An effective Hamiltonian with auxiliary bosons and auxiliary fermions is proposed to treat the Hubbard Hamiltonian with strong correlation. Auxiliary particles themselves can not describe any real excitations. In particular, the Bose condensation of auxiliary bosons never occurs, and auxiliary fermions have no Fermi surfaces. Real excitations are described by two kinds of pair-excitations of auxiliary particles, such as fermionic and bosonic pair-excitations. Superconductivity in the effective Hamiltonian is nothing but the condensation of Cooper pairs between fermionic pair-excitations, which are formed by the superexchange interaction mediated by auxiliary fermions. The proposed model of superconductivity is consistent with anisotropic-singlet superconductivity previously examined by the present author (Jpn. J. Appl. Phys. 26 (1987) L652.), which is based on the Fermi liquid theory of the Hubbard Hamiltonian.An effective Hamiltonian with auxiliary bosons and auxiliary fermions is proposed to treat the Hubbard Hamiltonian with strong correlation. Auxiliary particles themselves can not describe any real excitations. In particular, the Bose condensation of auxiliary bosons never occurs, and auxiliary fermions have no Fermi surfaces. Real excitations are described by two kinds of pair-excitations of auxiliary particles, such as fermionic and bosonic pair-excitations. Superconductivity in the effective Hamiltonian is nothing but the condensation of Cooper pairs between fermionic pair-excitations, which are formed by the superexchange interaction mediated by auxiliary fermions. The proposed model of superconductivity is consistent with anisotropic-singlet superconductivity previously examined by the present author (Jpn. J. Appl. Phys. 26 (1987) L652.), which is based on the Fermi liquid theory of the Hubbard Hamiltonian.

Journal of the Physical Society of JapanNov 15, 19889 citations

Spin-nematic order induced superconductivity

Naoum Karchev

We explore a spin-fermion model with fermion-spin-quadrupolar interaction. In a nematic phase, this interaction reduces to a four-fermion interaction that is the basis of superconductivity. When the coupling constant is positive the superconductivity is a p -wave with spin-parallel–paired fermions. When it is negative the superconductivity is a p -wave and fermions are spin-antiparallel paired. For a system with zero chemical potential, even a very small coupling can bind fermions into a bound state that leads to superconductivity. When the chemical potential is non-zero the system possesses quantum critical transition from the normal spin-nematic phase to the phase where superconductivity coexists with spin-nematicity. The value of the quantum critical fermion-spin-nematicity coupling constant depends on the chemical potential.We explore a spin-fermion model with fermion-spin-quadrupolar interaction. In a nematic phase, this interaction reduces to a four-fermion interaction that is the basis of superconductivity. When the coupling constant is positive the superconductivity is a p -wave with spin-parallel–paired fermions. When it is negative the superconductivity is a p -wave and fermions are spin-antiparallel paired. For a system with zero chemical potential, even a very small coupling can bind fermions into a bound state that leads to superconductivity. When the chemical potential is non-zero the system possesses quantum critical transition from the normal spin-nematic phase to the phase where superconductivity coexists with spin-nematicity. The value of the quantum critical fermion-spin-nematicity coupling constant depends on the chemical potential.

arXiv:1908.02514Europhysics Letters (EPL)Feb 17, 20200 citations

$η$ -pairing in a two-band model of spinless fermions$η$-pairing in a two-band model of spinless fermions

Igor N. Karnaukhov

We study the two-band model of spinless fermions in which itinerant fermions interact with localized fermions through the two-particle hybridization. In 1D version, the model has exact solution using the Bethe ansatz. It has been shown that accounting for two-particle hybridization reduces the repulsive interaction between itinerant fermions. In the case of strong interaction, the effective interaction between itinerant fermions is attractive, and $η$ -pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to $p$ -superconducting states with $η$ -pairing. $η$ -pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.We study the two-band model of spinless fermions in which itinerant fermions interact with localized fermions through the two-particle hybridization. In 1D version, the model has exact solution using the Bethe ansatz. It has been shown that accounting for two-particle hybridization reduces the repulsive interaction between itinerant fermions. In the case of strong interaction, the effective interaction between itinerant fermions is attractive, and $η$-pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to $p$-superconducting states with $η$-pairing. $η$-pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.

arXiv:2604.21318Apr 23, 20260 citations

Boson-Fermion model of superconductivity

Richard M. Friedberg, T.D. Lee

Physics Letters AJul 1, 198980 citations

η

-pairing in a two-band model of spinless fermions

η

-pairing of spinless fermions is realized. The proposed pairing mechanism via two-particle hybridization can lead to

p

-superconducting states with

η

-pairing.

η

-pairing of spinless fermions could explain the phenomenon of high-temperature superconductivity experimentally observed in hydrogen-rich materials at high pressures.