Coherent Phonon-Driven Band Renormalizations in 1T$'$-MoTe$_2$

Abstract

Here, we investigate phonon mode- and electron band-selective electron-phonon couplings in centrosymmetric 1T$'$-MoTe$_2$ using time- and angle-resolved photoemission spectroscopy combined with frequency-domain analysis. Femtosecond near-infrared pulses excite coherent $A_g$-symmetric phonon modes at 2.34 THz, 3.34 THz, and 3.86 THz, which manifest as oscillatory modulations in photoemission intensity and binding energy across the valence bands. Pixel-wise Fourier analysis using recently developed methodologies reveals pronounced band selectivity with distinct coupling strengths for different electronic states and phonon modes, enabling the evaluation of band-renormalization amplitudes in the range of few meV. Ab initio calculations qualitatively reproduce the experimentally observed coupling patterns and relative trends, demonstrating the capability of combined experimental and theoretical approaches to resolve ultrafast electron-phonon interactions in quantum materials.

Figures (5)

• Figure 1: (a) Schematic illustration of the tr-ARPES experiment. (b) Crystal structure of 1T'-$\mathrm{MoTe}_2$. (c) First Brillouin zone of 1T'-$\mathrm{MoTe}_2$ with high symmetry points indicated. (d) Room-temperature ARPES spectrum at $h\nu=5.9eV$ (left panel) and spectral function calculated from the DFT band structure (right panel) along the $\Gamma$-X direction. The experimental data is overlayed with the DFT band structure (dashed lines). $k_{\parallel}$ denotes the electron wave vector parallel to the sample surface. (e) Calculated phonon dispersions of 1T'-$\mathrm{MoTe}_2$. A$_g$-symmetric phonon modes that are coherently excited and observed in the experiment are marked in red.
• Figure 2: (a) Tr-ARPES spectrum along $\Gamma$-X at $\Delta t=1.5p s$. To highlight the nonequilibrium response to photoexcitation, a tr-ARPES spectrum recorded at negative $\Delta t$ has been subtracted from the raw data. Red (blue) regions denote gain (loss) of spectral weight relative to the equilibrium state. The ROIs marked in green, red, and turquoise indicate different electronic bands. (b) Difference EDCs at $k_{\parallel}\approx 0.18{\angstrom^{-1}}$ as a function of $\Delta t$. The grey shaded area marked in (a) indicates the momentum range that was used for integration. The oscillations in photoemission hint to the excitation of coherent phonons. (c) Transient integral photoemission intensities for $\Delta t>1p s$ from the three ROIs marked in (a). (d) Normalized Fourier spectra of the transients in (c), revealing band-specific couplings to different coherent phonon modes.
• Figure 3: FDARPES maps for the three coherent phonon modes ($\nu_1$, $\nu_2$, $\nu_3$) dominating the electronic response. The data are overlaid with DFT band structures for comparison (dashed lines). The color intensity is a measure of the Fourier amplitude, while the color coding represents its sign, so that both strength and phase of the response of the electronic system to the phonon excitation are depicted.
• Figure 4: (a) Selected energy-momentum region of the ARPES data $I(k,E)$ shown in Fig. 1(d). (b) Energy gradient $\partial I(k,E)/\partial E$ as a function of energy and momentum of the data shown in (a). (c) FDARPES map for the $\nu_1$ mode in the energy-momentum region covered by the ARPES data in (a). (d), (e) Comparison of $I(E)$, $\partial I(k,E)/\partial E$, and $F_\mathrm{PI}$ along the grey shaded areas marked in Figs. (a)--(c). The discussion in the text focuses on ROI A (d) and B (e) marked in purple and green. All data in (d) and (e) are normalized to their maximum value.
• Figure 5: (a), (d) Results of the PI analysis of the experimental data for $\nu_1$ (a) and $\nu_2$ (d). (b), (e) Corresponding results of the PI analysis of the theory data for comparison. (c), (f) ab initio data of the band renormalization used to generate the data shown in (b) and (e). The dashed lines in the figures indicate an avoided crossing in the band structure as deduced from the band structure mask determined from the experimental FDARPES data [(a), (d)] and the DFT band structure [(b), (c), (e), (f)]. The evaluated energy shifts $\Delta E$ due to band renormalizations are superimposed with a mask derived from an edge detection applied to the corresponding FDARPES maps and the photoemission intensity to highlight only contributions to the data near or in the vicinity of electronic bands. The five ROIs (A--D) marked in (a)--(f) indicate different electronic bands. (g), (h) Amplitudes of $\Delta E$, determined from the respective average value in the ROIs A--E in (a) and (d) as well as (c) and (f). The experimental values are scaled with the mean ratio between the experimental and theoretical values. Black points show the ab initio values of the amplitudes in the ROIs displayed (c) and (f).