Amplitude dynamics of the charge density wave in LaTe3 : Theoretical description of pump-probe experiments

Abstract

We formulate a dynamical model to describe a photo-induced charge density wave (CDW) quench transition and apply it to recent multi-probe experiments on LaTe3 [A. Zong et al., Nat. Phys. 15, 27 (2019)]. Our approach relies on coupled time-dependent Ginzburg-Landau equations tracking two order parameters that represent the modulations of the electronic density and the ionic positions. We aim at describing the amplitude of the order parameters under the assumption that they are homogeneous in space. This description is supplemented by a three-temperature model, which treats separately the electronic temperature, temperature of the lattice phonons with stronger couplings to the electronic subsystem, and temperature of all other phonons. The broad scope of available data for LaTe3 and similar materials as well as the synergy between different time-resolved spectroscopies allow us to extract model parameters. The resulting calculations are in good agreement with ultrafast electron diffraction experiments, reproducing qualitative and quantitative features of the CDW amplitude evolution during the initial few picoseconds after photoexcitation.

Nonequilibrium charge-density-wave order beyond the thermal limit

“…This leaves us with only two global fit parameters for the simulations: damping γ and scaling s in the nonthermal regime (see Supplementary Note 1 for details of the model). For the timescale connecting both regimes, we find a good description of the data by choosing the lattice thermalization time τ ph−ph = 2.2 ps reported for the closely related compound LaTe 3 27 . Energy redistribution processes within the electron and lattice systems are often modeled by a three temperature model (3TM) 51 , 52 , as presented in Fig.…”

“…Near the transition temperature, the order parameter can be approximated by the Landau theory of second-order phase transitions 2 . Thus, to simulate the dynamics of the order parameter in TbTe 3 , we make the following ansatz for the effective potential energy surface (in dimensionless units) based on time-dependent Ginzburg–Landau (tdGL) theory 11 , 27 , 37 , 49 , 50 : Upon perturbation, the dynamics of the order parameter are determined by the equation of motion derived from Eq. ( 1 ) (see Supplementary Note 1 ).…”

“…c 3TM of electronic, hot phonon and lattice temperatures T e , T hot−ph and T l in the regime of strong perturbation ( F = 0.35 mJ cm −2 ). In the 3TM, the optical excitation of the electronic system is followed by an energy transfer to certain strongly coupled optical phonons, widely observed in materials with selective electron-phonon coupling 27 , 51 , 52 , 61 – 63 . Subsequently, this hot phonon subset equilibrates with the remaining lattice phonon bath on a ps timescale ( τ ph−ph ).…”

“…The black dashed line indicates the rescaled critical temperature . In the 3TM simulations, material properties of the related compound LaTe 3 27 were used. …”

“…While mean field theory captures the phase transition on a qualitative level, thermal lattice fluctuations reduce the critical temperature T c of long-range 3D order significantly below the predicted mean field value T MF 1 , 2 . It is of strong interest how our understanding of phase transitions in the adiabatic limit can be adapted to a nonequilibrium, dynamical setting induced by an impulsive excitation 11 , 23 – 27 . It remains an open question whether the thermal transition temperature is still a relevant quantity in the description of such an out-of-equilibrium state, and which parameters permit transient control of T c 20 , 28 – 32 .…”