Universal layer number in graphite

K Sasaki,K Hitachi

doi:10.1038/s42005-020-0354-y

Abstract

Graphene absorbs light in accordance with the fine-structure constant α ≃ 1/137. The α value is universal in the sense that it is unrelated to material parameters but solely related to the elementary charge, which is a fundamental constant governing the coupling of light and matter. A new universality governed only by α has yet to be discovered in graphene optics. However, since α is a dimensionless quantity, it can be anticipated that the reciprocal of α appears as a characteristic number of layers in the light absorptance of an N-layer graphene. Here, we report that this number is 2/πα. We show simultaneously that for light in the infrared to visible range, an N-layer graphene with N above 1500 may be regarded as graphite. This also enables us to obtain the simplest expression for the optical constants of graphite, which is written in terms of α and interlayer distance only.

Highlights

Graphene absorbs light in accordance with the fine-structure constant α ≃ 1/137
Layer graphene with N above 1500 may be regarded as graphite, on the basis of a convergence criterion. This enables us to obtain the simplest expression for the optical constants of graphite, which is written in terms of α and interlayer distance only[5]
The solid curves are obtained by the transfer matrix method for different wavelengths, while the dashed curve at the top is from a simpler model that neglects the reflection

Summary

Introduction

Graphene absorbs light in accordance with the fine-structure constant α ≃ 1/137. We show simultaneously that for light in the infrared to visible range, an N-layer graphene with N above 1500 may be regarded as graphite. This enables us to obtain the simplest expression for the optical constants of graphite, which is written in terms of α and interlayer distance only. It is widely recognized that because of the conical band structure unique to massless Dirac fermions, graphene absorbs light in accordance with the fine-structure constant[2,4,5]. We show the universal layer number in graphite to be 2/πα. By employing the transfer matrix method, we show simultaneously that for light in the infrared to visible range, an N-

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