钠纳米球量子流体动力学仿真方法的能量泛函研究  

Energy functional study of quantum hydrodynamics theory method for sodium nanosphere

作　　者：胡奇宏 杨红[1] 黄勇刚[1] HU Qihong;YANG Hong;HUANG Yonggang(College of Physics and Mechanical&Electrical Engineering,Jishou University,Jishou 416000,China)

机构地区：[1]吉首大学物理与机电工程学院,湖南吉首416000

出　　处：《湘潭大学学报（自然科学版）》2023年第2期48-55,共8页Journal of Xiangtan University(Natural Science Edition)

基　　金：国家自然科学基金(11964010,11464013,11464014);湖南省自然科学基金(2020JJ4495);湖南省教育厅科研基金(21A0333);湖南省研究生创新基金(CX20211038,CX2018B706);吉首大学校级自然科学类科研项目(Jdy20029)。

摘　　要：金属微纳结构的表面等离激元能将电磁场局域在纳米尺度,在增强光与物质相互作用以及设计亚波长集成光学器件等方面具有重要的作用.随着金属纳米结构尺寸的减小,非局域和电子溢出等量子效应凸显,经典局域响应模型逐渐失效,而全量子的含时密度泛函(time-dependent density functional,TDDFT)方法只能处理超小体系,自洽量子流体动力学理论(self consistent quantum hydrodynamics theory,SCQHT)是计算介观尺度金属纳米结构表面等离激元共振的有效手段.SCQHT中,能量泛函至关重要,也是其区别TDDFT方法的重要方面.然而,von Weizs cker(vW)动能泛函的比重悬而未决,此外,局域和非局域交换关联泛函均被广泛采用,但其对表面等离激元偶极共振有何影响尚不明确.该文以钠纳米球为研究对象,以TDDFT偶极共振频率为参照,证明了局域和非局域交换关联泛函对偶极共振频率影响不大,最大仅有0.1 eV.在局域和非局域交换关联泛函下,vW动能泛函的比重分别为0.25和0.22.对不同尺寸纳米球的偶极共振能量,两种SCQHT的平均误差分别为10.2 meV和7.7 meV.这些结果为高效准确仿真表面等离激元提供了重要的理论方法.Plasmonic in metal micro-nano structures can localize electromagnetic fields at the nanometer scale,and play an important role in enhancing the light-matter interaction and designing subwavelength integrated optical devices.With the reduction of the size of metal nanostructures,quantum effects of nonlocality and spill-out become prominent,and the classical local response model breaks down,while the all-quantum time-dependent density functional(TDDFT)can only deal with ultra-small systems.The self consistent quantum hydrodynamics theory(SCQHT)is an effective method to calculate the plasmonic resonance of mesoscale nanostructures.In SCQHT,the energy functional is of vital important,and it is also a distinctive part from TDDFT.However,the fraction of the vW contribution is not well defined.Furthermore,its effect on surface plasmon dipole resonances is unclear,though both local and non-local exchange-correlation functionals are widely used.In this paper,Na nanospheres are taken as the research object,and the TDDFT dipole resonance frequency is used as a reference.It is numerically proved that the local and non-local exchange-correlation functionals have limited effect on the dipole resonance frequency,in whose maximum is only 0.1 eV.Under the local and non-local exchange-correlation functional,the fraction of the vW is 0.25 and 0.22,respectively.The relative error of LDA and NLDA self-consistent SCQHT for the dipole resonance energies of nanospheres of different sizes is 10.2 meV and 7.7 meV,respectively.These results provide an important theoretical approach for efficient and accurate simulation of surface plasmons.

关 键 词：自洽量子流体动力学 表面等离激元 能量泛函 长程相互作用 

分 类 号：O414.1[理学—理论物理]