jun yan, zhe yuan and shiwu gao- end and central plasmon resonances in linear atomic chains

8/3/2019 Jun Yan, Zhe Yuan and Shiwu Gao- End and Central Plasmon Resonances in Linear Atomic Chains

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End and Central Plasmon Resonances in Linear Atomic Chains

Jun Yan,1,2 Zhe Yuan,3,1 and Shiwu Gao1,2,*1Institute of Physics, Chinese Academy of Sciences, 100080 Beijing, China

2Department of Physics, Goteborg University, SE-41296, Goteborg, Sweden3 Department of Applied Physics, Chalmers University of Technology, SE-41296, Goteborg, Sweden(Received 28 January 2007; revised manuscript received 17 April 2007; published 25 May 2007)

The existence and nature of end and central plasmon resonances in a linear atomic chain, the 1D analogto surface and bulk plasmons in 2D metals, has been predicted by ab initio time-dependent densityfunctional theory. Length dependence of the absorption spectra shows the emergence and development ofcollectivity of these resonances. It converges to a single resonance in the longitudinal mode, and twotransverse resonances, which are localized at the ends and center of the atom chains. These collectivemodes bridge the gaps, in concept and scale, between the collective excitation of atomic physics andnanoplasmonics. It also outlines a route to atomic-scale engineering of collective excitations.

DOI: 10.1103/PhysRevLett.98.216602 PACS numbers: 72.15.Nj, 71.45.Gm, 73.20.Mf

Collective electron oscillations in nanostructures formlocalized surface plasmon resonances (LSPR) [17],which exhibit unusual properties in energy, lifetime, opti-

cal spectroscopy, and short-time dynamics. Such propertiesof LSPRs, which are tunable by the shapes and sizes of thestructures, are promising for applications in sensing andspectroscopy [1,2], catalytic reactions [8], and biomedicaltreatment [9]. The quest for new nanostructures of desiredpurpose and function has been a major ongoing effort innanoplasmonics and condensed matter physics [10 12].Various structures with different shapes have been fabri-cated using electron beam and colloidal lithography [13].The minimal dimension reachable by lithography has sofar been limited by a few tens nanometers. The plasmonexcitations in this regime (101000 nm) can be qualita-tively understood by electrodynamic models like the Mie

theory [14].This letter draws attention to collective excitations of a

different class of structures, artificial atomic structuresassembled with a scanning tunneling microscope (STM).Prototype structures of this kind include, for example,linear atomic chains [15,16], quantum corrals [17], andartificial molecular structures [18]. Different from thenanostructures created by lithography and self-assembly,the sizes and shapes of such artificial structures are tunabledown to the precision of a single atom. Collectivity ofelectron oscillations at such scales is a fundamental subjectof its own interest [19]. It should be strongly influenced bytwo competing factors: the local atomic confinement andglobal quantization imposed by the geometric boundary ofthe systems. The aim of the present study was to find outwhether and how collective plasmon excitation are deter-mined by the structural tunability at atomic scale.

As both a conceptual model and a concise numericalstudy, we have calculated the plasmon excitation of a linearatomic chain of sodium atoms, which can be assembledatom by atom with an STM [16]. Using an ab initio de-scription of the valence electrons, the optical spectra are

calculated by time-dependent density functional theory(TDDFT). The evolution of absorption spectra, as the chainlength was varied, clearly demonstrates the integration of

its oscillator strength, which starts from two atoms andaccumulates atom by atom. These collective oscillationsconverge into a single plasmon resonance in the longitudi-nal mode but splits into two separate transverse modes, onelocated at the ends (the end or surface plasmon) and theother in the center of the chain (the central or bulkplasmon). In addition, the frequency and polarization ofthese resonances can be manipulated by attaching a singleatom or molecule at different registry to the chains. Theseatomic plasmons naturally complement and bridge thegaps, in concept and size, between the nanoplasmonics(101000 nm) and collective excitation in atomic (a fewA) and nuclear (a few fermis) systems [20]. They have also

general implications in atomic-scale engineering and ma-nipulations of optical properties atom by atom.

All of our calculations have been done by a real-spaceand real-time TDDFT code, OCTOPUS [21], which treats theNa atoms using norm-conserving pseudopotentials. Local-density approximation (LDA) for the exchange-correlationis used in both the ground state and excited state calcula-tions. The simulation zone is defined by assigning a spherearound each atom with a radius of 6 A and a uniform meshgrid of 0.3 A. The absorption spectra were obtained by twoapproaches: 1) real-time propagation of electron wavepacket [22] under an impulse excitation, and 2) linear-response formalism in frequency domain developed byCasida [23]. In the real-time propagation, the electronicwave packets were evolved for typically 10 000 steps witha time step of 0.003 fs. Excitation spectrum is extracted byFourier transform of the dipole strength. Such a scheme isextensively tested on several well-studied examples, onwhich reliable absorption spectra have been reproduced.Linear-response calculation in the frequency domain givesessentially the same excitation spectra for all the chains wecalculated. Here we demonstrate our results with chains

PRL 98, 216602 (2007)P H Y S I C A L R E V I E W L E T T E R S week ending

25 MAY 2007

0031-9007=07=98(21)=216602(4) 216602-1 2007 The American Physical Society
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built from simple metal atoms like Na, calculations forsilver atoms (with d electrons) have also been performed,which shows qualitatively similar results.

