Intrinsic band gap and electrically tunable flat bands in twisted double bilayer graphene

We present atomistic calculations on structural and electronic properties of twisted double bilayer graphene (TDBG) consisting of two sets of rotationally misaligned Bernal-stacked bilayer graphene. Obtained equilibrium atomic structures exhibit in-plane strains and the modulation of the interlayer distances at the rotationally mismatched interface layers. We find that the electronic structure of TDBG can have an intrinsic band gap at the charge neutral point for a large range of the twist angle θ. Near θ=1.25∘, the intrinsic band gap disappears and TDBG hosts flat bands at the Fermi level that are energetically well separated from higher and lower energy bands. We also show that the flat bands are easily tunable by applying vertical electric fields, and extremely narrow bandwidths less than 10 meV can be achieved for the electron-side flat bands in a wide range of the twist angle. Our results serve as a theoretical guide for exploring emergent correlated electron physics in this versatile moiré superlattice system.