Molecular Fingerprints in the Electronic Properties of Crystalline Organic Semiconductors: From Experiment to Theory

By comparing photoemission spectroscopy with a nonperturbative dynamical mean field theory extension to many-body ab initio calculations, we show in the prominent case of pentacene crystals that an excellent agreement with experiment for the bandwidth, dispersion, and lifetime of the hole carrier bands can be achieved in organic semiconductors, provided that one properly accounts for the coupling to molecular vibrational modes and the presence of disorder. Our findings rationalize the growing experimental evidence that even the best band structure theories based on a many-body treatment of electronic interactions cannot reproduce the experimental photoemission data in this important class of materials.

Figure 1

(a) Color density plot of experimental ARPES data. The second derivative of the data has been taken to best visualize the energy positions of the dispersive features. The (green) dots are the peak positions as derived from Gaussian fits of the individual spectra. The (blue) square corresponds to a scan with a different incoming photon energy, which recovers the $H2$ spectral weight around $\overline{\Gamma }$ that is hidden due to the matrix element dependence on the photon incoming energy (see the Supplemental Material [18]). The gray line is the ab initio band dispersion from Ref. 19. (b) Calculated spectrum in the presence of EMV interactions and disorder (see text). The dots are the experimental peak positions from panel (a). (c) Theoretical HOMO band dispersion, as obtained from the poles of the spectral function. Ab initio (light gray), disordered (black: $\Delta =75\mathrm{meV}$, $E_P=0$), and with EMV interactions (dark gray [red]: $\Delta =75\mathrm{meV}$, $E_P=69\mathrm{meV}$). The inset shows the corresponding path in the Brillouin zone.

Figure 2

(a) Photoemission spectrum measured at the $\overline{M}$ point. The dashed line is a fit of the data with three Gaussian peaks. (b) Calculated spectrum and fit. Parameters are $E_P=69\mathrm{meV}$ and $\Delta =75\mathrm{meV}$. $W$ is the total bandwidth defined as the distance between the $H1$ and $H2$ peak. (c) The fine structure induced by the EMV interaction is unveiled by removing the disorder in the calculation. (d) The calculated spectrum in the absence of EMV interactions, but with the same degree of disorder. In (b), (c), and (d) the spectrum has been convoluted with a Gaussian of $\mathrm{FWHM}=40\mathrm{meV}$ to mimic the experimental resolution.

Figure 3

(a) Calculated HOMO bandwidth as a function of the EMV coupling strength for different values of the disorder parameter. The shaded area is the measured value (see text). The horizontal bar indicates the range of calculated $E_P$ values in the literature. (b) Renormalization of the $H1$ band along Pa2 ($\overline{M}\mathrm{\text{−}}\overline{\Gamma }$ distance, see Fig. 1). The dashed line is the polaronic renormalization expected in the molecular limit.