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Physical review. B, Condensed matter

Theorem on pseudospin and η-pairing superconductivity

Shun-Qing Shen

Published Oct 1, 1996• 3 citations
Publisher

Abstract

We present a theorem on total pseudospin as an eigenvalue in a state. The total pseudospin is determined by the summation of the phase factors, written in terms of pseudospin operator and number of electrons. We discuss its relation with \ensuremath{\eta}-pairing superconductivity and ground-state energy level ordering of a system with pseudospin symmetry. Finally as an application of the theorem we show that the ground state of a generalized Hubbard model is superconducting for any electron filling. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.9039

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We present a theorem on total pseudospin as an eigenvalue in a state. The total pseudospin is determined by the summation of the phase factors, written in terms of pseudospin operator and number of electrons. We discuss its relation with \ensuremath{\eta}-pairing superconductivity and ground-state energy level ordering of a system with pseudospin symmetry. Finally as an application of the theorem we show that the ground state of a generalized Hubbard model is superconducting for any electron filling. \textcopyright{} 1996 The American Physical Society.
We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang ``\ensuremath{\eta}-paired'' state for any nonvanishing positive value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping. \textcopyright{} 1996 The American Physical Society.
The authors study the $\ensuremath{\eta}$-pairing phenomenon in correlated fermion models with spin-orbit coupling. Spin-orbit coupled systems are usually thought to possess no continuous symmetries, except the conventional U(1) particle-number symmetry. The $\ensuremath{\eta}$-pairing reveals an exact SU(2) pseudospin symmetry in a broad class of spin-orbit coupled Hubbard models. Furthermore, the authors construct an exactly solvable interacting Dirac-semimetal model that exhibits an exact pseudospin symmetry with fine-tuned parameters. This model hosts $\ensuremath{\eta}$-pairing and charge density wave ground states, which meet at an exactly solvable multicritical line.
It is proved explicitly that the strong on-site attractive interaction acts to form \ensuremath{\eta} pairings which make full use of the phase coherence of Bloch electrons. The U(1) gauge symmetry breaks spontaneously in the formation, which is accompanied by the creation of \ensuremath{\eta}-paired boson, ``\ensuremath{\eta} pairon.'' The condensation of \ensuremath{\eta} pairons takes place at a finite temperature to make up the ground-state condensate which has off-diagonal long-range order. The resulting ground state is a singlet and the energy spectrum has a gap. This type of superconductivity based on \ensuremath{\eta} pairing exhibits the same peculiar properties as observed in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ oxide superconductors.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron-hopping terms, the ground state has Ising-type N\'eel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.