Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

Swagatam Nayak,Sanjeev Kumar,Navketan Batra

doi:10.1038/s41598-021-02175-5

Abstract

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

Highlights

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders
The general consensus about the novel high Tc cuprate superconductors is that they are identified as strong candidates for unconventional d-wave superconductors[9,10,11], which support the formation of spin-singlet Cooper pairs with an anisotropic d-wave orbital order parameter (OP) symmetry
The Hamiltonian corresponding to the Extended Attractive Hubbard Model on a two-dimensional square lattice can be written as, H = Hkin + Hμ + Hionntsite + Hinnnt + HB, (1)

Summary

Introduction

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. The general consensus about the novel high Tc cuprate superconductors is that they are identified as strong candidates for unconventional d-wave superconductors[9,10,11], which support the formation of spin-singlet Cooper pairs with an anisotropic d-wave orbital OP symmetry. A pair of Majorana fermions, bound to topological defects, together known as Ising anyons, exhibit non-Abelian exchange statistics and such an object can be considered to be the potential building block for decoherence free quantum computation[17] Regardless of their technological relevance, superconductors with triplet-superconductivity emerging due to the intrinsic properties of the material itself are quite rare in nature. The effect of an in-plane magnetic field has been studied in various contexts, including quasi-2D systems like cuprates, emergence of a dissipative state in a superconducting Mo0.79Ge0.21 nanostrip, anisotropy of the upper critical field in Sr2RuO4 , and magnetic field driven nodal topological superconductivity in monolayer transition metal dichalcogenides[49,50]

Methods

Results

Conclusion