Coherent phonon

A number of solid compounds have been examined with this time-domain method since the first report of coherent phonons in GaAs [10]. Coherent phonons were created at the metal/semiconductor interface of a GaP photodiode [29] and stacked GaInP/GaAs/GalnP layers [30]. Cesium-deposited [31-33] and potassium-deposited [34] Pt surfaces were extensively studied. Manipulation of vibrational coherence was further demonstrated on Cs/Pt using pump pulse trains [35-37]. Magnetic properties were studied on Gd films [38, 39]. 

Chang, Y.-M. (2003) Coherent phonon spectroscopy of GaP Schottky diode. Appl. Phys. Lett., 82, 1781-1783. 

Summary. Coherent optical phonons are the lattice atoms vibrating in phase with each other over a macroscopic spatial region. With sub-10 fs laser pulses, one can impulsively excite the coherent phonons of a frequency up to 50THz, and detect them optically as a periodic modulation of electric susceptibility. The generation and relaxation processes depend critically on the coupling of the phonon mode to photoexcited electrons. Real-time observation of coherent phonons can thus offer crucial insight into the dynamic nature of the coupling, especially in extremely nonequilibrium conditions under intense photoexcitation. 

Fig. 2.2. Two generation models of coherent optical phonons, (a), (c), (e) impulsive stimulated Raman scattering (ISRS). (b), (d), (f) displacive excitation of coherent phonons (DECP). Graphs (e) and (f) display the time evolution of the driving force (grey areas) and that of the displacement (solid, curves) for ISRS and DECP, respectively...

The classical equation of motion1 describing the coherent phonons for a small nuclear displacement Q is that of a driven harmonic oscillator [9,10,15]... 

Up to now, only Raman active modes at the r point of the Brillouin zone have been observed as coherent phonons in bulk crystals.2 The selection rule can be... 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Experimental verification of the ISRS generation can be primarily given by the pump polarization dependence. The coherent phonons driven by ISRS (second order process) should follow the symmetry of the Raman tensor, while those mediated by photoexcited carriers should obey the polarization dependence of the optical absorption (first order process). It is possible, however, that both ISRS and carrier-mediated generations contribute to the generation of a single phonon mode. The polarization dependence is then described by the sum of the first- and second-order processes [20-22], as shown in Fig. 2.3. 

Fig. 2.3. The Fourier-transformed (FT) intensity of coherent phonons as a function of the pump polarization angle ip for a GaAs/Alo.36Gao.64As MQW. The excitation wavelength is slightly above the n = 1 exciton resonance (left) and slightly above the n = 2 subband energy (right), ( -dependent component is attributed to ISRS, while the ( -independent component is to TDFS and forbidden Raman scattering. From [20]...

As the lattice interacts with light only through electrons, both DECP and ISRS should rely on the electron-phonon coupling in the material. Distinction between the two models lies solely in the nature of the electronic transition. In this context, Merlin and coworkers proposed DECP to be a resonant case of ISRS with the excited state having an infinitely long lifetime [26,28]. This original resonant ISRS model failed to explain different initial phases for different coherent phonon modes in the same crystal [21,25]. Recently, the model was modified to include finite electronic lifetime [29] to have more flexibility to reproduce the experimental observations. 

The third term describes the polarization set up by ultrafast drift-diffusion currents, which can excite coherent phonons via TDFS (or via the buildup of electric Dember fields [9,10]). The first two terms represent the second- and the third-order nonlinear susceptibilities, respectively [31]. The fourth term describes the polarization associated with coherent electronic wavefunctions, which becomes important in semiconductor heterostructures. 

For surface coherent phonons of ferromagnetic metals, a spin-driven generation mechanism was proposed, as will be described in Sect. 2.6. 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

Semimetals bismuth (Bi) and antimony (Sb) have been model systems for coherent phonon studies. They both have an A7 crystalline structure and sustain two Raman active optical phonon modes of A g and Eg symmetries (Fig. 2.4). Their pump-induced reflectivity change, shown in Fig. 2.7, consists of oscillatory (ARosc) and non-oscillatory (ARnonosc) components. ARosc is dominated by the coherent nuclear motion of the A g and Eg symmetries, while Af nonosc is attributed to the modification in the electronic and the lattice temperatures. 

Coherent Phonons in Group IV Crystals and Graphitic Materials... 

