Abstract
This paper reviews recent efforts to understand the dynamics of coherent surface vibrations of alkali atoms adsorbed on metal surfaces. Time-resolved second harmonic generation is used for the coherent excitation and detection of the nuclear wavepacket dynamics of the surface modes. The principles of the measurement and the experimental details are described. The main focus is on coverage and excitation photon energy dependences of the coherent phonon dynamics for Na-, K-, and Cs-covered Cu(111). The excitation mechanism of the coherent phonon has been revealed by the ultrafast time-domain technique and theoretical modelings.
1. Introduction
When a material is excited with a laser pulse with duration shorter than a vibrational period, coherent vibration in which molecules or atoms oscillate in phase over a macroscopic region is induced [1, 2]. This “impulsive” excitation of vibrational (nuclear) wavepacket has been observed for a variety of substances: from gas-phase molecules to solids. The coherent nuclear motions can be probed via modulation of optical response of the materials due to the influence of the nuclear displacement on the complex refractive indices. Typically, changes of absorbance or reflectance of a time-delayed probe pulse are measured as a function of pump-probe delay time and the coherent vibrational motions emerge as oscillatory intensity modulations. Elucidation of the excitation mechanism and the decay dynamics of the nuclear wavepacket leads to detailed understanding of the electron-vibration (phonon) coupling and photochemical dynamics.
Phenomenological equation of motion of the amplitude of the relevant coherent vibrational mode can be described as a forced harmonic oscillator with damping, where is the natural frequency of the undamped oscillator, is the damping rate, is the effective mass of the oscillator, and is the force exerted on the system. With this driving force, a time evolution of the amplitude is given by [3] where and is the initial phase. The initial phase provides information on the nature of the driving force through the following general relationship [3]: where is the Fourier transform of . If the driving force is impulsive, the initial phase is and the oscillation becomes sin-like. If the force is a step function like in time domain, the initial phase is 0 or and the oscillation becomes cos-like.
While there exists a body of literature on coherent vibration in gas phase and in bulk condensed matter, those at surfaces or interfaces are relatively less explored. This is because the signal intensity from surface monolayer of atoms and molecules is generally very small and the experimental observation is demanding. Second-order nonlinear optical process paves the way for probing the dynamics at surfaces and interfaces. We have found that time-resolved second harmonic generation (TRSHG) [4] is a powerful technique to probe the coherent vibration (phonon) of alkali atoms adsorbed on metal surfaces [5–8]. In this paper, we describe our recent achievements in understanding the dynamics of coherent surface phonons at alkali-metal-covered metal surfaces [9–11]. One of the most important issues in the study of coherent phonons at metal surfaces is to determine what electronic transition is most responsible for their creation. Thus, we focus on the electronic structure of alkali-covered metal surfaces and the excitation mechanism of the coherent vibration.
2. Alkali Metals on Metal Surfaces and Enhancement of Nonlinear Susceptibility
Here we describe general features of alkali atoms on metal surfaces particularly focusing on their electronic structure and optical responses. Overlayers of alkali metal atoms on metal surfaces are typical model systems of metals on metals, and detailed information on the adsorption geometries [12], the vibrational [13, 14] and electronic structures [15], and the electronic excitation [16] has been reported. Here we briefly summarize some features of the electronic structure of alkali-covered Cu(111) [17]. The bonding of alkali atoms on metal surfaces strongly depends on alkali coverage. At low coverages the work function decreases sharply with the increase of the coverage. As the coverage increases further, the work function reaches to a minimum and increases toward that of the bulk alkali metal. In the classical model of Gurney [18], an alkali atom donates an outermost occupied electron to the metal to form a positive ion at the low coverages; this results in a surface dipole layer that induces the large drop in work function. As the coverage increases, the lateral interaction of alkali atoms becomes stronger; alkali atoms are depolarized and the alkali overlayer becomes metallic.
The metallic character of the alkali overlayer at high coverages is due to emergence of two bands: an overlayer resonance (OR) located below the -band gap and a quantum well state (QWS) around the Fermi level. These bands correlate to those of a free standing alkali monolayer in the vacuum: the -like lowest and the -like second lowest bands [19]. When the monolayer is brought closer to the metal surface, these bands are stabilized by the interaction with the metal, while maintaining the integrity. The -like band correlates to OR; the -like band correlates to QWS. Because QWS is located in the -band gap, its wave function is localized at the surface. In contrast, the wave function of OR extends more into the substrate, because it is located below the lower edge of -band gap.
