Magnetic pairing mechanism for superconductivity in the Heisenberg model

Twelve compounds with the formula RBa2Cu3O7-δ where δ≍0.1 and R=Y or a lanthanide element except Ce, Pm, or Tb, crystallize in the same layered orthorhombic perovskite-like structure (see the article by I.K. Schuller and J.D. Jorgensen in this issue). All such compounds are superconducting with superconducting transition temperatures Tc≍92-94 K, except for R=Pr. The compound PrBa2Cu3O7-δ appears to be a special case, since it does not exhibit metallic behavior and is not superconducting. Historically, the prototype YBa2Cu3O7-δ compound is singularly important since it was the first superconducting material with a Tc greater than 77 K, the boiling point of liquid nitrogen. In the meantime, yet higher Tc's have been obtained in YBa2Cu3O7-δ at very high pressure (Tc˜107 K at 150 kbar)5 and in new layered compounds in the Bi-Sr-Ca-Cu-O (maximum Tc≍110 K)6 and Tl-Ba-Ca-Cu-O (maximum Tc≍125 K)7 systems (see the article by A.W. Sleight, M.A. Subramanian, and C.C. Torardi in this issue).The origin and nature of the high Tc superconductivity of the RBa2Cu3O7-δ compounds, and the other layered copper oxide compounds as well, are presently not understood and constitute a formidable challenge to experimentalists and theorists alike. One of the most intriguing possibilities is that a magnetic mechanism, rather than the electronphonon interaction, is responsible for the formation of the superconducting electron pairs in the high Tc copper oxides. The primary evidence for a magnetic pairing mechanism is the proximity of antiferromagnetism and superconductivity as the concentration of holes in the conducting CuO2 planes is varied,8 as discussed below for the RBa2Cu3O7-δ compounds.

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MAGNETIC PAIRING IN TWO-DIMENSIONAL ANTIFERROMAGNETIC XY MODEL

International Journal of Modern Physics B ◽

10.1142/s021797928900004x ◽

1989 ◽

Vol 03 (01) ◽

pp. 65-76

Author(s):

K. Y. SZETO

Keyword(s):

High Temperature ◽

Coulomb Repulsion ◽

Coulomb Gas ◽

The Self ◽

Xy Model ◽

Two Dimensional ◽

Pairing Mechanism ◽

Spin Variable ◽

Self Consistent ◽

Magnetic Pairing

A two-dimensional Ising Coulomb gas is introduced to describe the frustrated plaquettes of the two-dimensional antiferromagnetic XY model with Coulomb repulsion. The Ising spin variable corresponds to the two possible chiralities of the frustrated plaquettes, which repel each other with a screened Coulomb potential. Using the self-consistent screening analysis, the Ising Coulomb gas is shown to have a Kosterlitz-Thouless transition from a pairing phase at low temperature to a plasma phase at high temperature. The phase diagram is obtained numerically as a function of density and relative strength of the attraction between particles of opposite chiralities and the Coulomb repulsion. Possible applications to the magnetic pairing mechanism of high temperature superconductors is discussed in the context of Li doped La 2 CuO 4. It is also argued that the Aharony et al. model of magnetic pairing with the dipolar attraction can be derived as a special case of the Ising Coulomb gas model and is superceded by a stronger attractive interaction in magnetic pairing mechanism in the self-consistent analysis.

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ELECTRON DIFFRACTION STUDIES OF SUPERCONDUCTORS OF THE K-BA-BI-O SYSTEM AND RELATED OXIDES

International Journal of Modern Physics B ◽

10.1142/s0217979205028311 ◽

2005 ◽

Vol 19 (01n03) ◽

pp. 239-241

Author(s):

V. I. NIKOLAICHIK ◽

L. A. KLINKOVA

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

Electron Diffraction ◽

Cuprate Superconductors ◽

Pairing Mechanism ◽

Chemical Methods ◽

Ordered Structures ◽

Physical Chemical ◽

Transmission Electron ◽

Magnetic Pairing

The application of transmission electron microscopy in combination with physical-chemical methods has made it possible to discover a large number of discrete oxides of ordered structures in the Ba - Bi - O system, which is the parent system for the K - Ba - Bi - O superconducting system. Cation-ordered superconductors Ba 1-x K x BiO 3 with the crystalline structure of a non-cubic and layered nature have been synthesized. This result removes the crystallographic contradiction between bismuthate and cuprate superconductors that provides support to the existence of a common non-magnetic pairing mechanism.

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Integrable Models

10.1093/oso/9780198805021.003.0009 ◽

2018 ◽

Author(s):

S. G. Rajeev

Keyword(s):

Fluid Mechanics ◽

Soliton Solution ◽

Water Waves ◽

Heisenberg Model ◽

Kdv Equation ◽

Short Review ◽

Lax Pair ◽

Shallow Water Waves ◽

Initial Value ◽

The Kdv Equation

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.

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Monte Carlo simulations of an unconventional phase transition for a two-dimensional dimerized quantum Heisenberg model

Physical Review B ◽

10.1103/physrevb.85.014414 ◽

2012 ◽

Vol 85 (1) ◽

Cited By ~ 17

Author(s):

F.-J. Jiang

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Monte Carlo Simulations ◽

Heisenberg Model ◽

Two Dimensional

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Evolution of spin excitations from bulk to monolayer FeSe

Nature Communications ◽

10.1038/s41467-021-23317-3 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Jonathan Pelliciari ◽

Seher Karakuzu ◽

Qi Song ◽

Riccardo Arpaia ◽

Abhishek Nag ◽

...

Keyword(s):

Quantum Monte Carlo ◽

Spin Dynamics ◽

Spin Fluctuations ◽

Superconducting Transition ◽

Pairing Mechanism ◽

Range Magnetic Order ◽

X Ray Scattering ◽

Spin Excitations ◽

Order Of Magnitude ◽

Long Range Magnetic Order

AbstractIn ultrathin films of FeSe grown on SrTiO3 (FeSe/STO), the superconducting transition temperature Tc is increased by almost an order of magnitude, raising questions on the pairing mechanism. As in other superconductors, antiferromagnetic spin fluctuations have been proposed to mediate SC making it essential to study the evolution of the spin dynamics of FeSe from the bulk to the ultrathin limit. Here, we investigate the spin excitations in bulk and monolayer FeSe/STO using resonant inelastic x-ray scattering (RIXS) and quantum Monte Carlo (QMC) calculations. Despite the absence of long-range magnetic order, bulk FeSe displays dispersive magnetic excitations reminiscent of other Fe-pnictides. Conversely, the spin excitations in FeSe/STO are gapped, dispersionless, and significantly hardened relative to its bulk counterpart. By comparing our RIXS results with simulations of a bilayer Hubbard model, we connect the evolution of the spin excitations to the Fermiology of the two systems revealing a remarkable reconfiguration of spin excitations in FeSe/STO, essential to understand the role of spin fluctuations in the pairing mechanism.

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