[Paper Review] Coherent Phonon-Driven Band Renormalizations in 1T$'$-MoTe$_2$

Carl E. Jensen, Christoph Emeis+4 more|arXiv (Cornell University)|Feb 23, 2026

2D Materials and Applications0 citations

TL;DR

The paper uses time- and angle-resolved photoemission with frequency-domain analysis to show band-selective coherent phonon–electron coupling in 1T′-MoTe2 and compares measured band renormalizations with ab initio calculations.

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.

Motivation & Objective

• Investigate band-selective electron–phonon coupling (EPC) in centrosymmetric 1T′-MoTe2 using time- and angle-resolved photoemission spectroscopy (tr-ARPES).
• Identify coherent A_g-symmetric phonon modes excited by near-infrared pulses and their coupling to electronic bands.
• Quantify band-renormalization amplitudes induced by specific phonon modes using PI (photoemission intensity) analysis and FM (first-moment) analysis.
• Compare experimental band-renormalization amplitudes with ab initio DFT/DFPT-based calculations and assess agreement and deviations.

Proposed method

• Perform tr-ARPES with 837 nm pump (1.5 eV) and 210 nm probe (5.9 eV) to excite and probe MoTe2 at room temperature.
• Apply frequency-domain ARPES (FDARPES) with pixel-by-pixel FFT to resolve mode-specific EPC signatures in I(k,E) maps.
• Use PI analysis to relate Fourier components to band renormalizations via F_PI ≈ −ΔE × ∂I/∂E and to extract ΔE through regression.
• Utilize ab initio calculations (DFT/DFPT) with Quantum ESPRESSO/EPW to generate time- and momentum-resolved spectral functions including coherent phonon effects, analyzed with the same FDARPES protocol for direct comparison.

Figure 1: (a) Schematic illustration of the tr-ARPES experiment. (b) Crystal structure of 1 T’ - $\mathrm{MoTe}_{2}$ . (c) First Brillouin zone of 1 T’ - $\mathrm{MoTe}_{2}$ with high symmetry points indicated. (d) Room-temperature ARPES spectrum at $h\nu=$5.9\text{\,}\mathrm{e}\mathrm{V}$$ (left pa

Experimental results

Research questions

• RQ1 How do specific A_g phonon modes (ν1, ν2, ν3) couple to distinct electronic bands in 1T′-MoTe2?
• RQ2 Can FDARPES disentangle band renormalizations from oscillations in spectral weight or linewidth to quantify ΔE?
• RQ3 Do ab initio calculations reproduce the observed band-selective EPC patterns and amplitudes observed experimentally?
• RQ4 What are the amplitudes and initial directions of coherent phonon-driven band renormalizations across identified ROIs?

Key findings

• Six FFT peaks corresponding to ν1=2.34 THz, ν2=3.34 THz, ν3=3.86 THz, ν4=4.81 THz, ν5=7.25 THz, and ν6=7.78 THz, matching AG phonon modes and agreeing with prior studies.
• Each electronic band shows distinct coupling strengths to ν1–ν3, e.g., band 1 dominated by ν1, band 2 by ν2, band 3 by ν2 with some ν5/ν6 contributions.
• PI analysis yields band renormalizations ΔE in the range of a few 100 μeV to ~1 meV experimentally, while ab initio values span ~0.5–4.0 meV, with experimental amplitudes typically smaller than theory.
• Ab initio calculations qualitatively reproduce the initial signs and relative amplitudes of band renormalizations; quantitative deviations attributed to analysis underestimation, kz offsets, excitation fluence uncertainties, and residual spectral-weight effects.
• Demonstrate strong qualitative agreement between experiment and theory and establish a framework for exploring EPC in quantum materials via FDARPES and first-principles methods.

Figure 2: (a) Tr-ARPES spectrum along $\Gamma$ -X at $\Delta t=$1.5\text{\,}\mathrm{p}\mathrm{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 spectr