It has been known that alkali overlayers enhance the conversion efficiency of second harmonic generation (SHG) by a few orders of magnitude in comparison with clean metal surfaces [20]. When an optical field increases, the macroscopic polarization induced in a medium shows nonlinearity with respect to the field. The nonlinear polarization responsible for SHG is given by where is the second-order nonlinear susceptibility for SHG. In a medium with centrosymmetry, of the medium is zero within the electric dipole approximation. In contrast, at a surface where centrosymmetry is generally broken, dipole-allowed SH signals are generated from the surface. Thus, SH generation spectroscopy provides an inherent surface sensitivity if bulk materials have centrosymmetry [21].
Figure 1 shows how the SH intensity of 800 nm (hν = 1.55 eV) photons depends on coverage of alkali atoms on Cu(111) surfaces. The coverage has been calibrated by measuring the ratio of Auger electron signals of alkali adsorbates to that of the substrates as a function of the deposition time [10]. Throughout this paper, we define the alkali coverage as one monolayer when the first layer is completed, although in the original articles the coverage was defined as a ratio of the alkali atomic density to that of the substrate.
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The SH intensity is enhanced by a few orders of magnitude compared to the clean surface when alkali atoms are adsorbed [10]. There are two major origins of the SH enhancement associated with alkali adsorption: interband transitions between surface electronic states and multipole plasmon excitation [16, 22]. At the low coverages, interband transitions from occupied surface state (SS) to alkali-induced antibonding state (AS) [23] or from SS to image potential states (IPSs) become resonant to 2hν (= 3.10 eV) below . Therefore, the “resonant” peaks observed at in Figure 1 are likely due to resonant or near-resonant transitions in which the surface localized bands, SS, AS, and IPSs, are involved. As coverage increases over , the alkali overlayer is depolarized and the metallic QWS and OR bands are formed. The transitions from the occupied-OR band to the , bands of the substrate and interband transitions from QWS to the substrate bands contribute to the SH intensity.
At , the contribution to SH intensity from multipole plasmon excitation may be larger than that from the interband transitions because the photon energy 2hν (= 3.1 eV) is close to plasmon resonance energies: and 3.5 eV for K and Cs, respectively, where is the bulk-plasma frequency. Irradiation of a metal surface with an oscillating electromagnetic field induces a dynamic screening field [24]. If the optical frequency is close to 0.8, electronic transitions at the surface excite resonantly a damped collective mode along the surface normal. This coupling between the optical field and multipole plasmons at the surface results in the local field enhancement of the nonlinear response such as SHG. Liebsch calculated the frequency dependence of SH dipole moments of alkali overlayers at by using the time-dependent density-functional method [22] and found that the resonant peak of the imaginary part of the dipole moment is located at 2.0, 1.4, and 1.3 eV for Na, K, and Cs on Al, respectively. The photon energy of hν = 1.55 eV is close to the resonance of the potassium overlayer at . This is consistent with the significant increase of SH intensity at the saturation coverage of K on Cu(111) as shown in Figure 1.
3. Principles of the Time-Resolved Second Harmonic Generation
In TRSHG spectroscopy, the SH intensity of a probe pulse is measured as a function of pump-probe delay time . Transient changes in the SH intensity are defined as where is the SH intensity at a delay time and is that without a pump pulse, respectively.
When a metallic alkali monolayer is brought from the vacuum to a metal surface, the electronic bands of the free-standing alkali monolayer shift their binding energies as a result of interactions with the metal substrate. Thus, the binding energies of the alkali-induced bands depend on the displacement of the overlayer along the surface normal . Consequently, the oscillation of due to coherent excitation of the alkali-substrate stretching mode (S mode) alters the binding energies and populations of the alkali-induced bands; in this way, the coherent vibration of alkali atoms contributes to TRSHG signals. Because the lateral displacements of the alkali overlayer are not expected to shift the binding energies of alkali-induced bands as large as the vertical ones, the lateral motions of alkali adsorbates contribute little to TRSHG signals.
