Phonon Amplitude Research Articles

A momentum-resolved view of polaron formation in materials

An ab-initio computational methodology for interrogating the phonon contribution to polaron formation in real materials is developed that can be directly compared to experiment. Using LiF as an example, we show that the recent ab-initio theory of Sio et al.1 makes predictions of the momentum- and branch dependent phonon amplitudes in polaron quasiparticles that are testable using ultrafast electron diffuse scattering (UEDS) and related techniques. The large electron polaron in LiF has UEDS signatures that are qualitatively similar to those expected from a simple isotropic strain field model, but the small hole polaron exhibits a profoundly anisotropic UEDS pattern that is in poor agreement with an isotropic strain field. We also show that these polaron diffuse scattering signatures are directly emblematic of the underlying polaron wavefunction. The combination of new time and momentum resolved experimental probes of nonequilibrium phonons with novel computational methods promises to complement the qualitative results obtained via model Hamiltonians with a first principles, material-specific quantitative understanding of polarons and their properties.

Renewing Fundamental Understanding of Ionic Transport in Inorganic Crystalline Solid‐State Electrolytes from the Perspective of Lattice Dynamics

AbstractLattice dynamics has been widely employed to study various properties of crystalline materials, by revealing the atomic vibration rules with phonon dispersion curves. Modulating lattice‐dynamics‐related factors is an emerging trend in the design of inorganic crystalline solid‐state electrolytes (ICSSEs) with promoted ionic conductivity. Nevertheless, due to complicated interplay of these enormous factors, fundamental understanding of lattice‐dynamics‐influenced ionic transport is still limited. In this review, all related factors are classified into lattice static and dynamic ones based on their variability in ionic transport process, facilitating a methodological evaluation of their individual and interrelated influences. The previous efforts are affirmed to design ICSSEs by constructing potential energy surfaces for ionic transport based on lattice static factors (e.g., ionic arrangement, time‐scale dependent ionic concentration, and lattice softening). As for lattice dynamic factors, the possibility to quantify ionic transport activation energy and to screen the type of migration ions by phonon frequency and amplitude, respectively is validated. Specifically, it is highlighted that the optimization of specific phonon mode and the coupling of both lattice static and dynamic factors are essential to achieve superior ionic transport in ICSSEs. Finally, challenges and opportunities are pointed out in this field, which can potentially guide the future development of ICSSEs.

Terahertz sum-frequency excitation of coherent optical phonons in the two-dimensional semiconductor WSe2

Driving fundamental excitations via strong light fields is one of the most important issues in solid state physics, which opens up new avenues to control material properties. Two-dimensional materials are fruitful platforms for future semiconductor applications, including opto-electronic and phononic devices, yet the phonon dynamics and nonlinear phonon–phonon coupling remain under-explored. Here, we demonstrate coherent phonon excitation in thin films of the layered two-dimensional semiconductor WSe2 induced by intense and broadband ultrafast terahertz (THz) pulses. We performed THz Kerr effect spectroscopy and observed coherent phonon oscillations assigned to the E2g optical phonon mode. The phonon amplitude displays a quadratic THz field strength dependence, indicating a sum-frequency THz excitation process. Furthermore, pump–probe polarization and crystal orientation relationships, supported by symmetry analysis of the nonlinear susceptibility and Raman tensors, provide helpful insight into nonlinear phonon–phonon interactions and potential coherent control schemes for the manipulation of phonon polarization and material properties in WSe2.

Coherent-Phonon-Driven Intervalley Scattering and Rabi Oscillation in Multivalley 2D Materials.

Resolving the complete electron scattering dynamics mediated by coherent phonons is crucial for understanding electron-phonon couplings beyond equilibrium. Here we present a time-resolved theoretical investigation on strongly coupled ultrafast electron and phonon dynamics in monolayer WSe_{2}, with a focus on the intervalley scattering from the optically "bright" K state to "dark" Q state. We find that the strong coherent lattice vibration along the longitudinal acoustic phonon mode [LA(M)] can drastically promote K-to-Q transition on a timescale of ∼400 fs, comparable with previous experimental observation on thermal-phonon-mediated electron dynamics. Further, this coherent-phonon-driven intervalley scattering occurs in an unconventional steplike manner and further induces an electronic Rabi oscillation. By constructing a two-level model and quantitatively comparing with abinitio dynamic simulations, we uncover the critical role of nonadiabatic coupling effects. Finally, a new strategy is proposed to effectively tune the intervalley scattering rates by varying the coherent phonon amplitude, which could be realized via light-induced nonlinear phononics that we hope will spark experimental investigation.

