Large graphene-induced shift of surface-plasmon resonances of gold films: Effective-medium theory for atomically thin materials

Md Kamrul Alam,Yanan Wang,Chong Dai,Xiaonan Shan,Jonathan Hu,Tian Tong,Chao Niu,Jiming Bao,Yandi Hu,Earl Charlson,Zhiming Wang,Zhaoping Liu,Xiang-Tian Kong,Yang Li,Steven Pei,Wei Wang,Gila Stein,Alexey Belyanin

doi:10.1103/physrevresearch.2.013008

Abstract

Despite successful modeling of graphene as a 0.34-nm thick optical film synthesized by exfoliation or chemical vapor deposition (CVD), graphene induced shift of surface plasmon resonance (SPR) of gold films has remained controversial. Here we report the resolution of this controversy by developing a clean CVD graphene transfer method and extending Maxwell-Garnet effective medium theory (EMT) to 2D materials. A SPR shift of 0.24 is obtained and it agrees well with 2D EMT in which wrinkled graphene is treated as a 3-nm graphene/air layered composite, in agreement with the average roughness measured by atomic force microscope. Because the anisotropic built-in boundary condition of 2D EMT is compatible with graphene's optical anisotropy, graphene can be modelled as a film thicker than 0.34-nm without changing its optical property; however, its actual roughness, i.e., effective thickness will significantly alter its response to strong out-of-plane fields, leading to a larger SPR shift.

Highlights

Maxwell-Garnett effective-medium theory (EMT) was developed more than 100 years ago to obtain the macroscopic dielectric property of an inhomogeneous medium [1,2]
A surface-plasmon resonance (SPR) shift of 0.24° is obtained and it agrees well with 2D EMT in which wrinkled graphene is treated as a 3-nm graphene/air layered composite, in agreement with the average roughness measured by atomic force microscopy
The original and revised mixing formulas have been proven to be powerful tools in accurately capturing the macroscopic electromagnetic responses of composite materials, and good agreements have been demonstrated between theory and experiment for many systems such as metal-ceramic films [6,16], polymer-ceramic composites [17], amorphous silicon thin films [18], polymer-single-walled carbon nanotube composite [8], and aligned carbon nanotube film [19,20]

Summary

INTRODUCTION

Maxwell-Garnett effective-medium theory (EMT) was developed more than 100 years ago to obtain the macroscopic dielectric property of an inhomogeneous medium [1,2]. The original and revised mixing formulas have been proven to be powerful tools in accurately capturing the macroscopic electromagnetic responses of composite materials, and good agreements have been demonstrated between theory and experiment for many systems such as metal-ceramic films [6,16], polymer-ceramic composites [17], amorphous silicon thin films [18], polymer-single-walled carbon nanotube composite [8], and aligned carbon nanotube film [19,20] All these studies only investigated one- or threedimensional (3D) structures in three-dimensional host media; EMT for two-dimensional (2D) layered structures have not been evaluated thoroughly the theory was developed long ago [21] and atomically thin 2D structures have become widely available. Its picture as a 0.34-nm film, no matter if it is exfoliated or grown by chemical vapor

Published by the American Physical Society

RESULTS AND DISCUSSION

CONCLUSIONS