---
author:
- 'Ken-ichi Sasaki'
title: |
    Layered Dynamical Conductivity for a Transfer Matrix Method\
    $-$Application to an ${\cal N}$-layer Graphene$-$
---

Introduction
============

The exfoliation of a single-layer graphene from graphite provided a great opportunity to explore the behavior of massless Dirac fermions. [@Novoselov2005; @zhang2005] The number of layers in graphite decreases by the mechanical cleavage method from a huge number to unity. [@Novoselov2005a] Considering the fact that graphite generally possesses massive Dirac fermions, there should be interesting physics, relevant to a change in the “mass” of Dirac fermions that is governed by the change in the layer number from $\infty$ to $1$. The “mass” is closely related to the stacking order and interlayer distance which are changed by thermal expansion caused by absorption of light. Therefore, it is meaningful to investigate the optical properties of an $N$-layer graphene as a function of $N$. The potential of graphene expands with just one additional layer, especially when thermal instability is introduced. This fact is evident from the appearance of many-body effects such as superconductivity and magnetism in a thermally unstable twisted bilayer which are unseen in a single layer. [@Cao2018; @Cao2018a]

We have two different approaches to calculating the optical 