5021
Author(s):  
R.L. DAVIS
Keyword(s):  
Field Theory ◽  
Landau Theory ◽  
Fluid Model ◽  
Ginzburg Landau ◽  
Bosonic Field ◽  
Thermomechanical Effect ◽  
First Sound ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Landau Criterion

The very low temperature dynamics of an isotropic superfluid is derived from a repulsive bosonic field theory. The field theory is a fully dynamical generalization of the Ginzburg-Landau theory, which at zero temperature has semiclassical superfluid solutions. It is shown that supercurrent quenching occurs above some intrinsic critical velocity. The speed of first sound is calculated and the Landau criterion for a maximum superfluid velocity is derived. At finite temperature, the thermodynamic potential is computed, the order parameter and gap equations are derived, the origin of the Landau two-fluid model is identified and the thermomechanical effect is explained. This theory successfully describes many of the features of 4He well below the critical temperature, as well as relativistic generalizations.

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.

GINZBURG-LANDAU FROM FIELD THEORY

1991 ◽  
Vol 06 (01) ◽  
pp. 73-81 ◽  
Author(s):  
R. L. DAVIS
Keyword(s):  
Field Theory ◽  
Particle Density ◽  
Landau Theory ◽  
Mean Field Theory ◽  
Goldstone Boson ◽  
Index Of Refraction ◽  
Classical Solutions ◽  
Global Symmetry ◽  
Complex Scalar ◽  
Ginzburg Landau

A complex scalar mean-field theory has semi-classical solutions that display macroscopic superfluidity. The U (1) global symmetry is spontaneously broken by a ground-state with uniform particle density. The Nambu-Goldstone boson of that breaking is sound, but unlike the case for vacuum configurations the speed at which the Nambu-Goldstone boson travels is variable; it is determined by an index of refraction due to fluctuations in the magnitude of the order parameter. This field-theoretic description is shown to be a fully dynamical generalization of the Ginzburg-Landau theory. It is confirmed that Abrikosov vortices of the Ginzburg-Landau theory are spinning vortices of the field theory. While vacuum configurations are time-independent points in the manifold of degenerate minima to the effective potential, the ground states for superfluid systems are characterized by geodesic trajectories, and the symmetry is always restored in the limit of zero density.

scholarly journals Effect of Higher Landau Levels on the Transverse Thermoelectric Conductivity in High-\(T_{c}\) Superconductors

2017 ◽  
Vol 26 (3) ◽  
pp. 279
Author(s):  
Bui Duc Tinh
Keyword(s):  
Gaussian Approximation ◽  
Landau Theory ◽  
Landau Levels ◽  
Time Dependent ◽  
Dimensional Model ◽  
Ginzburg Landau ◽  
High Tc ◽  
High Tc Superconductor ◽  
Self Consistent ◽  
Good Agreement

We investigate effect of higher Ladau levels on the transverse thermoelectricconductivity \(\alpha_{xy}\), describing the Nernst effect in high-\(T_c\) superconductors, by using the time-dependent Ginzburg-Landau theory in two dimensional model withthermal noise. The transverse thermoelectric conductivity is calculated inthe self-consistent Gaussian approximation. Our results indicate that thehigher Landau levels are, the less these levels contribute to the transversethermoelectric conductivity. Our results are in good agreement with experimental dataon high-Tc superconductor.

CRITICAL TEMPERATURE OF HIGH-Tc SUPERCONDUCTORS AND BOUNDARY CONDITIONS IN GINZBURG-LANDAU THEORY

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4269-4276 ◽  
Author(s):  
A. LYKOV
Keyword(s):  
Boundary Condition ◽  
Critical Temperature ◽  
Order Parameter ◽  
Cuprate Superconductors ◽  
Landau Theory ◽  
Structural Elements ◽  
High Tc Superconductors ◽  
Ginzburg Landau ◽  
High Tc ◽  
Insulating Properties

New boundary condition for the order parameter in the Ginzburg-Landau theory is applied to the case of CuO 2 planes which are the main structural elements responsible for superconductivity in high-Tc superconductors. It was found that the order parameter in these superconductors is significantly depressed in the CuO 2 planes. As a result, this boundary condition to the GL equations is found to limit the critical temperature of high-Tc superconductors. Thus, in order to increase Tc of cuprate superconductors, the number of CuO 2 planes that are within a short distance of each other in unit cell or insulating properties of the layers located in the vicinity to the CuO 2 planes should be increased.

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