Electron-Vibration Coupling in Molecular Materials: Assignment of Vibronic Modes from Photoelectron Momentum Mapping

Electron-phonon coupling is one of the most fundamental effects in condensed matter physics. We here demonstrate that photoelectron momentum mapping can reveal and visualize the coupling between specific vibrational modes and electronic excitations. When imaging molecular orbitals with high energy resolution, the intensity patterns of photoelectrons of the vibronic sidebands of molecular states show characteristic changes due to the distortion of the molecular frame in the vibronically excited state. By comparison to simulations, an assignment of specific vibronic modes is possible, thus providing unique information on the coupling between electronic and vibronic excitation.

Figure 1

(a) Momentum-integrated EDCs of 1 ML coronene on Au(111) recorded at a sample temperature of 15 K (red data points). The HOMO signal consists of three components (indicated by arrows). The corresponding data derived from a clean Au(111) sample considering the backfolding on the $4\times 4$ superstructure of the adsorbate are plotted in black [see Fig. 2 and the corresponding text for details]. (b) Experimental spectrum derived from a short scan (red data points), fitted by a vibrational progression consisting of three equally spaced Voigt peaks of identical line width (black solid curves) and a linear background (black dotted line).

Figure 2

(a)–(c) Photoelectron momentum maps of the HOMO of $\mathrm{coronene}/\mathrm{Au}(111)$ recorded at the energy of the (0-0) peak and the vibronic sidebands (0-1) and (0-2). (d) Simulated background from the Au substrate derived by backfolding of a momentum map of a clean Au(111) sample (recorded at $E_B=1.95\mathrm{eV}$; see Fig. S1 in Supplemental Material [18]) on the $4\times 4$ superstructure of the adsorbate (see the text for details). The color scaling of the intensity was chosen individually to optimize the contrast.

Figure 3

Simulated photoelectron momentum maps derived for the Dyson orbital of (a) the ${\mathrm{coronene}}^{+}$ HOMO with the nuclei in equilibrium position and (b) the HOMO of the distorted ${\mathrm{coronene}}^{+}$ at a mean displacement amplitude of 0.15 Å according to the $A_g$ mode at 196 meV. (c) Illustration of the geometric relaxation of an isolated coronene molecule upon ionization. The point group symmetry is reduced from $D_{6h}$ to $D_{2h}$. Red arrows show the change in nuclear equilibrium positions enhanced by a factor of 50 for better visualization. The black dotted lines mark planes of symmetry, indicating an $A_g$ symmetry of the distorted molecule. (d) Illustration of the respective $A_g$ mode. The dark image indicates the undistorted molecule and is overlaid by a lighter image depicting the vibronic displacement. The associated force vectors are indicated as elongated red arrows.