  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 theta. Near theta = 1.25
degree, 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 moire superlattice system.
