Electronic structure of biased alternating-twist multilayer graphene

TL;DR

This paper provides an analytical and numerical study of the electronic and optical properties of biased alternating-twist multilayer graphene, revealing tunable spectra and Dirac cone modifications under electric fields.

Contribution

It introduces a general analytical framework for the low-energy Hamiltonian of ATMG with arbitrary layers under bias, validated against numerical results for twist angles above 2.2°.

Findings

Optical spectrum is tunable by interlayer bias.

Dirac cones acquire different Fermi velocities under bias.

Optical conductivity shows step-like features due to cone splitting.

Abstract

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