After the fabrication of the graphene sheet at the beginning of this century, multilayer thin films are attracting huge attention. Since we can control the property by stacking and deforming the layers, these systems are regarded as a new platform for material design. 

In contrast to the interest, these systems lack periodicity in general. As solid state physics today relies heavily on translational symmetry, this hinders us from using the conventional picture in the wave number space and makes the theoretical analysis difficult. However, in the multilayer system, we can also use the wave number space as an approximation. When we stack layers, the layers are coupled through the Van der Waals interaction. As this interaction is very weak and we can treat it as a perturbation for the periodic systems. Through this approximation, we can construct a moiré Hamiltonian and use the wave number space.
 In this talk, I begin with a review of the moiré Hamiltonian approach, and after that, explain the analysis of the second-order optical response[1-2].

[1] T. Akamatsu, T. Ideue, S. Kitamura, M. Yoshii, T. Morimoto, Y. Iwasa, et al., Science, 372, 6537, pp. 68-72 (2021)