From chiral d-wave to nodal line superconductivity in the harmonic honeycomb lattices

TL;DR

This paper explores the evolution of superconducting states in harmonic honeycomb lattices, revealing a transition from chiral d-wave to nodal line states influenced by lattice geometry and symmetry, with implications for topological properties.

Contribution

It provides a comprehensive analysis of superconducting states across harmonic honeycomb lattices, identifying how lattice geometry and symmetry determine the nature of the superconducting phase.

Findings

Chiral d±id state appears in large lattices at certain doping levels.

Nodal lines emerge in the superconducting gap at intermediate doping.

Symmetry analysis shows many states belong to trivial irreducible representations.

Abstract

Motivated by the recent realization of the three-dimensional hyperhoneycomb and stripyhoneycomb lattices in lithium iridate (Li$_2$IrO$_3$), we study the possible spin-singlet superconducting states on the whole series of harmonic honeycomb lattices. Beginning with an isolated out-of-plane twist making the honeycomb lattice three-dimensional, we find that the chiral d$\pm$id state, well-known from the honeycomb lattice, is realized in the largest members of the series at low to intermediate doping. Along the twist, four chiral edge states form a two-dimensional dispersive band. Reducing the distance between the twists to form the smaller members of the harmonic honeycomb lattices, the degeneracy between the d-wave states is lifted, which finally destroys the chiral state. By analyzing the hyper- and stripyhoneycomb lattices and generalizing using the $D_{2h}$ point group of all the harmonic honeycomb lattices, we show that the superconducting state often belongs to the trivial irreducible representation. This state has nodal lines at low to intermediate doping, which is possible because the full lattice symmetry allows sign changes between different sets of bonds. We also find time-reversal symmetry broken states, which are either fully gapped or feature nodal points, in certain parts of the phase diagram. Finally, we draw a comparison between the states classified in terms of the $D_{2h}$ symmetries and those observed on the $D_{6h}$ honeycomb lattice.