Optical properties of 30 degree twisted bilayer graphene quasicrystal

We propose a theoretical approach to calculate the optical response function in non-periodic twisted bilayer graphene systems. It is well known that a twist bilayer with low twist angle can be approximately treated as a periodic Bloch system with a moire superlattice period. When arbitrary 2D materials are overlaid with an arbitrary rotation angle, however,

there are generally no noticeable effective periods and the system becomes truly quasiperiodic.

A typical example of this is a 30-degree twisted bilayer graphene, where the electronic structure exhibits a quasi-periodic pattern with 12-fold rotational symmetry. It is generally difficult to calculate the physical quantities in such systems

because the Bloch theory is not applicable.

In this work, we proprose a theoretical framework to calculate response function for general twisted bilayer quasicrystals.

We first construct the Hamiltonian in k-space bases with a certain cut-off and calculate the quasi-band structure. The velocity operator can be computed by differentiating the Hamiltonian in k, and the optical absorption spectrum (dynamic conductivity) is obtained just as in the usual Bloch system.