Unfrustrating the t-J Model: d-wave BCS Superconductivity in the $t^{\prime }$-$J_z$-$V$ Model

Abstract

The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a $t^{\prime }$-$J_z$-$V$ model on a square lattice, which has a second-nearest-neighbor hopping $t^{\prime }$ (instead of a nearest-neighbor hopping $t$), an Ising (instead of Heisenberg) antiferromagnetic coupling $J_z$, and a nearest-neighbor repulsion $V$. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.

arXiv comment6+9 pages, 3+3 figures. v3 fixes typos in Eq 4 and 24

References in corpus (28)

• A Common Thread: the pairing interaction for the unconventional superconductors
• Theory of Intertwined Orders in High Temperature Superconductors
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Plaquette Boson-Fermion Model of Cuprates
• Competition between d-wave superconductivity and antiferromagnetism in the 2D Hubbard model
• Phases of the infinite U Hubbard model
• Superconductivity from repulsive interaction
• Holes in the t-J_z model: a thorough study
• Coexistence of Superconductivity and Antiferromagnetism in the Hubbard model for cuprates
• Myriad phases of the Checkerboard Hubbard Model
• Quantum Phase Diagram of the t-Jz Chain Model
• Fractons from polarons
• Doped Antiferromagnets in High Dimension
• Emergent gauge fields and the high temperature superconductors
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions
• Concepts in High Temperature Superconductivity
• Effective approach to the Nagaoka regime of the two dimensional t-J model
• $Z_2$ fractionalized phases of a solvable, disordered, $t$-$J$ model
• Superconductivity in strongly repulsive fermions: the role of kinetic-energy frustration
• Quantum antiferromagnetism and high $T_C$ superconductivity: a close connection between the t-J model and the projected BCS Hamiltonian
• Exact Solution to Haldane-BCS-Hubbard Model Along the Symmetric Lines: Interaction Induced Topological Phase Transition
• Exact Solution of a Repulsive Fermi Model With Enhanced Superconducting Correlations
• A Simple Mechanism for Unconventional Superconductivity in a Repulsive Fermion Model
• Doping a Mott Insulator: Physics of High Temperature Superconductivity
• Hole-pair symmetry and excitations in the strong-coupling extended t-Jz model: competition between d-wave and p-wave
• The Ising version of the t-J model
• Solvable 2D superconductors with l-wave pairing
• Exact ground states of extended t-J_{z} models on a square lattice