$\eta$-pairing in correlated fermion models with spin-orbit coupling

Abstract

We generalize the $\eta$-pairing theory in Hubbard models to the ones with spin-orbit coupling (SOC) and obtain the conditions under which the $\eta$-pairing operator is an eigenoperator of the Hamiltonian. The $\eta$ pairing thus reveals an exact $SU(2)$ pseudospin symmetry in our spin-orbit coupled Hubbard model, even though the $SU(2)$ spin symmetry is explicitly broken by the SOC. In particular, these exact results can be applied to a variety of Hubbard models with SOC on either bipartite or non-bipartite lattices, whose noninteracting limit can be a Dirac semimetal, a Weyl semimetal, a nodal-line semimetal, and a Chern insulator. The $\eta$ pairing conditions also impose constraints on the band topology of these systems. We then construct and focus on an interacting Dirac-semimetal model, which exhibits an exact pseudospin symmetry with fine-tuned parameters. The stability regions for the exact $\eta$-pairing ground states (with momentum $\mathbf{\pi }$ or $0$) and the exact charge-density-wave ground states are established. Between these distinct symmetry-breaking phases, there exists an exactly solvable multicritical line. In the end, we discuss possible experimental realizations of our results.

Published version (PRB Editors Suggestion)

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• Theory of pair density wave on a quasi-one-dimensional lattice in the Hubbard model
• Spin and pair density waves in 2D altermagnetic metals
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Quantum many-body scars with unconventional superconducting pairing symmetries via multibody interactions
• Thermodynamic and electromagnetic properties of the eta-pairing superconductivity in the Penson-Kolb model
• Spin density wave order in interacting type-I and type-II Weyl semimetals
• Edge-Edge Correlations without Edge-States: $\eta$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain