Photoexcited Bismuth Research Articles

Transient dielectric function dynamics driven by coherent phonons in Bismuth crystal

In this study, we investigate the transient dynamics of the dielectric function in photoexcited bismuth using a double-probe experiment. We demonstrate how the A1g coherent phonon mode influences both the real and imaginary components of the dielectric function, extending to a quasi-steady state. Additionally, we compare this transient behavior to ellipsometry measurements taken at varying crystal temperatures under equilibrium conditions. Our findings reveal that bismuth crystals, when excited by femtosecond laser pulses, enter a quasi-stationary state that follows the coherent phonon oscillations. This transient state is distinct from a liquid phase or a simple thermalized state. We interpret this quasi-steady state as a heated, excited state where electron-hole recombination has not yet occurred.

Coherent energy exchange between carriers and phonons in Peierls-distorted bismuth unveiled by broadband XUV pulses

In Peierls-distorted materials, photoexcitation leads to a strongly coupled transient response between structural and electronic degrees of freedom, always measured independently of each other. Here we use transient reflectivity in the extreme ultraviolet to quantify both responses in photoexcited bismuth in a single measurement. With the help of first-principles calculations based on density-functional theory (DFT) and time-dependent DFT, the real-space atomic motion and the temperature of both electrons and holes as a function of time are captured simultaneously, retrieving an anticorrelation between the ${A}_{1g}$ phonon dynamics and carrier temperature. The results reveal a coherent, bidirectional energy exchange between carriers and phonons, which is a dynamical counterpart of the static Peierls-Jones distortion, providing validation of previous theoretical predictions.

Measurements of nonequilibrium interatomic forces using time-domain x-ray scattering

We determine experimentally the excited-state interatomic forces in photoexcited bismuth. The forces are obtained by a constrained least-squares fit of the excited-state dispersion obtained by femtosecond time-resolved x-ray diffuse scattering to a fifteen-nearest neighbor Born-von Karman model. We find that the observed softening of the zone-center $A_{1g}$ optical mode and transverse acoustic modes with photoexcitation are primarily due to a weakening of three nearest neighbor forces along the bonding direction. This provides a more complete picture of what drives the partial reversal of the Peierls distortion previously observed in photoexcited bismuth.

Towards jitter-free ultrafast electron diffraction technology

Stroboscopic visualization of nuclear or electron dynamics in atoms, molecules or solids requires ultrafast pump and probe pulses and a close to perfect synchronization between the two. We have developed a 3 MeV ultrafast electron diffraction (UED) probe technology that nominally reduces the electron bunch duration and the arrival time jitter to the subfemtosecond level. This simple configuration uses a radiofrequency photogun and a 90° achromatic bend and is designed to provide effectively jitter-free conditions. Terahertz streaking measurements reveal an electron bunch duration of 25 fs, even for a charge as high as 0.6 pC, and an arrival time jitter of 7.8 fs, the latter limited by only the measurement accuracy. From pump–probe measurements of photoexcited bismuth films, the instrument response function was determined to be 31 fs. This pioneering jitter-free technique paves the way towards UED of attosecond phenomena in atomic, molecular and solid-state dynamics. An ultrafast electron diffraction facility with an overall temporal resolution of 31 fs root mean square is developed. Even for a charge as high as 0.6 pC, the electron bunch duration and timing jitter are 25 fs and less than 10 fs, respectively.

Transient FTIR Measurements at Nanoseconds Resolution: Correlating between Faceting and Photocatalytic Activity in BiOCl

Transient IR measurements of photo-excited bismuth oxychloride (BiOCl) were performed by a step-scan technique at a resolution of 2.5 nanoseconds. Six types of faceted BiOCl particles, which differed also in their average size, were used. Following excitation, an increase in the intensity of the Bi-O signal, which lasted for 70–130 nanoseconds was observed. A negative correlation between the characteristics of the transient signal (duration of signal and intensity) versus the photocatalytic activity toward the reduction of Cr(VI) was found. In parallel, a positive correlation was found between the duration of the transient signal and the specific surface area of the various types of particles. The increased transient intensity is explained in terms of formation of deep traps, most likely at the surface of the particles. The results demonstrate that transient vibrational spectroscopy may serve as an important tool for studying photocatalytic materials.