The modulation of due to the displacement of the th phonon mode, , can be approximated by (neglecting the modulation due to the electronic population change) [25] Because the SH intensity is proportional to the square of , the dominant contribution of the coherent phonons to is expressed as in which the SH intensity modulation is proportional to the displacement of the phonon mode.
4. TRSHG Experimental Setup [7, 10, 11]
The experiments were carried out in an ultrahigh vacuum chamber equipped with a cylindrical analyzer for Auger electron spectroscopy (AES) and low energy electron diffraction. Alkali atoms from a degassed alkali dispenser (SAES Getters) were deposited on a clean substrate at 90–110 K. The coverage was determined by the ratio of AES intensity of adsorbate and substrate atoms.
For the TRSHG measurements we used home-made noncollinear optical parametric amplifiers (NOPAs) pumped with the second harmonic (400 nm) output of a Ti: sapphire regenerative amplifier (1 kHz, 130 fs). NOPA delivers 25–35 fs pulses whose center photon energy is tunable from 2.0 eV to 2.4 eV. In addition, we also used a fundamental (800 nm) output of the regenerative amplifier with an extra pulse compression apparatus: the output was focused into a 2 m long cylindrical tube filled with Kr gas. The bandwidth of the output pulse is broadened and the pulse compression to 35 fs was attained with additional multiple reflections on negative group-delay dispersion mirrors.
-Polarized pump and probe pulses were focused onto the sample with an incidence angle of about 70 degrees, and the second harmonic intensity of the probe pulse that is generated coaxially with the probe was detected as a function of pump-probe delay. All the measurements were carried out with sample temperature at 85–110 K.
5. Coverage Dependence
Figures 2 and 3 show coverage dependence of TRSHG traces from K and Cs on Cu(111). In both cases, the coherent nuclear motions emerge as damped oscillatory components. The TRSHG traces are analyzed by using singular value decomposition [7] assuming the following linear combination of damped cosinusoids and exponential decay components: where and are phonon frequency and initial phase, respectively, and is a dephasing time of a vibrational coherence or a decay time of a background component. The first term represents the coherent nuclear motions of the S modes and the second term describes the SH modulation due to the electronic population changes.
The oscillation frequencies were found to be 3.0-3.1 THz (at ) for K/Cu(111) and 1.8 THz for Cs/Cu(111); these values are in consistence with the S mode frequencies found by other surface vibrational spectroscopy [10, 11]. Large oscillation amplitudes are observed only for coverages higher than . This is also the case for Cs/Pt(111) [7] and K/Pt(111) [26]: the S mode oscillation amplitudes in TRSHG signals are not proportional to the alkali coverage but show an onset at around a half monolayer. According to the discussion on the electronic structure of alkali overlayer, the formation of OR and QWS is the expected feature occurring at around half monolayer. Consequently, the coherent excitation of the S mode is in line with the emergence of these surface states.
6. Excitation Mechanisms for Na and K Overlayers on Cu(111)
The pump pulse creates hot electrons and holes in substrate and in the surface bands. However, not all electronic excitations are effective to couple with motions of alkali atoms. There are two extreme cases in photo-induced nuclear dynamics at surfaces, as has been frequently discussed in the studies of surface photochemistry: adsorbate-localized excitation versus substrate-mediated excitation. [27] For the alkali adsorption systems in the coverage range from to 1.0, transitions of OR→QWS, OR→IPSs, and QWS→IPSs are candidates for the adsorbate-localized excitation. Intra- and interband excitations of , , and bands of bulk are involved in the substrate-mediated excitation: electrons or holes created by the electronic excitation of bulk bands transiently transfer to the alkali-induced electronic state, resulting in modulation of the electron density near alkali adatoms. In addition, another possible excitation mechanism specific to alkali overlayers is the multipole plasmon excitation. This excitation produces a longitudinally oscillating electron density at an alkali-covered surface, which may also initiate the coherent motion of alkali adsorbates.
In order to distinguish the excitation mechanisms, the excitation photon energy dependence of the initial amplitude of the S mode coherent motion was measured for K/Cu(111) (Figure 4) [10]. The excitation photon energy dependence was found to resemble the absorption curve of bulk copper: that corresponds well to the carrier density curve (solid curve) estimated from substrate absorption. Therefore, the substrate electronic excitation is likely responsible for the coherent phonon excitation of alkalis on copper. Similar results have been obtained also for Na/Cu(111) [9].
