Emergence of superconductivity in doped multiorbital Hubbard chains

Niravkumar D Patel,Nitin Kaushal,Alberto Nocera,Gonzalo Alvarez,Elbio Dagotto

doi:10.1038/s41535-020-0228-2

Abstract

We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.

Highlights

Quantum materials merge topological concepts[1], as in Haldane chains with non-local order parameters[2,3], with electronic correlation effects, as in iron-based superconductors with robust Hubbard U and Hund JH couplings[4,5,6]
We use a canonical two-orbital Hubbard model with kinetic energy and interaction terms written as H = HK + HI + HD
The hopping symmetry between the two orbitals, and the absence of crystal-field splitting, prevents the appearance of the orbital-selective Mott physics recently studied in related multiorbital models[52,53,54]

Summary

INTRODUCTION

Quantum materials merge topological concepts[1], as in Haldane chains with non-local order parameters[2,3], with electronic correlation effects, as in iron-based superconductors with robust Hubbard U and Hund JH couplings[4,5,6]. More recent efforts using multiorbital Hubbard models unveiled robust tendencies to spin-singlet pairing, an exciting result[45,46]. We lack a simple intuitive picture connecting the topological properties of Haldane chains and the emergence of hole pairs in Hubbard models Developing such a simple “cartoon” may allow generalizations to other systems and facilitate the experimental search for realizations in particular materials. Our results, and the hole binding found in multiorbital ladders[33], show that magnetic fluctuations induce pairing in repulsive Hubbard models In this framework, these efforts are as important as the theoretical studies of Cu ladders in the 1990s13,15: if pairing occurs convincingly in 1D systems, the same Hamiltonian may induce analogous tendencies in higher dimensions where many-body techniques are not as accurate

RESULTS

DISCUSSION

METHODS

CODE AVAILABILITY