Topological properties of the Lieb lattice, i.e., the edge-centered square lattice, have been extensively studied and are, however, mostly based on theoretical models without identifying real material systems. Here, based on tight-binding and first-principles calculations, we demonstrate the Lieb-lattice features of the experimentally synthesized phthalocyanine-based metal-organic framework (MPc-MOF), which holds various intriguing topological phase transitions through band engineering. First, we show that the MPc-MOFs indeed have a peculiar Lieb band structure with 1/3 filling, which has been overlooked because of its unconventional band structure deviating from the ideal Lieb band. The intrinsic MPc-MOF presents a trivial insulating state, with its gap size determined by the on-site energy difference (Δ E) between the corner and edge-center sites. Through either chemical substitution or physical strain engineering, one can tune Δ E to close the gap and achieve a topological phase transition. Specifically, upon closing the gap, topological semimetallic/insulating states emerge from nonmagnetic MPc-MOFs, while magnetic semimetal/Chern insulator states arise from magnetic MPc-MOFs, respectively. Our discovery greatly enriches our understanding of the Lieb lattice and provides a guideline for experimental observation of the Lieb-lattice-based topological states.
Bibliographical noteFunding Information:
This project is partly supported by U.S. DOE-BES (Grant DE-FG02-04ER46148). W.J. and T.L. acknowledge the support from SMART, one of seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by National Institute of Standards and Technology (NIST). S.Z. acknowledges the support from NSFC under Grant 11774196. Z.W. acknowledges the support from NSFC (Grants 11774325 and 21603210), National Key Research and Development Program of China (Grant 2017YFA0204904), and Fundamental Research Funds for the Central Universities. Computations of this work were supported by MSI of University of Minnesota and CHPC at University of Utah.
Copyright © 2020 American Chemical Society.
- Lieb lattice
- electronic topology
- first-principles calculations
- metal-organic framework
PubMed: MeSH publication types
- Journal Article