Metal-organic frameworks: Strain-tunable quantum phase transition and high-order topological insulator and emergent fermions

The exploration of topological quantum phases and their transitions has become a focus of intense research. In this paper, we introduce a family of two-dimensional (2D) metal-organic frameworks (MOFs) that host various emergent 2D fermions and second-order topological insulators (SOTIs) while also exhibiting strain-tunable quantum phase transitions. Using first-principles calculations, we demonstrate that these MOFs can exhibit either a narrow-band-gap semiconductor or a zero-band-gap semimetal state, with three key bands in the low-energy region. Importantly, we find that applying biaxial strain can induce a semiconductor-to-semimetal quantum phase transition or vice versa. We further reveal that the semiconductor phase may possess nontrivial properties, including corner states, indicative of a second-order topological phase. At the critical strain point, a 2D triple point emerges, which transitions into a double-Weyl-fermion state under additional strain. We also construct effective models to describe these emergent 2D fermions. Our findings highlight the potential of MOFs as a versatile platform for studying quantum phases, emergent fermions, and SOTIs, paving the way for future applications in quantum materials and nanoscale technologies. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Density of statesEdge statesElectrical propertiesElectronic structureFlat bandsMagnetismSpin-orbit coupling