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 sub ...

, 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 be s ...

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 previ ...

, and in particular the superconductivity in

cuprate Cuprate loosely refers to a material that can be viewed as containing anionic copper complexes. Examples include tetrachloridocuprate ( uCl4sup>2−), the superconductor YBa2Cu3O7, and the organocuprates (e.g., dimethylcuprate u(CH3)2sup>� ...

compounds. It was first proposed by an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

physicist

P. W. Anderson Philip Warren Anderson (December 13, 1923 – March 29, 2020) was an American theoretical physicist and Nobel laureate. Anderson made contributions to the theories of localization, antiferromagnetism, symmetry breaking (including a paper in 1 ...

and Indian theoretical physicist

Ganapathy Baskaran Ganapathy Baskaran is an Indian theoretical physicist, known for his work on condensed matter physics and strongly correlated quantum materials. Baskaran is an Emeritus Professor of physics at the Institute of Mathematical Sciences in Chennai ...

in 1987. The theory states that in

copper oxide Copper oxide is a compound from the two elements copper and oxygen. Copper oxide may refer to: * Copper(I) oxide (cuprous oxide, Cu2O) * Copper(II) oxide Copper(II) oxide or cupric oxide is an inorganic compound with the formula CuO. A black so ...

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, these electrons can act as mobile

Cooper pairs In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...

and are able to superconduct. Anderson observed in his 1987 paper that the origins of superconductivity in doped cuprates was in the

Mott insulator Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures). These insulators fail to be correctly described by band ...

nature of crystalline copper oxide. RVB builds on the

Hubbard Hubbard may refer to: Places Canada *Hubbard, Saskatchewan *Hubbards, Nova Scotia Canada/United States * Mount Hubbard, a mountain on the Alaska/Yukon border *Hubbard Glacier, a large freshwater glacier in Alaska and Yukon Greenland *Hubbard Gla ...

and

t-J model In solid-state physics, the ''t''-''J'' model is a model first derived in 1977 from the Hubbard model by Józef Spałek to explain antiferromagnetic properties of the Mott insulators and taking into account experimental results about the streng ...

s 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 fermion ...

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 el ...

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 Gutzwiller is a surname. Notable people with the surname include: *Kathryn Gutzwiller Kathryn J. Gutzwiller is a professor of classics at the University of Cincinnati. She specialises in Hellenistic poetry, and her interests include Greek and Lati ...

, 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