Figure 1 shows the evolution of dipole strength as afunction of the chain length, which is measured by thenumber of atoms Na. The left (a) and right panels (b)correspond to longitudinal (L) and transverse (T) polar-izations of dipole excitations, respectively. For a single Na

atom (the bottom curve), only one peak at 2.37 eVappears.It is comparable to 2.10 eV in literature [24,25]. It consistsof predominantly the 3s! 3p transition. For the Na dimer,the interatomic distance is taken to be 2.89 A, chosen fromthe experimental configuration of atom chains on theNiAl(110) surface [16]. The dipole excitation (the secondcurve from the bottom) splits into two peaks, a longitudinalmode (the L mode) at 2.20 eV and a transverse one (the Tmode) at 2.92 eV with comparable strength. These energiesare again comparable to absorption peaks 2.092.63 eV[24,25] documented in the literature. The minor offset inenergies can be attributed to the difference in the inter-atomic distances used in the calculations.

As more atoms are added to the chain, different evolu-tions were observed for the L and Tmodes. Starting fromNa3, the L mode, panel (a), redshifts in energy and itsintensity increases linearly with the chain length. Thelinear increase in intensity results from the accumulationof collectivity in the dipole oscillation, as found in aprevious model using a confined quasi-one-dimensionalelectron gas (CQ1DEG) [26]. The redshift of the resonancefrequency at increased chain length can be understood bythe reduction of the energy gaps involved in the dipoleexcitation. Similar redshift was found in the CQ1DEG[26]. The self-consistent calculation in this study yieldsmore reliable excitation energies and oscillator strengths.

In particular, the f-sum rule, which was not strictly sat-isfied in the CQ1DEG, is now fulfilled at all lengths. Apartfrom the lowest dipole mode, multiple excitations (n 2and 3) of the L mode are also discernible in longer chains,which was not found in CQ1DEG. In the rest of this Letter,we will focus on theTmode, which was not studied before.

The evolution of the Tmodes, panel (b), differs drasti-cally from that of the L mode. The transverse peak of the

dimer at 2.92 eV is blueshifted and splits into two branchesat Na3 with a low-energy resonance at 3.11 eV and a high-energy band at 4.44 eV. These two peaks gain intensity andbecome more prominent as the length increases. Figure 2shows the length dependence of energies (a) and oscillatorstrength (b) of the transverse dipole modes. For chainsshorter than 5 atoms, the transverse modes are dominatedby the low-energy resonance, !TE. From Na5, the high-energy branch increases in intensity and forms a well-defined resonance, !TC, which is separated from !TE bya finite gap. It suggests that the two modes are nondegen-erate in energy and character. In longer chains, the strengthof the !TC mode increases almost linearly with the length.

In contrast, the intensity of the !TE mode becomes satu-rated with an integral oscillator strength of about 4 elec-trons. The strength of the two Tmodes indicates that both

0 1 2 3 4

0

20

40

60

80

L

T

Na=18

Na=10

Na

= 4

Na= 1

TE

TCL

(a) (b)

Energy (eV)

Strength(1/eV)

FIG. 1 (color online). The dipole response (optical absorption)of a linear sodium chain, with variable number of atoms Na, toan impulse excitation, resulting in a momentum change k 1=0:05 A), polarized in the longitudinal (a) and transversedirection (b). The series of spectra corresponds, counting fromthe bottom, to Na 1, 2, 3, 4, 6, 8, 10, 14, and 18.

0 4 8 12 16 200

20

(b)

Na

L TC

TE

0

2

4

L

TC

Strength

(1/eV)

Energy(eV)

(a)

TE

FIG. 2. The excitation energy (a) and the dipole strength (b) asa function of the number of atoms Na for the three resonancepeaks shown in Fig. 1. They can be assigned to the longitudinal(!L) and transverse plasmon modes (!TC and !TE), as discussedin the text.


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are collective in character. Although there is no measure-ment available for these collective resonances in atomicchains, qualitative length dependence (the blueshift andenhancement) were indeed observed in nanoparticle arrays[27,28]. In the experiment, it was however impossible toidentify the number of the T modes due to the energyresolution and the small number of particles (up to 7)assembled in the experiment.

