Fig. 2: Fluence-dependent phonon dynamics and electronic order recovery.
From: Phonon-assisted formation of an itinerant electronic density wave
a Time-resolved total displacement \({A}_{{{{{{{\mathrm{tot}}}}}}}}\left(t\right)\) normalized by the ground state periodic lattice distortion (PLD) amplitude \({A}_{{{{{{{\mathrm{tot}}}}}}}}\left(t\right){/A}_{{{{{{{\mathrm{tot}}}}}}},{{{{{{\mathrm{GS}}}}}}}}\) (proportional to the X-ray satellite-peak intensity) as a function of the laser pump fluence shown as a color scale difference (color scale shown above the graph). b The amplitude of the transient order parameter, \({A}_{\psi }\left(t\right)\), normalized by the amplitude in the ground state, \({A}_{\psi ,{GS}}=\) \({A}_{{{{{{{\mathrm{tot}}}}}}},{{{{{{\mathrm{GS}}}}}}}}\), and shown for three different incident fluences: 1 mJ/cm2 (blue), 3 mJ/cm2 (green), and 5 mJ/cm2 (red). The inset shows the transient PLD amplitude for all fluences measured in a as a color scale difference (color scale shown above the right inset). c The spin density wave (SDW) quench amount \(\Delta {A}_{\psi }={A}_{\psi }\left(0{{{{{{\mathrm{ps}}}}}}}\right)-{A}_{\psi }\left(0.1{{{{{{\mathrm{ps}}}}}}}\right)\) (blue squares: data from a and green circles: higher statistics data) and the recovery amount (orange stars) determined from the transient PLD amplitude shown in b. The amplitude of the phonons (standing wave) Aph is also shown (magenta crosses). d The recovery time determined as the area indicated in the left inset in b, where \({\widetilde{A}}_{\psi }\)= [\(\left.{{A}_{\psi }\left(t-0.1{{{{{{\mathrm{ps}}}}}}}\right)-{A}_{\psi }\left(0.1{{{{{{\mathrm{ps}}}}}}}\right)}\right]/\left[{A}_{\psi }\left(2{{{{{{\mathrm{ps}}}}}}}\right)-{A}_{\psi }\left(0.1{{{{{{\mathrm{ps}}}}}}}\right)\right]\) is integrated from 0 to 1 ps. We choose the area because the exponential fit poorly reproduces the data at higher fluences due to the shoulder feature and the flat region. The uncertainty in b, c, d is estimated as the standard deviation of the data at time delays above 1 ps, where we expect the residual between the harmonic oscillator fit and the data to be zero.
