Electronic structure of biased alternating-twist multilayer graphene

We theoretically study the energy and optical absorption spectra of alternating twist multilayer graphene (ATMG) under a perpendicular electric field. obtain analytically low-energy effective Hamiltonian ATMG up to pentalayer in presence interlayer bias by means first-order degenerate-state perturbation theory, present general rules for constructing an arbitrary number layers. Our analytical results agree excellent degree accuracy with numerical calculations angles $\theta \gtrsim 2.2^{\circ}$ that are larger than typical range magic angles. also calculate conductivity determine its characteristic spectrum, which is tunable bias. When potential difference applied between consecutive layers ATMG, Dirac cones at two moir\'{e} Brillouin zone corners $\bar{K}$ $\bar{K}'$ acquire different Fermi velocities, generally smaller monolayer graphene, split proportionally resulting step-like feature conductivity.