condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...

, the resonating valence bond theory (RVB) is a theoretical model that attempts to describe high-temperature superconductivity, and in particular the superconductivity in cuprate compounds. It was proposed by P. W. Anderson and Ganapathy Baskaran in 1987. The theory states that in copper oxide lattices, electrons from neighboring copper atoms interact to form a valence bond, which locks them in place. However, with doping, these electrons can act as mobile Cooper pairs and are able to superconduct. Anderson observed in his 1987 paper that the origins of superconductivity in doped cuprates was in the Mott insulator nature of crystalline copper oxide. RVB builds on the Hubbard and t-J models used in the study of

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 ...

s. In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by EPFL scientists, lending support for Anderson's theory.

Description

The physics of Mott insulators is described by the repulsive

Hubbard model The Hubbard model is an Approximation, approximate model used to describe the transition between Conductor (material), conducting and Electrical insulation, insulating systems. It is particularly useful in solid-state physics. The model is named ...

Hamiltonian Hamiltonian may refer to: * Hamiltonian mechanics, a function that represents the total energy of a system * Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system ** Dyall Hamiltonian, a modified Hamiltonian ...

: :

H=-t\sum_(c^_c_+\text)+U\sum_in_n_

In 1971, Anderson first suggested that this Hamiltonian can have a non-degenerate ground state that is composed of disordered spin states. Shortly after the high-temperature superconductors were discovered, Anderson and Kivelson et al. proposed a ''resonating valence bond'' ground state for these materials, written as :

, \text\rangle=\sum_C, C\rangle

where

C

represented a covering of a lattice by nearest neighbor dimers. Each such covering is weighted equally. In a mean field approximation, the RVB state can be written in terms of a Gutzwiller projection, and displays a superconducting phase transition per the Kosterlitz–Thouless mechanism. However, a rigorous proof for the existence of a superconducting ground state in either the Hubbard or the t-J Hamiltonian is not yet known. Further the stability of the RVB ground state has not yet been confirmed.

References

{{Superconductivity High-temperature superconductors Correlated electrons Condensed matter physics Theoretical physics