Ultrafast quantum path interferometry to determine the electronic decoherence time of the electron-phonon coupled system in n -type gallium arsenide

Quantum coherence is the key to new quantum technologies, although the details of decoherence processes and times are still not well understood in solids. We demonstrate how to measure the decoherence time of electronic excited states in $n$-type gallium arsenide ($n$-GaAs) crystals using a relative-phase locked double pulse excitation method and quantitatively evaluate with a simple model including temperature dependence. The interference patterns of both electronic and phonon coherence are observed in $n$-GaAs using ultrafast quantum path interferometry with $\ensuremath{\pi}/4$ polarized femtosecond pulses, via the amplitude of longitudinal optical phonons as a function of pump-pump delay. The electronic coherence shows uplifting and splitting in the collapse and revival of the electronic interference, which is sensitive to temperature, and these features are well reproduced using a simple quantum mechanical model. The decoherence time is determined using quantum calculations, from the splitting and uplifting in the interference shape, to be $27.8\ifmmode\pm\else\textpm\fi{}0.5, 23.0\ifmmode\pm\else\textpm\fi{}0.3$, and $12.9\ifmmode\pm\else\textpm\fi{}0.3$ fs at 10, 90, and 290 K, respectively. The temperature dependence of the decoherence time is well reproduced by the density of electrons in the conduction band with the group velocity of the photoinduced electrons.

Selective coupling of coherent optical phonons in YBa2Cu3O7−δ with electronic transitions

We investigate coherent lattice dynamics in optimally doped ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ driven by ultrashort ($\ensuremath{\sim}12$ fs) near-infrared and near-ultraviolet pulses. Transient reflectivity experiments, performed at room temperature and under moderate ($<0.1$ mJ/${\mathrm{cm}}^{2}$) excitation fluence, reveal ${A}_{g}$-symmetry phonon modes related to the O(2,3) bending in the ${\mathrm{CuO}}_{2}$ planes and to the apical O(4) stretching at frequencies between 10 and 15 THz, in addition to the previously reported Ba and Cu(2) vibrations at 3.5 and 4.5 THz. The relative coherent phonon amplitudes are in stark contrast to the relative phonon intensities in the spontaneous Raman scattering spectrum excited at the same wavelength. This contrast indicates mode-dependent contributions of the Raman and non-Raman mechanisms to the coherent phonon generation. We show that the particularly intense coherent Cu(2) phonon, together with its initial phase, supports its generation predominately via a displacive mechanism, possibly involving the charge transfer within the ${\mathrm{CuO}}_{2}$ planes. The small amplitude of the coherent out-of-phase O(2,3) bending mode at 10 THz also suggests the involvement of non-Raman generation mechanism. The generation of the other coherent phonons can in principle be explained within the framework of Raman mechanism. When the pump light has the polarization component perpendicular to the ${\mathrm{CuO}}_{2}$ plane, the coherent O(4) mode at 15 THz is strongly enhanced compared to the in-plane excitation, corresponding to the large polarizability component associated with the hopping between the apical and the chain oxygens, O(4) and O(1).

Theory of radial oscillations in metal nanoparticles driven by optically induced electron density gradients.

We provide a microscopic approach to describe the onset of radial oscillation of a silver nanoparticle. Using the Heisenberg equation of motion framework, we find that the coupled ultrafast dynamics of coherently excited electron occupation and the coherent phonon amplitude initiate periodic size oscillations of the nanoparticle. Compared to the established interpretation of experiments, our results show a more direct coupling mechanism between the field intensity and coherent phonons. This interaction triggers a size oscillation via an optically induced electron density gradient occurring directly with the optical excitation. This source is more efficient than the incoherent heating process currently discussed in the literature and well-describes the early onset of the oscillations in recent experiments.