To elucidate the nature of the T modes, the inducedcharge response has been analyzed in real-time propaga-tion. Figure 3 shows the Fourier transform of the induceddensity, obtained from time-evolution, in a plane crossingthe chains at the plasmon frequencies for Na 3 (row a), 8(row b), and 18 (row c), respectively. The density profilesfor both modes are dipole like in character and differ intheir spatial distributions. The !TE mode is localized at thetwo ends, while !TC is distributed in the center of thechains. This difference is already discernible, despitestrong mixing, for short chains as Na 3 (row a), becomesclearer at Na 8 (b), and is completely separated in Na 18 (c). This charge distribution is consistent with the

energy and strength of the two modes shown in Fig. 2,where the strength of!TC starts to increase linearly in thelong chain limit. It is interesting to note that the chargeoscillation of the central mode has nearly vanishing am-

plitudes on the 6 atoms at the two ends. For the !TE mode,the intensity and charge distribution does not change sig-nificantly for chains longer than 8 atoms, and are com-pletely localized on the 6 end atoms (3 on each side). Sucha spatial separation in the transverse excitation between!TE and !TC resembles the density distribution of thesurface and bulk plasmons of solids and thin films: wherethe surface (end) plasmons are lower in energy than the

bulk (central) plasmon. The induced charge oscillations arelocalized at the surfaces (the interior region) of the solids.

The existence and nature of two transverse plasmonresonances has in general two different origins: (i) thevariation of electron potential on different atoms alongthe chains, which is mainly responsible for the energysplitting; and (ii) the bonding and interaction betweenelectrons residing on different atoms. The latter wouldmainly determine the collectivity and strength of the endmode. In order to further differentiate these two effects,extensive calculations have been done for sodium chainswith variable interatomic distances by elongating or con-tracting the distances for up to 1 A. In the range of

distances calculated, the strength of the end mode wasfound to change only slightly (by less than 10%).Calculations for other atomic chains like Ag and K havealso been performed, which verified the general existenceof the end and central modes. The strength of the end mode

-0.01

0.01

-0.002

0.002

-0.01

0.01

(c)

(b)

-0.01

0.01

(a)

-0.01

0.01

TCTE

-0.01

0.01

FIG. 3 (color online). Fourier transform of the induced densityfor Na 3 (a), Na 8 (b), and Na 18 (c) at the two trans-verse plasmon resonances !TE (the middle column) and !TC(the right column). The black squares specify the position of theatoms. The small panels to the left show the ground state electrondensity.

2 3 4 50

10

20

Na8

Ag-Na8

(c)

Strength(1/eV)

Energy (eV)

(a)

(b)

-0.012

0.012

-0.003

0.003

FIG. 4 (color online). (a) The dipole strength of the Na8 atomchain (black curve) modified by attaching a single silver atom atone end, forming an Ag-Na8 chain (red curve). The end modereduces in its intensity (b), and splits into a high-energy mode atthe Ag side (c).


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was found to depend more sensitively on the atomic spe-cies, with about 6 electrons for Ag chains, and 2 for K. Thistrend in the strength of the end mode is in line with thebonding order (interaction) among the three elements, withAg> Na>K, which is justifiable both in the chains and intheir solids. Stronger electronic coupling favors largerstrength in the end mode.

In the light of potential application of the chain plasmon

resonances and their mediated processes, it is desirable tocontrol such atomic plasmons in both energy and space,using, for example, atomic manipulation with an STM. Toexplore the tunability of these chain plasmon resonances,we calculated the plasmon modes by attaching a singleatom at different positions of the chains. Figure 4(a) showsthe dipole strength of the Na8 chain (black) with a singlesilver atom attached at one end, forming an Ag-Na8 (red)chain. The bond-length of Ag-Na was still 2.89 A. The endmode at 3.26 eV decreases in intensity, and splits into ahigh-energy mode at 4.5 eV, which localizes at the silverend of the Ag-Na8 chain (c). In the meantime, the centralmode of Na8 at 3.75 eV increases in its intensity due to the

fact that one more atom is added to the chain. Splitting ofthe end mode results from the broken symmetry in thechains and the coupling to the attached Ag atom. Figure 4demonstrates the sensitivity and tunability of collectiveexcitation of the chains by modifying the atomic environ-ment of the chains.

End electronic states have recently been observed inlinear gold chains by scanning tunneling spectroscopy[29]. It is our belief that the collective plasmon resonancesreported in this work should be observable [30,31] in futureexperiments. In addition, the ultimate chemical and geo-metric sensitivities of these plasmon resonances shouldfind unique and profound applications in atomic-scale en-

gineering of optical spectroscopy and associated dynami-cal processes. The splitting between the end and centralmodes, for example, makes it possible to selectively inducecharge excitations in different spaces, selective control ofcharge localization and transport, local field enhancementand chemical reactions, and plasmon-medium interactionat the atomic scale.

The authors acknowledge Peter Nordlander and BengtKasemo for discussions and comments. This work has beensupported by the 100-Talent Program of Chinese Academyof Sciences, the ATOMICS and PhotoNano consortium ofSSF, and the Institutional Grant Programme of STINT.

*To whom correspondence should be addressed.Electronic address: [email protected]

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jun yan, zhe yuan and shiwu gao- end and central plasmon resonances in linear atomic chains

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