A close connection between antiferromagnetism and superconductivity is at the core of high-temperature superconductivity. Here, we put forward the projected BCS theory for the unification of antiferromagnetism and strongly correlated superconductivity. Specifically, it is shown that, with the $d$ -wave pairing symmetry, the projected BCS theory can provide excellent trial states at general doping for the exact ground states of the $t\text{\ensuremath{-}}J$ model in the square lattice, generating a unified theory of high-temperature superconductivity as a continuous function of hole concentration. A key to the success of the projected BCS theory is an accurate treatment of the strong correlation between Cooper pairs, which not only causes the breakdown of superconductivity itself at half filling but also defines the precise nature of strongly correlated superconductivity at moderate doping. Also, via the proper incorporation of particle number fluctuations, the projected BCS theory allows direct computation of the superconducting order parameter, shedding important light on the pseudogap phenomenon.A close connection between antiferromagnetism and superconductivity is at the core of high-temperature superconductivity. Here, we put forward the projected BCS theory for the unification of antiferromagnetism and strongly correlated superconductivity. Specifically, it is shown that, with the $d$-wave pairing symmetry, the projected BCS theory can provide excellent trial states at general doping for the exact ground states of the $t\text{\ensuremath{-}}J$ model in the square lattice, generating a unified theory of high-temperature superconductivity as a continuous function of hole concentration. A key to the success of the projected BCS theory is an accurate treatment of the strong correlation between Cooper pairs, which not only causes the breakdown of superconductivity itself at half filling but also defines the precise nature of strongly correlated superconductivity at moderate doping. Also, via the proper incorporation of particle number fluctuations, the projected BCS theory allows direct computation of the superconducting order parameter, shedding important light on the pseudogap phenomenon.

arXiv:1912.13064Physical Review ResearchFeb 11, 20221 citation

EFFECT OF PARTICLE-HOLE EXCITATIONS ON THE BCS GROUND STATE

J. D. Fan, Y. M. Malozovsky

We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.

International Journal of Modern Physics BJan 30, 20050 citations

BCS theory of driven superconductivity

Andreas Komnik, Michael Thorwart

arXiv:1607.03858The European Physical Journal BNov 1, 201645 citations

Quantum antiferromagnetism and high Tc superconductivity: A close connection between the t−J model and the projected BCS Hamiltonian

K. Park

A connection between quantum antiferromagnetism and high ${T}_{c}$ superconductivity is theoretically investigated by analyzing the $t\text{\ensuremath{-}}J$ model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the $t\text{\ensuremath{-}}J$ model at half filling [i.e., the two-dimensional (2D) antiferromagnetic Heisenberg model] is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wave function overlap between the ground states of the $t\text{\ensuremath{-}}J$ model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the $t\text{\ensuremath{-}}J$ model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.A connection between quantum antiferromagnetism and high ${T}_{c}$ superconductivity is theoretically investigated by analyzing the $t\text{\ensuremath{-}}J$ model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the $t\text{\ensuremath{-}}J$ model at half filling [i.e., the two-dimensional (2D) antiferromagnetic Heisenberg model] is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wave function overlap between the ground states of the $t\text{\ensuremath{-}}J$ model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the $t\text{\ensuremath{-}}J$ model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.

arXiv:cond-mat/0508357Physical Review BDec 29, 200511 citations

d

-wave pairing symmetry, the projected BCS theory can provide excellent trial states at general doping for the exact ground states of the $t\text{\ensuremath{-}}J$ model in the square lattice, generating a unified theory of high-temperature superconductivity as a continuous function of hole concentration. A key to the success of the projected BCS theory is an accurate treatment of the strong correlation between Cooper pairs, which not only causes the breakdown of superconductivity itself at half filling but also defines the precise nature of strongly correlated superconductivity at moderate doping. Also, via the proper incorporation of particle number fluctuations, the projected BCS theory allows direct computation of the superconducting order parameter, shedding important light on the pseudogap phenomenon.

A connection between quantum antiferromagnetism and high

{T}_{c}

superconductivity is theoretically investigated by analyzing the $t\text{\ensuremath{-}}J$ model and its relationships to the Gutzwiller-projected BCS Hamiltonian. After numerical corroboration via exact diagonalization, it is analytically shown that the ground state of the $t\text{\ensuremath{-}}J$ model at half filling [i.e., the two-dimensional (2D) antiferromagnetic Heisenberg model] is entirely equivalent to the ground state of the Gutzwiller-projected BCS Hamiltonian with strong pairing. Combined with the high wave function overlap between the ground states of the $t\text{\ensuremath{-}}J$ model and the projected BCS Hamiltonian at moderate doping, this equivalence provides strong support for the existence of superconductivity in the $t\text{\ensuremath{-}}J$ model. The relationship between the ground state of the projected BCS Hamiltonian and Anderson's resonating valence bond state (i.e., the projected BCS ground state) is discussed.