The influence of initial phonon states on the generation of coherent optical phonons

The generation of coherent phonons is theoretically studied using a thermal equilibrium phonon distribution as the initial condition. The time evolution of the coherent phonon amplitude and phonon population is calculated for 4.5-THz phonons with initial phonon distributions at 10 and 300 K. It is determined that the coherent-phonon amplitudes of state-selected phonons are dependent on the initial phonon distribution. The coherent-phonon amplitudes, when considering all phonon states instead of selecting certain phonon levels, are almost the same for both initial distributions. The variance of the coherent-phonon amplitudes is found to oscillate with twice the phonon frequency, and its oscillation amplitude depends on the initial phonon distribution.

Phonon-Suppressing Intermolecular Adhesives: Catechol-Based Broadband Organic THz Generators.

Solid‐state molecular phonons play a crucial role in the performance of diverse photonic and optoelectronic devices. In this work, new organic terahertz (THz) generators based on a catechol group that acts as a phonon suppressing intermolecular adhesive are developed. The catechol group is widely used in mussel‐inspired mechanical adhesive chemistry. Newly designed organic electro‐optic crystals consist of catechol‐based nonlinear optical 4‐(3,4‐dihydroxystyryl)‐1‐methylpyridinium (DHP) cations and 4‐(trifluoromethyl)benzenesulfonate anions (TFS), which both have multiple interionic interaction capability. Interestingly, compared to benchmark organic crystals for THz generators, DHP‐TFS crystals concomitantly achieve top level values of the lowest void volume and the highest crystal density, resulting in an exceptionally small amplitude of solid‐state molecular phonons. Simultaneously achieving small molecular phonon amplitude, large optical nonlinearity and good phase matching at infrared optical pump wavelengths, DHP‐TFS crystals are capable of generating broadband THz waves of up to 16 THz with high optical‐to‐THz conversion efficiency; one order of magnitude higher than commercial inorganic THz generators.

Spectrally Resolving the Phase and Amplitude of Coherent Phonons in the Charge Density Wave State of 1T‐TaSe2

AbstractThe excitation and detection of coherent phonons have given unique insights into the condensed matter, in particular for materials with strong electron–phonon coupling. A study of coherent phonons is reported in the layered charge density wave (CDW) compound 1T‐TaSe2 performed using transient broadband reflectivity spectroscopy, in the photon energy range 1.75–2.65 eV. Several intense and long‐lasting (>20 ps) oscillations, arising from the CDW superlattice reconstruction, are observed allowing for detailed analysis of the spectral dependence of their amplitude and phase. For energies above 2.4 eV, where transitions involve Ta d‐bands, the CDW amplitude mode at 2.19 THz is found to dominate the coherent response. At lower energies, instead, beating arises between additional frequencies, with a particularly intense mode at 2.95 THz. Interestingly, the spectral analysis reveals a π phase shift at 2.4 eV. Results are discussed considering the selective coupling of specific modes to energy bands involved in the optical transitions seen in steady‐state reflectivity. The work demonstrates how coherent phonon spectroscopy can distinguish and resolve optical states strongly coupled to the CDW order and provide additional information normally hidden in conventional steady‐state techniques.

Operational regimes of lasers based on gain media with a large Raman scattering cross-section

We report on unusual regimes of operation of a laser with a gain medium with a large Raman scattering cross-section, which is often inherent in new types of gain media such as colloidal and epitaxial quantum dots and perovskite materials. These media are characterized by a strong electron–phonon coupling. Using the Fröhlich Hamiltonian to describe the electron–phonon coupling in such media, we analyze the operation of the system above the lasing threshold. We show that below a critical value of the Fröhlich constant, the laser can only operate in the conventional regime: namely, there are coherent cavity photons but no coherent phonons. Above the critical value, a new pump rate threshold appears. Above this threshold, either joint self-oscillations of coherent phonons in the gain medium and photons in a cavity or a chaotic regime are established. We also find a range of the values of the Fröhlich constant, the pump rate, and the resonator eigenfrequency, in which more than one dynamical regime of the system is stable. In this case the laser dynamics is determined by the initial values of the resonator field, the active medium polarization, the population inversion, and phonon amplitude.