Femtosecond reflectivity study of coherent phonons in doubly photoexcited bismuth

Ultrafast optical excitation generates coherent A1g optical phonons in bismuth via the mechanism of displacive excitation of coherent phonons (DECP). Here, femtosecond pump-probe reflectivity spectroscopy examines the dynamics of coherent phonons in doubly photoexcited bismuth. Two successive pump pulses are employed to generate optic phonons and thus to investigate the phonon dynamics including bond softening and dephasing with variable pump fluence and inter-pump separation times. Combined with thermal analysis, it distinguishes thermal and nonthermal effects of photoexcitation on the phonon dynamics. It also reveals that photocarriers relax via electron-hole recombination and diffusion out of the optical penetration depth on ultrafast timescales of 10–20 ps.

Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon.

We report channel-resolved measurements of the anharmonic coupling of the coherent A_{1g} phonon in photoexcited bismuth to pairs of high wave vector acoustic phonons. The decay of a coherent phonon can be understood as a parametric resonance process whereby the atomic displacement periodically modulates the frequency of a broad continuum of modes. This coupling drives temporal oscillations in the phonon mean-square displacements at the A_{1g} frequency that are observed across the Brillouin zone by femtosecond x-ray diffuse scattering. We extract anharmonic coupling constants between the A_{1g} and several representative decay channels that are within an order of magnitude of density functional perturbation theory calculations.

Carrier confinement and bond softening in photoexcited bismuth films

Femtosecond pump-probe spectroscopy of bismuth thin films has revealed strong dependencies of reflectivity and phonon frequency on film thickness in the range of $25\ensuremath{-}40\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$. The reflectivity variations are ascribed to distinct electronic structures originating from strongly varying electronic temperatures and proximity of the film thickness to the optical penetration depth of visible light. The phonon frequency is redshifted by an amount that increases with decreasing film thickness under the same excitation fluence, indicating carrier density-dependent bond softening that increases due to suppressed diffusion of carriers away from the photoexcited region in thin films. The results have significant implications for nonthermal melting of bismuth as well as lattice heating due to inelastic electron-phonon scattering.

First-principles calculation of femtosecond symmetry-breaking atomic forces in photoexcited bismuth.

We present a first-principles method for the calculation of the polarization-dependent atomic forces resulting from optical excitation in a solid. We calculate the induced force driving the E(g) phonon mode in bismuth immediately after absorption of polarized light. When radiation with polarization perpendicular to the c axis is absorbed, the photoexcited charge density breaks the threefold rotational symmetry, leading to an atomic force component perpendicular to the axis. We calculate the initial excited electronic distribution as a function of photon energy and polarization and find the resulting atomic force components parallel and perpendicular to the axis. The magnitude of the calculated force is in excellent agreement with that derived from recent measurements of the amplitude of E(g) atomic motion and the decay time of several femtoseconds for the driving force.

Direct observation of electron thermalization and electron-phonon coupling in photoexcited bismuth

We investigate the ultrafast response of the bismuth (111) surface by means of time-resolved photoemission spectroscopy. The direct visualization of the electronic structure allows us to gain insights on electron-electron and electron-phonon interaction. Concerning electron-electron interaction, it is found that electron thermalization is fluence dependent and can take as much as several hundreds of femtoseconds at low fluences. This behavior is in qualitative agreement with Landau's theory of Fermi liquids, but the data show deviations from the behavior of a common three-dimensional degenerate electron gas. Concerning electron-phonon interaction, our data allows us to directly observe the coupling of Bloch states to the coherent ${A}_{1g}$ mode. It is found that surface states are much less coupled to this mode when compared to bulk states. This is confirmed by ab initio calculations of surface and bulk bismuth.

Time- and momentum-resolved probe of heat transport in photo-excited bismuth

We use time- and momentum-resolved x-ray scattering to study thermalization in a photo-excited thin single crystal bismuth film on sapphire. The time-resolved changes of the diffuse scattering show primarily a quasi-thermal phonon distribution that is established in ≲100ps and that follows the time-scale of thermal transport. Ultrafast melting measurements under high laser excitation show that epitaxial regrowth of the liquid phase occurs on the time-scale of thermal transport across the bismuth-sapphire interface.