Because the emergence of oscillatory modulations in TRSHG traces is concomitant with stabilization of the QWS band to the Fermi level, it is likely that the population change in the QWS band is responsible for a driving force to alkali atoms along the alkali atom-Cu coordinate. One possible excitation path for generating the impulsive force is hole creation in the QWS. Electron-hole pairs are formed in the substrate by the -band→, -band transition, followed by subsequent Auger recombination of an electron in the QWS band with the -band hole, resulting in creation of holes in the QWS. An appreciable coupling between the hole creation at the alkali-derived QWS and surface (or interface) phonon excitation has been suggested [28]. Alternatively, hot electrons created by the -band→, -band transition could be injected into the QWS above , resulting in abrupt fluctuations of electron density at alkali atoms. In either case, the rapid changes in charge density at the surface, particularly in the QWS band, are likely to be the origin for the driving force along the alkali atom-Cu stretching coordinate.
7. Switching of the Excitation Mechanism for Cs/Cu(111) Depending on the Pump Photon Energy [11]
As has been described in the previous section, investigation on Na/Cu(111) and K/Cu(111) system has revealed that the S mode excitation occurs via substrate-mediated process. However, this is not the whole story, and here we show that the Cs monolayer on Cu(111) provides a good opportunity to elucidate further the excitation mechanisms [11]. A peculiar feature of the Cs/Cu(111) is that at high coverages, in addition to the OR and QWS bands, an unoccupied band originating from Cs 5 band is located at 1.6 eV above the Fermi level [29]. Thus, the resonance transition from QWS to the unoccupied Cs 5 band is expected to take place at around 1.6 eV. Note that no transitions take place from bulk Cu bands at hν = 1.6 eV because the top of the Cu bands are located at ~2.0 eV below the Fermi level. Consequently, it is possible to examine how the characteristics of surface coherent phonons depend on the nature of electronic excitation by varying the excitation photon energy: adsorbate-localized excitation versus substrate-mediated excitation.
Figure 5(a) shows typical traces of TRSHG signals from Cs-covered Cu(111) () for excitations at the wavelengths and 800 nm. Although both TRSHG traces at and 400 nm show a prominent oscillating component with frequency of 1.8 THz, the initial phase of the oscillating component at nm is very different from that at nm, as shown in Figure 5(b). Cs–Cu stretching is sin-like () at nm, while this is close to cos-like () at nm. The initial phase difference provides useful information of the temporal profiles of the driving force: it is impulsive like for nm, but step function like for nm (see (3)). In addition to the initial phase, the pump fluence dependence of the oscillation amplitude was found to be very different between and 800 nm (Figure 6). While the amplitude at nm increases linearly with the pump fluence, the amplitude at nm shows strong saturation feature. This indicates that surface localized excitation plays a role at nm.
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8. Theoretical Modeling of the Excitation Mechanism [11]
The significant dependences on excitation photon energy found for Cs/Cu(111) indicate different excitation mechanisms operating for the two excitation photon energies. Since adsorbate-localized excitation is expected at nm, Yasuike and Nobusada (YN) developed a theoretical modeling to rationalize the observed feature applying the transient-adsorbate mediation (TAM) mechanism recently proposed by themselves [30, 31].
The TAM mechanism is schematically depicted in Figure 7. Three potential energy curves (PECs) are considered: one is that of the ground state, , and another one is that of the excited state with adsorbate localized nature, , and the third one is that of bulk excited state, . In the adsorbate-localized excited state, the Cs–Cu equilibrium distance is shifted from that in the ground state. In addition, the state has a finite width because of interactions with bulk continuum electronic states. The bulk excited states are composed of a continuum caused by electron-hole pair creations in bulk bands. Unless bulk excitations lead to electron transfer to the adsorbate-localized unoccupied band, they do not directly trigger Cs nuclear motions. Thus, the potential energy curves of the bulk excited states are assumed to have the same dependence as but shifted vertically by the excitation energy of bulk electrons.
After the irradiation of near-resonant light pulse, the population partially transfers to the adsorbate-localized excited state. The wavepacket on this PEC starts to propagate toward vacuum owing to the repulsive force and gains momentum. Because the back donation of charge to the bulk occurs rapidly, the lifetime of this state is very short. Thus, the quenching of the adsorbate-localized excited state brings the wavepacket to the PEC of bulk continuum states; then, an oscillatory motion of the wavepacket takes place on the PEC, while bulk electrons dissipate energy via electron-phonon coupling.
