Research Article

Transient dielectric function dynamics driven by coherent phonons in Bismuth crystal

¹ Laboratoire d’Optique Appliquée, ENSTA Paris, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91761 Palaiseau, France
² Institut de Physique de Rennes, CNRS, Université de Rennes, UMR 6251, Rennes, France

^* Corresponding author: davide.boschetto@ensta.fr

Received: 22 August 2024
Accepted: 10 October 2024

Abstract

In this study, we investigate the ultrafast transient dynamics of the dielectric function in bismuth crystal, excited by femtosecond laser pulses and modulated by coherent phonons. The primary aim is to understand the influence of the coherent A_1g phonon mode on the dielectric function and to characterize the nature of the quasi-steady state that persists for tens of picoseconds after the coherent oscillations vanish. Our findings reveal that the dielectric function undergoes damped oscillations corresponding to the A_1g phonon mode, with the real and imaginary parts of the dielectric function oscillating out of phase but sharing the same frequency and lifetime as the oscillatory component. Once the oscillations vanish, the system reaches a quasi-steady state around 20 ps after excitation. In this state, the dielectric function deviates significantly from the values expected for the liquid phase, indicating that no phase transition occurs, even though the calculated lattice temperature exceeds the melting point of bismuth. To probe the nature of this quasi-steady state, we compare the transient dielectric function to equilibrium ellipsometry measurements taken at various temperatures, ranging from room temperature to temperatures approaching the melting point. This comparison allows us to estimate the real and imaginary parts of the dielectric function as a function of temperature, particularly in a warmed state, where the crystal temperature is elevated but still below the melting threshold. The comparison reveals a clear discrepancy between the dielectric function values in the quasi-steady state and those measured in a thermally equilibrated warmed state. This suggests that the quasi-steady state cannot be solely attributed to crystal heating. Instead, we propose that the persistence of the quasi-steady state is because electron-hole recombination has not fully occurred within the measured time range.