Free-carrier relaxation and lattice heating in photoexcited bismuth

We report ultrafast surface pump and interface probe experiments on photoexcited carrier transport across single crystal bismuth films on sapphire. The film thickness is sufficient to separate carrier dynamics from lattice heating and strain, allowing us to investigate the time scales of momentum relaxation, heat transfer to the lattice, and electron-hole recombination. The measured electron-hole ($e\ensuremath{-}h$) recombination time is 12--26 ps and ambipolar diffusivity is 18--40 cm${}^{2}$/s for carrier excitation up to $\ensuremath{\sim}{10}^{19}{\text{cm}}^{\ensuremath{-}3}$. By comparing the heating of the front and back sides of the film, we put lower limits on the rate of heat transfer to the lattice, and by observing the decay of the plasma at the back of the film, we estimate the time scale of electron-hole recombination. We interpret each of these time scales within a common framework of electron-phonon scattering and find qualitative agreement between the various relaxation times observed. We find that the carrier density is not determined by the $e\ensuremath{-}h$ plasma temperature after a few picoseconds. The diffusion and recombination become nonlinear with initial excitation $\ensuremath{\gtrsim}{10}^{20}{\text{cm}}^{\ensuremath{-}3}$.

Coherent Phonon Coupling to Individual Bloch States in Photoexcited Bismuth

We investigate the temporal evolution of the electronic states at the bismuth (111) surface by means of time- and angle-resolved photoelectron spectroscopy. The binding energy of bulklike bands oscillates with the frequency of the A(1g) phonon mode, whereas surface states are insensitive to the coherent displacement of the lattice. A strong dependence of the oscillation amplitude on the electronic wave vector is correctly reproduced by ab initio calculations of electron-phonon coupling. Besides these oscillations, all the electronic states also display a photoinduced shift towards higher binding energy whose dynamics follows the evolution of the electronic temperature.

Thermalization of photoexcited carriers in bismuth investigated by time-resolved terahertz spectroscopy andab initiocalculations

The charge carrier dynamics of photoexcited bismuth generates a Drude response that evolves over time. Our data show that the plasma frequency of bismuth displays an initial increase and a subsequent decay. We have performed ab initio calculations on bulk bismuth within the density functional theory and show that this peculiar behavior is due to local extrema in the valence and conduction bands. It follows that most of the carriers first accumulate in these extrema and reach the Fermi level only 0.6 ps after the photoexcitation.

Investigation of ultrafast processes in photoexcited bismuth by broadband probing in the wavelength range 0.4–0.9 μm

The decay of the photoexcited state of a bismuth single crystal is investigated in the wavelength range from 400 to 900 nm by means of femtosecond laser reflection spectroscopy. Oscillations produced by coherent fully symmetric A1g phonons have been detected in the photoinduced response, along with a relaxation component. The dynamics of the electronic subsystem of the crystal is shown to be characterized by three values of the decay time: 1 ps, 7 ps, and ∼1 ns. The spectral dependence of the reflectivity oscillation amplitude has been measured; the possible cause of the shape of the derived curve is described.

Effect of lattice anharmonicity on high-amplitude phonon dynamics in photoexcited bismuth

Separate theoretical and experimental investigations of the effect of lattice anharmonicity on the ${A}_{1g}$ phonon dynamics in photoexcited bismuth are presented. First-principles density functional calculations show that the anharmonic contribution to the phonon period is negligible for an excitation of 1.25% or less of the valence electrons, corresponding to electronic frequency softening from $2.9\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}2.3\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$. Experiments using optical double-pump-probe excitation of coherent phonon motion clearly separate the role of lattice anharmonicity from electron-hole plasma and other dynamics, confirming that the effect of anharmonicity on the phonon period is much smaller than the observed softening.

Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit

The study of phase-transition dynamics in solids beyond a time-averaged kinetic description requires direct measurement of the changes in the atomic configuration along the physical pathways leading to the new phase. The timescale of interest is in the range 10(-14) to 10(-12) s. Until recently, only optical techniques were capable of providing adequate time resolution, albeit with indirect sensitivity to structural arrangement. Ultrafast laser-induced changes of long-range order have recently been directly established for some materials using time-resolved X-ray diffraction. However, the measurement of the atomic displacements within the unit cell, as well as their relationship with the stability limit of a structural phase, has to date remained obscure. Here we report time-resolved X-ray diffraction measurements of the coherent atomic displacement of the lattice atoms in photoexcited bismuth close to a phase transition. Excitation of large-amplitude coherent optical phonons gives rise to a periodic modulation of the X-ray diffraction efficiency. Stronger excitation corresponding to atomic displacements exceeding 10 per cent of the nearest-neighbour distance-near the Lindemann limit-leads to a subsequent loss of long-range order, which is most probably due to melting of the material.