Designing Flat Bands in TaS₂ Heterostructures: From T/H Bilayers to T/T/H Trilayers

Recent theory for 1T/1H-TaS₂ bilayer heterostructure shows that substantial charge transfer (~0.4-0.6 e per Star-of-David (SoD)) drives the 1T layer far from half-filling, placing the system in a doped-Mott rather than a heavy-fermion limit [1]. This motivates architectures that decouple Mottness from uncontrolled charge transfer. Building on this basis, we design a T/T/H trilayer where the T/T bilayer is a band insulator in which interlayer hybridization quenches local moments and yields a very flat valence band, while 1H remains a weakly spin-polarized metal [2]. Crucially, the SoD stacking in T/T (T_A/T_B/T_C) tunes flat-band filling and enables a crossover between doped-Mott and Kondo-like states. T_C stacking restores a half-filled Mott band, while T_A/T_B produce partially doped-Mott states, enabling direct control of (partially) occupied flat bands and their correlation strength. The T/T/H platform thus provides a clean route to engineer flat bands and modulate their filling without extrinsic disorder, establishing a tunable playground for Kondo screening, doped-Mott physics, and potentially unconventional superconductivity emerging from correlated flat bands coupled to a spin-polarized metal.