Realization of Lieb Lattice in Covalent-organic Frameworks with Tunable Topology and Magnetism

TL;DR

This paper predicts that two recently synthesized covalent organic frameworks are the first real material realizations of Lieb lattices, exhibiting tunable electronic, topological, and magnetic properties through lattice distortion and doping.

Contribution

It demonstrates the first realization of Lieb lattices in organic materials and explores their tunable topological and magnetic properties via theoretical modeling.

Findings

Identification of sp2C-COF and sp2N-COF as Lieb lattices

Lattice distortion controls Dirac-flat band bandwidth and magnetic instability

Doping induces phase transitions from paramagnetic to ferromagnetic and antiferromagnetic states

Abstract

Lieb lattice, a two-dimensional edge-depleted square lattice, has been predicted to host various exotic electronic properties due to its unusual band structure, i.e., Dirac cone intersected by a flat band (Dirac-flat bands). Until now, although a few artificial Lieb lattices have been discovered in experiments, the realization of a Lieb lattice in a real material is still unachievable. In this article, based on tight-binding modeling and first-principles calculations, we predict that the two covalent organic frameworks (COFs), i.e., sp2C-COF and sp2N-COF, which have been synthesized in the recent experiments, are actually the first two material realizations of organic-ligand-based Lieb lattice. It is found that the lattice distortion can govern the bandwidth of the Dirac-flat bands and in turn determine its electronic instability against spontaneous spin-polarization during carrier doping. The spin-orbit coupling effects could drive these Dirac-flat bands in a distorted Lieb lattice presenting nontrivial topological properties, which depend on the position of Fermi level. Interestingly, as the hole doping concentration increases, the sp2C-COF can experience the phase transitions from a paramagnetic state to a ferromagnetic one and then to a N\'eel antiferromagnetic one. Our findings not only confirm the first material realization of Lieb lattice in COFs, but also offer a possible way to achieve tunable topology and magnetism in d- (f-) orbital-free organic lattices.