From a numerical analysis based on the model, the sin-like initial phase and the saturation behavior in the pump fluence dependence were successfully reproduced [11]. Figure 8 shows initial phases calculated from TAM model as a function of the lifetime of the excited state. The sin-like behavior is due to a short lifetime in the adsorbate-localized state, and the saturation (Figure 6) originates primarily in the limited density of states of the initial state: only a small fraction of the QWS band is occupied.
At nm, bulk excitations from the bands of copper generate the coherent Cs–Cu stretching vibration. In contrast to the case of nm, the coherent oscillation is nearly cos-like and the amplitude of oscillatory signals linearly increases with pump fluence (Figure 6). In general, absorption of an intense fs laser pulse generates quasithermal equilibrium in the surface electron gas, and its peak temperature reaches several thousand K over a time scale of several hundred fs. At nm, the effect of the hot electrons may play a crucial role: under the circumstances, the adsorbate-localized state is temporarily occupied with hot electrons. The force exerted on Cs is generated by transient occupation of the adsorbate-localized band by resonant electron transfer from bulk bands. Because the excitation takes place much faster than the period of Cs–Cu stretching, the indirect excitation can coherently excite this mode. Note that the electron temperature decays with a slower time scale than the Cs–Cu oscillation period, and the driving force is no longer close to a delta function but rather like a step function.
YN proposed that the effective PEC for the adsorbate vibration excitation under the influence of the substrate hot electrons is given by [11, 32] where is the Fermi-Dirac distribution at electron temperature . The function is an effective occupation number of the adsorbate-localized excited states and is defined by the integration of the local density of states for the adsorbate-localized excited state, where and is the effective band width. In the limit of the step function profile of the driving force, the oscillation should be pure cosine because Cs atoms oscillate on the displaced potential energy surface. However, we found experimentally that the oscillation deviates from the pure cosine function. Theoretical simulations using (9) and (10) successfully reproduced the deviations of initial phase from pure cosine by considering relaxation of hot electrons: the effective PEC shows a transient shift in line with the electron temperature decay, and the phase of the Cs vibration is modulated by the change of the PEC. In addition, the simulations verify the linear dependence of the initial amplitude on the pump fluence if the band width of the unoccupied state is 1.0 eV [11].
9. Summary and Outlook
We describe the principle of time-resolved SHG spectroscopy under an ultrahigh vacuum condition and its application to the alkali metal adsorption systems. Electronic excitation of the adsorption systems by ultrafast laser pulses induces coherent surface phonons. The large enhancement in SH intensity at the alkali-covered metal surfaces allows to monitor precisely the time-evolution of the coherent phonons. Electronic excitations of both adsorbate-induced and substrate bands by using ultrafast light pulses can induce abrupt fluctuations of charge density around alkali adatoms, resulting in coherent nuclear motions of adsorbates via electron-phonon couplings. For Na and K/Cu(111), excitation-photon-energy dependence for coherent surface phonons clearly indicates that substrate electronic excitation induces the coherent motions of the S mode. For Cs/Cu(111), we observed clear switching of the excitation mechanism from bulk excitation for nm to adsorbate localized excitation at nm. Attempts for theoretical modeling of the both excitation processes have been described.
TRSHG is versatile to investigate coherent phonon dynamics at surfaces. This method is ideally suited for alkali overlayers because of the marked enhancement of SH intensity. However, applications of TRSHG to other adsorption systems have been very limited, mainly because they lack such large enhancement in SH intensity. This obstacle can be removed if SH intensity is enhanced by tuning the photon energy of probe pulses to an electronic resonance of adsorption systems. In addition, using much shorter pump pulses extends the applicability of TRSHG to coherent surface phonons and adsorbate vibrations at higher frequencies.
Acknowledgments
The authors would like to thank their collaborators in the research program summarized in this paper. This work was supported in part by Grants-in-Aid for Scientific Research (S) (Grant no. 17105001) and for Young Scientists (B) (Grant no. 19750012) from Japan Society for the Promotion of Science (JSPS) and Scientific Research on Priority Area (461 Molecular Theory for Real Systems) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. K. Watanabe gratefully acknowledges financial support by the PRESTO program of JST.