d-Wave pair density wave superconductivity in a two-orbital model

TL;DR

This paper investigates multi-orbital models on a square lattice, revealing regimes of incommensurate pair density wave superconductivity driven by interband pairing, with implications for correlated materials and atomic fermions.

Contribution

It uncovers the stability of interband PDW states in two-orbital models using RPA and effective Hamiltonians, highlighting the role of orbital content and multiband Fermi surfaces.

Findings

Identified regimes of incommensurate $d$-PDW superconductivity driven by interband pairing.

Derived an effective hard-core Cooper pair Hamiltonian revealing a period-2 PDW state.

Found a checkerboard charge density wave at quarter-filling.

Abstract

Motivated by exploring superconductivity in multi-orbital systems, we study two orbital models of spinful fermions representing ($p_x,p_y$) or ($d_{xz}, d_{yz})$ orbitals on the square lattice. For minimal interorbital $t$-$J$ or $t$-$V$ on-site interactions, a random phase approximation uncovers regimes of instability towards incommensurate $d_{xy}$ pair density wave ($d$-PDW) superconductivity with driven by interband pairing. We study the competition of PDW order with uniform nodal $d_{xy}$ pairing states and magnetic and charge density wave (CDW) instabilities. At strong coupling, we derive an effective hard-core Cooper pair Hamiltonian which we study using a bosonic Gutzwiller ansatz to reveal a period-$2$ PDW over a wide range of fillings as well as a checkerboard CDW at quarter-filling. Our results apply to correlated multi-orbital materials with quasi-1D bands, Hubbard models on the square-octagon lattice, and atomic fermions in $p$-orbitals. Our work highlights the role of the orbital content and multiband Fermi surfaces in stabilizing interband PDW states.