Isotope superlattices of nonpolar semiconductors gave an insight on how the coherent optical phonon wavepackets are created [49]. High-order coherent confined optical phonons were observed in 70Ge/74Ge isotope superlattices. Comparison with the calculated spectrum based on a planar force-constant model and a bond polarizability approach indicated that the coherent phonon amplitudes are determined solely by the degree of the atomic displacement, and that only the Raman active odd-number-order modes are observable. 

When metals have Raman active phonons, optical pump-probe techniques can be applied to study their coherent dynamics. Hase and coworkers observed a periodic oscillation in the reflectivity of Zn and Cd due to the coherent E2g phonons (Fig. 2.17) [56]. The amplitude of the coherent phonons of Zn decreased with raising temperature, in accordance with the photo-induced quasi-particle density n.p, which is proportional to the difference in the electronic temperature before and after the photoexcitation (Fig. 2.17). The result indicated the resonant nature of the ISRS generation of coherent phonons. Under intense (mJ/cm2) photoexcitation, the coherent Eg phonons of Zn exhibited a transient frequency shift similar to that of Bi (Fig. 2.9), which can be understood as the Fano interference [57], A transient frequency shift was aslo observed for the coherent transverse optical (TO) phonon in polycrystalline Zr film, in spite of much weaker photoexcitation [58],... 

Fig. 2.19. Temperature dependence of the amplitudes of coherent phonons of Gd(0001) and Tb(0001). On the right axis, and Ap show the square of calculated spontaneous magnetization given by the Brillouin function with Jq =7/2 and =6/2 representing the magnetic moment of 4f electrons. From [59]...

Systematic TRSHG studies on alkali-atom adsorbed metal surfaces by Matsumoto and coworkers provided a deep insight on how coherent motions are created under very different electronic configurations [15, 77, 78]. The results showed that the coherent phonon generation critically depends on the surface and bulk electronic structure of the substrate. 

Coherent optical phonons can couple with localized excitations such as excitons and defect centers. For example, strong exciton-phonon coupling was demonstrated for lead phtalocyanine (PbPc) [79] and Cul [80] as an intense enhancement of the coherent phonon amplitude at the excitonic resonances. In alkali halides [81-83], nuclear wave-packets localized near F centers were observed as periodic modulations of the luminescence spectra. 

T. Dekorsy, G.C. Cho, H. Kurz, in Coherent Phonons in Condensed Media ed. by M.Cardona, G. Giintherodt. Light Scattering in Solids VIII (Springer, Berlin, 2000), p. 169... 

M. Forst, T. Dekorsy, Coherent Phonons in Bulk and Low-Dimensional Semiconductors, ed. by S. De Silvestri, G. Cerullo, G. Lanzani. Coherent Vibrational Dynamics (CRC, Boca Raton, 2007), p. 129... 

Coherent lattice motions can create periodic modulation of the electronic band structure. Time-resolved photo-emission (TRPE) studies [20-22] demonstrated the capability to detect coherent phonons as an oscillatory shift of... 

The earliest control experiments were performed in double- (or multiple-) pump and probe scheme on optical phonons generated via ISRS in transparent materials by Nelson and coworkers [24,25], Shortly later, similar experiments were carried out on coherent phonons generated in semiconductors via TDFS by Dekorsy and coworkers [26], and on those generated in semimetals via DECP by Hase and coworkers [27] (Fig. 2.1 in the previous chapter). These experiments demonstrated that the amplitude of the coherent oscillation can be controlled by varying the temporal separation At between the two pump pulses. At = nT leads to the maximum enhancement of the amplitude with an integer n and the phonon period T, while At = (n + 1/2)T results in complete cancelation. 

Fig. 3.10. Schematics of interferences of coherent phonons in double-pump experiments. (a) constructive interference in ISRS mechanism. Bold grey arrows indicate the first and the second ISRS driving forces, (b) constructive interferences in DECP mechanism, (c) destructive interferences in DECP mechanism...

If the dephasing time of the coherent phonons depend critically on the carrier density, photo-injection of carriers with the second pump pulse can annihilate them partially or completely, depending on its fluence but not on its relative timing. Such incoherent control was demonstrated for the LO phonons of GaAs [37],... 

Fig. 3.14. Left transient reflectivity change of Te obtained with transform limited, negatively chirped, and positively chirped pulses. Right coherent phonon amplitude as a function of the pulse chirp. Adapted from [42]...

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