Dual Yin-Yang Flat Bands: Construction and Excitonic Insulator State

In this talk, I will introduce a new type interesting band structure in 2D materials, consisting of a flat valence band and a flat conduction band around the Fermi level, named yin-yang flat bands characterized with opposite chirality (Chern number). I will first discuss the construction of the yin-yang flat bands based on line graph theorem and its extension to multiple atoms and orbitals per lattice site in 2D tight-binding lattice models. I will then present one exotic quantum phase, the excitonic insulator (EI) state that the yin-yang flat bands may host (1). The EI is a strongly correlated many-body ground state, arising from an instability in the band structure toward exciton formation. We show that the flat valence and conduction bands of a semiconducting diatomic Kagome lattice, as exemplified in a superatomic graphene lattice, can conspire to enable a triplet EI state, based on density-functional theory calculations combined with many-body GW and Bethe-Salpeter equation. Our results indicate that massive carriers in flat bands with highly localized electron and hole wave functions significantly reduce the screening and enhance the exchange interaction, leading to an unusually large triplet exciton binding energy (∼1.1 eV) exceeding the GW band gap by ∼0.2 eV and a large singlet-triplet splitting of ∼0.4 eV. I will end the talk discussing on-going studies and future directions to explore other possible exotic many-body quantum states associated with the yin-yang flat bands, such as excitonic spin-1 superfluid. [(1). G. Sethi, et. al., Phys. Rev. Lett. 126, 196403 (2021)]