Differential equations for localized plasmons in the random phase approximation

被引：5
作者：
Ichikawa M. [1 ]
机构：
[1] Department of Applied Physics and, Quantum-Phase Electronics Center, Graduate School of Engineering, University of Tokyo, Bunkyo-ku, Tokyo
来源：
e-Journal of Surface Science and Nanotechnology | 2017年 / 15卷
关键词：
Metal nanostructures; Model calculations; Plasmon; Semi-empirical models;
D O I：
10.1380/ejssnt.2017.103
中图分类号：
学科分类号：
摘要：
Differential equations are derived for localized bulk and surface plasmons in metal nanostructures in the random phase approximation (RPA) at the high frequency condition. A differential equation for the scalar potential in the RPA gives a position-dependent Drude-like dielectric function. Using the dielectric function, a differential equation for the vector potential is derived in the Lorentz gauge. A corrected RPA differential equation for the scalar potential is then derived by using the differential equation for the vector potential and the Lorentz condition. The vector potential contribution to the electric field in the Lorentz gauge is found negligible compared with the scalar potential one in metal nanostructures. This indicates that the scalar potential plays important roles in analyzing the localized plasmons in metal nanostructures as reported previously. The corrected RPA differential equations are found equivalent to the Maxwell equations using the position-dependent Drude-like dielectric function. © 2017 The Surface Science Society of Japan.
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页码：103 / 107
页数：4
相关论文
共 32 条
[21]  
Yamamoto N., Araya K., Garcia De Abajo F.J., Phys. Rev. B, 64, (2001)
[22]  
Garcia De Abajo F.J., Rev. Mod. Phys., 82, (2010)
[23]  
Liu M., Guyot-Sionnest P., Lee T.-W., Gray S.K., Phys. Rev. B, 76, (2007)
[24]  
McMahon J.M., Gray S.K., Schatz G.C., Phys. Rev. Lett., 103, (2009)
[25]  
Ichikawa M., J. Phys. Soc. Jpn., 80, (2011)
[26]  
Ichikawa M., E-j. Surf. Sci. Nanotech., 12, (2014)
[27]  
Ichikawa M., E-j. Surf. Sci. Nanotech., 13, (2015)
[28]  
Pines D., Nozieres P., The Theory of Quantum Liquids, 1, (1966)
[29]  
Yee K.S., IEEE Trans. Antennas Propag., 14, (1966)
[30]  
Oubre C., Nordlander P., J. Phys. Chem. B, 108, (2004)
1234