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本文运用紧束缚模型对介观尺寸原子链的等离激发进行了系统的研究, 通过量子响 应理论和相无规近似得到了等离激元的本征频率方程, 通过该方程计算了系统中等离子体的激发能量, 并分别对体系的本征振荡以及外电场作用在原子链上发生共振的情况进行了研究. 结果表明, 体系在外场作用下发生共振时, 偶极矩的峰值与等离子体的激发态相对应, 说明外场此时激发了等离激元; 体系处在共振情况下, 电荷振荡的幅度远远大于非共振的情况, 相对来说体系的电荷虚部的共振更为明显. 对于体系的本征等离振荡频率, 同等长度时等离子体的激发能量总是大于同级的单电子激发能量; 等离激元的能谱与原子链的长度和电子密度以及系统的库仑关联强度都有很大关系; 在原子链长度保持不变的情况下, 等离子体的激发能量随电子数目的变化以半满为中心呈对称关系.Plasmonic excitations in mesoscopic-sized atomic chains are investigated by employing the tight-binding model. Based on the quantum response theory and random phase approximation, a plasma oscillation eigen-frequency equation is derived for calculation of the plasmon energy spectrum. The plasmon energy spectrum has been numerically calculated, and the eigen-oscillation of the system and the resonance behavior under the external electric field applied on the atom chain are investigated, respectively. Dependence of plasmonic excitation energy on the length of systems and electron density has been discussed. Results suggest that in the case of resonance, the resonant peak of dipole moment is corresponding to the plasmonic excitation, and this indicates that the external electric field excites the plasmon of the system. In resonance the oscillation amplitude of the charge is much larger than that in the case of non-resonance, especially the imaginary part of the charge has a more obvious enhancement. For the eigen-oscillations, the plasmonic excitation energy is greater than the single-particle excitation state at the same level; the length of atomic chains, the electron density, and the strength of Coulomb correlation have significant effects on the plasmon spectroscopy. For the given atom-chain length, with variation of number of electrons, the plasmonic excitation energy varies symmetrically around the half-filling. This indicates that the plasmon spectrum of the system is symmetrical for the electrons and holes.
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Keywords:
- nanostructure /
- one-dimensional atomic chains /
- plasmon
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[2] Xu H X, Bjerneld E J, Käll M, Börjesson L 1999 Phys. Rev. Lett. 83 4357
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[12] Wang R Z, Li P F, Yan X H 2002 Acta Phys. Sin. 51 2139 (in Chinese) [王如志, 李鹏飞, 颜晓红 2002 物理学报 51 2139]
[13] Chen Y, Yu L P, Zhu Z Y 2002 Acta Phys. Sin. 51 1571 (in Chinese) [陈一, 余礼平, 朱志远 2002 物理学报 51 1571]
[14] Fang N, Lee H, Sun C, Zhang X 2005 Science 308 534
[15] Bell A T. 2003 Science 299 1688
[16] Hirsch L R, Stafford R J, Bankson J A, Sershen S R, Rivera B, Price R E, Hazle J D, Halas N J, West J L 2003 Proc. Natl. Acad. Sci. U.S.A. 100 13549
[17] Nordlander P, Halas N J 2010 Phys. Chem. C 114 7378
[18] Muniz R A, Haas S 2009 Phys. Rev. B 80 045413
[19] Cassidy A, Grigorenko I, Haas S 2008 Phys Rev. B 77 245404
[20] Xu H X, Käll M 2002 Phys. Rev. Lett. 89 246802
[21] Yan J, Gao S W 2008 Phys. Rev. B 78 235413
[22] Yan J, Yuan Z, Gao S W 2007 Phys. Rev. Lett. 98 216602
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[1] Nie S, Emory S R 1997 Science 257 1102
[2] Xu H X, Bjerneld E J, Käll M, Börjesson L 1999 Phys. Rev. Lett. 83 4357
[3] Zhang X F, Yan X 2013 Acta Phys. Sin. 62 037805 (in Chinese) [张兴坊, 闫昕 2013 物理学报 62 037805]
[4] Han Q Y, Tang J C, Zhang C, Wang C, Ma H Q, Yu L, Jiao R Z 2012 Acta Phys. Sin. 61 135202 (in Chinese) [韩清瑶, 汤俊超, 张弨, 王川, 马海强, 于丽, 焦荣珍 2012 物理学报 61 135202]
[5] Sun Y, Xia Y 2002 Science 298 2176
[6] Sönnichsen C, Franzl T, Wilk T, Plessen G V, Feldmann J, Wilson O, Mulvaney P 2002 Phys. Rev. Lett. 88 077402
[7] Cong C, Wu D J, Liu X J, Li B 2012 Acta Phys. Sin. 61 037301 (in Chinese) [丛超, 吴大建, 刘晓峻, 李勃 2012 物理学报 61 037301]
[8] Hervieux P A, Bigot J Y 2004 Phys. Rev. Lett. 92 197402
[9] Barnes W L, Dereux A, Ebbesen T W 2003 Nature(London) 424 824
[10] Pendry J B, Martin-Moreno L, Garcia-Vidia F J 2004 Science 305 847
[11] Yao H M, Chen X N, Chen X Z 2005 Acta Phys. Sin. 54 2645 (in Chinese) [姚汉民, 陈旭南, 陈献忠 2005 物理学报 54 2645]
[12] Wang R Z, Li P F, Yan X H 2002 Acta Phys. Sin. 51 2139 (in Chinese) [王如志, 李鹏飞, 颜晓红 2002 物理学报 51 2139]
[13] Chen Y, Yu L P, Zhu Z Y 2002 Acta Phys. Sin. 51 1571 (in Chinese) [陈一, 余礼平, 朱志远 2002 物理学报 51 1571]
[14] Fang N, Lee H, Sun C, Zhang X 2005 Science 308 534
[15] Bell A T. 2003 Science 299 1688
[16] Hirsch L R, Stafford R J, Bankson J A, Sershen S R, Rivera B, Price R E, Hazle J D, Halas N J, West J L 2003 Proc. Natl. Acad. Sci. U.S.A. 100 13549
[17] Nordlander P, Halas N J 2010 Phys. Chem. C 114 7378
[18] Muniz R A, Haas S 2009 Phys. Rev. B 80 045413
[19] Cassidy A, Grigorenko I, Haas S 2008 Phys Rev. B 77 245404
[20] Xu H X, Käll M 2002 Phys. Rev. Lett. 89 246802
[21] Yan J, Gao S W 2008 Phys. Rev. B 78 235413
[22] Yan J, Yuan Z, Gao S W 2007 Phys. Rev. Lett. 98 216602
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