Anisotropic electron and lattice dynamics in excitonic insulator Ta2NiSe5

We employ polarization-resolved femtosecond optical pump–probe spectroscopy to investigate the nonequilibrium photocarrier dynamics in excitonic insulator Ta2NiSe5. The electronic dynamics, including hot carrier cooling, exciton formation, and recombination in the timescale ranging from subpicoseconds to a few tens of picoseconds, have been established from the transient reflectivity spectra, showing strong in-plane anisotropy with respect to the probe polarization. Such anisotropic photocarrier dynamics possibly arise from the crystalline orientation dependence of the excitonic polarizability. Furthermore, we find that the amplitude of coherent phonons with a frequency of 1 THz is subject to the probe polarization, whereas it is not sensitive to the pump polarization. This substantiates that the displacive excitation of coherent phonons plays a decisive role in lattice dynamics. In addition, we find that the photo-induced dielectric screening tends to suppress the amplitude of coherent phonons with increasing pump fluence, manifesting a remarkable polarization dependence. Our work provides valuable insights into the excitonic dynamics and the origin of coherent phonon generation and also may contribute to the development of polarization-sensitive photoelectric devices based on Ta2NiSe5.

Interference of optical phonons in diamond studied using femtosecond pulses of polarized near-infrared light

The phononic interference of optical phonons in diamond is studied via transient transmittance change measurements using the double pump–probe protocol with polarized pump pulses. With orthogonal-polarized pulses, the phonon amplitude is enhanced/suppressed if the second pump pulse is irradiated by a half-integer/integer multiple of the phonon period. This is contrary to the usual phononic interference (enhancement at integer multiples of the phonon period) observed when using parallel-polarized pulses. These observed results are well explained using a quantum-mechanical model in calculations involving the Raman tensor of the diamond lattice structure. The amplitude of the optical phonons generated via the off-diagonal term of Raman tensor is proportional to the product of the x- and y−components of the optical electric field. The phase of the phonon oscillations is dependent on the angle between the crystal orientation and the polarization of the pump pulse.

Separation of interface and substrate carrier dynamics at a heterointerface based on coherent phonons

Transient reflectivity spectroscopy is widely used to study ultrafast carrier- and phonon-dynamics in semiconductors. In their heterostructures, it is often not straightforward to distinguish contributions to the signal from the various layers. In this work, we perform transient reflectivity measurements on lattice-matched GaP/Si(001) using a near infrared pulse, to which GaP is transparent. The pump laser pulse can generate coherent longitudinal optical (LO) phonons both in the GaP overlayer as well as in the Si substrate which have distinct frequencies. This enables us to track the amplitude of the respective signal contributions as a function of GaP layer thickness $d$. The Si phonon amplitude in the signal exhibits an oscillatory behavior with increasing $d$. This can be quantitatively explained by the interference of the probe light reflected at the air/GaP/Si heterointerface. Based on this knowledge, we can then separate the interface- and the substrate-contributions in the carrier-induced non-oscillatory transient reflectivity signal. The obtained interface signal provides evidence for ultrafast carrier injection from the Si substrate into the GaP overlayer. This is also corroborated by examining the deviation of the polarization-dependence of the GaP coherent optical phonon signal from that of the bulk semiconductor.

Theory for coherent control of longitudinal optical phonons in GaAs using polarized optical pulses with relative phase locking

A theoretical model for the coherent control of longitudinal optical phonons in GaAs (001) by double-pulse excitation was derived using a simplified band model and the allowed and forbidden Raman scattering. The time evolution of the electron-phonon states was calculated with the density-matrix formalism and second-order perturbation. The amplitude of the longitudinal optical phonons controlled by the two pulses was obtained as a function of the delay between the pulses for several polarization conditions. For parallel-polarized pulses, electronic and phonon interference fringes were predicted, which were independent of the crystal orientation and the ratio between the allowed and forbidden Raman scattering intensities. For orthogonally polarized pulses, only phonon interference fringes were obtained at an angle of $\ensuremath{\pi}/4$ from the [100] direction. When one of the pulses was along the [100] direction, electronic interference fringes were induced by the allowed Raman scattering, although the pump pulses do not interfere themselves.

Calculation of Kapitza Resistance with Kinetic Equation

A new method for the calculation of interfacial thermal resistance in the case of heat transport through the interface by phonons is introduced herein. The novelty of the suggested approach consists of the consideration of all the consequences of a nonequilibrium character of phonon‐distribution functions during heat transfer. The well‐described diffuse mismatch model is used to introduce a model set of transmission and reflection amplitudes of phonons at the interface. An exact analytical solution for the proposed model is derived. Finally, the problem is solved for a set of transmission and reflection amplitudes characterized by a free parameter.

