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 phases which arise from electromagnetic forces between atoms. More generally, the s ...

, the resonating valence bond theory (RVB) is a

theoretical model A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may ...

that attempts to describe

high-temperature superconductivity High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previo ...

, and in particular the superconductivity in cuprate compounds. It was first proposed by an American physicist P. W. Anderson and Indian theoretical physicist Ganapathy Baskaran in 1987. The theory states that in copper oxide lattices, electrons from neighboring copper atoms interact to form a

valence bond In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of ...

, which locks them in place. However, with

doping Doping may refer to: * Doping, adding a dopant to something * Doping (semiconductor), intentionally introducing impurities into an extremely pure semiconductor to change its electrical properties * Aircraft dope, a lacquer that is applied to fabr ...

, 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 of high-temperature superconductivity.

Description

The physics of Mott insulators is described by the repulsive

Hubbard model The Hubbard model is an approximate model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named for John Hubbard. The Hubbard model states that each ...

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 In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random ( stochastic) models by studying a simpler model that approximates the original by averaging over degrees o ...

, 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

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