Flatbands in frustrated lattice X3MnN3 (X = Ca, Sr, Ba): A first-principles study

Frustrated lattices with dispersionless band structures and fully localized states are an exciting platform for exploring many-body physics. In this work, we identify X3MnN3 (X= Ca, Sr, Ba) as a frustrated lattice and investigate its physical properties in the ferromagnetic (FM) and antiferromagnetic (AFM) states based on first-principles calculations. Our results show that all three materials in FM and A-type AFM configurations have flatbands with band touching in the kz∼0 and kz∼π planes with bandwidths less than 0.2 eV. Intriguingly, the flatband is tuned to the Fermi level when X3MnN3 is transformed into the FM state. Furthermore, we find the two-dimensional dice model hidden in X3MnN3 by treating the coupled Mn and N atoms as a basic site, revealing that the compact localized state is generated by destructive interferences between the hopping amplitudes, and the dice models stack the system staggered along the c-axis. Our work provides new candidate materials for exploring strong correlation physics and reveals the mechanism of their localized state.