Generation and coherent control of terahertz acoustic phonons in superlattices of perovskite oxides

We utilized transmission-type pump–probe technique to investigate coherent acoustic phonons in the superlattices of perovskite oxides such as SrIrO3/SrTiO3 and SrRuO3/SrTiO3. Because the films in the superlattices are of high-quality and their thicknesses are only several monolayers, quasi-monochromatic acoustic phonons with THz frequency have been achieved. By investigating the propagation of coherent acoustic phonons in the superlattices with different epitaxial periods, the phonon mean free paths of SrTiO3 were studied in the frequency range between 0.5 THz and 1 THz. We further demonstrated coherent control to amplify or cease the THz coherent acoustic phonon oscillations in the superlattices. By controlling the delay of two pulses for shining the superlattices, the amplitude and phase of the THz coherent acoustic phonons were manipulated. According to the measurements of time-domain Brillouin scatterings, we found the optoacoustic conversion efficiency of SrIrO3 outperforms that of SrRuO3 for generating acoustic phonons.

Magnetic field enhanced detection of coherent phonons in a GaMnAs/GaAs film

Using a two-color time-resolved pump-probe spectroscopy scheme, we studied the generation and detection of longitudinal coherent acoustic phonons, generated by ultrafast laser pulses in a semiconductor heterostructure. Our structure was a $p$-doped, 100-nm-thick ferromagnetic GaMnAs layer grown on a GaAs substrate. By probing the transient reflectivity in the time domain, we observed a strong dependence of the coherent phonon's amplitude on the external magnetic field. Our theoretical model relates this dependence to the increase in the detectability of coherent phonons in the presence of external magnetic fields. This enhancement comes from the formation of Landau levels in the absorption spectrum and leads to large changes in the real and imaginary parts of the dielectric function with strain. When the probe laser energy is close to an allowed Landau-level transition, the detectability of the coherent phonons can be significantly enhanced. Our results suggest that not only can one increase the detection of coherent phonons with magnetic fields, one can also enhance the generation by tuning the wavelength of the pump laser pulse to coincide with a Landau-level resonance.

Modulation of the probe signal in coherent phonon detection revisited: Analytical and first-principles computational analyses

Modulation of probe signal in pump-probe measurements of coherent phonons in dielectrics, with and without spectral resolution, are investigated theoretically taking diamond as an example. Analytical investigation as well as first-principles calculations based on time-dependent density functional theory is utilized to clarify the mechanism of the modulation of the probe signals. Boundary and bulk effects are investigated systematically, putting emphasis on the phase relation between the modulation and the atomic motion of the coherent phonon. They are summarized as follows: Modulation by the boundary effect is in phase with the coherent phonon amplitude, while that by the bulk effect shows $\pi/2$ phase difference. Strong frequency dependence appears in the modulation by the bulk effect, while no frequency dependence by the boundary effect. First-principles calculations support the reliability of the analytical result.

Strong phonon-magnon coupling of an O/Fe(001) surface

Using density functional calculations, we elucidate the interaction between magnons and phonons on Fe(001) and O/Fe(001) surfaces. The effective Heisenberg exchange parameters between neighbor sites ( J i ) were derived by fitting the ab initio spin spiral dispersion relation to a classical Heisenberg model. In bulk Fe, J 5 b has a larger amplitude than J 2 b - J 4 b . Surface magnons were softer on the Fe(001) surface than in bulk, but were strengthened on the O/Fe(001) surface through strong interactions between the O and Fe atoms. The four calculated high-energy phonon modes of O/Fe(001) excellently agreed with the experimental measurements. The J 1 in O/Fe(001) decreased significantly with increasing phonon amplitude. Phonon-magnon coupling occurred more easily on O/Fe(001) than on Fe(001). The softening of the magnon on the O/Fe(001) with phonon amplitude was attributed to the reduced amplitude of longitudinal excitations. Magnetic moment of the Fe atom of the second layer (Fe2) was especially sensitive to phonon amplitude, regardless of the motion direction of the Fe2 atoms.