Vibrational spectrum and electron-phonon coupling of doped solid picene from first principles

We study superconductivity in doped solid picene (C${}_{22}$H${}_{14}$) with linear response calculations of the phonon spectrum and electron-phonon ($\mathit{ep}$) interaction. We show that the coupling of the high-energy C bond-stretching phonons to the $\pi$ molecular orbitals for a doping of $~$3 electrons per picene molecule is sufficiently strong to reproduce the experimental $T_c$ of 18 K within Migdal-Eliashberg theory. For hole doping, we predict a similar coupling leading to a maximum $T_c$ of 6 K. However, we argue that, due to its molecular nature, picene may belong to the same class of strongly correlated $\mathit{ep}$ superconductors as fullerides. We propose several experimental tests for this hypothesis and suggest that intercalated hydrocarbons with different arrangements and numbers of benzene rings may be used to study the interplay between $\mathit{ep}$ interaction and strong electronic correlations in the highly nonadiabatic limit.

Figure 1

Calculated LDA electronic structure of solid picene. In green (light gray) and blue (dark gray) we show the two HOMO and the four LUMO${}^{*}$ derived bands, respectively, which are accessible by hole or electron doping. $n$ is the maximum number of electrons per picene molecule that can be doped. The two insets show the unit cell of solid picene in the $\mathit{xy}$ plane (left) and its Brillouin zone (right).

Figure 2

Vibrational properties of picene. (Top to bottom) Partial C and H contribution to the phonon eigenvectors of a picene molecule. Phonon DOS of (undoped) solid picene with numbers that mark the energy position of selected modes, whose $\Gamma$-point eigenvectors are shown in the bottom panel. For clarity, only one picene molecule is shown. Modes $4$ and $5$ give the highest contribution to the $\mathit{ep}$ coupling, shown in Fig. 3.

Figure 3

(Top) Spectral distribution of the $\mathit{ep}$ matrix elements of solid picene, doped with holes (green/light gray) or electrons (blue/dark gray). The two insets show the doping dependence of the corresponding $\mathit{ep}$ coupling strength $V_{\mathrm{ep}}=\int {\omega }^{-1}{\stackrel{̲}{\alpha }}^{2}F(\omega )\mathrm{d}\omega$ for different values of doping $x$. (Bottom) Electronic DOS per picene molecule, in states/(eV spin) as a function of doping $x$. The total $\mathit{ep}$ coupling constant $\lambda$ as a function of doping is given by $\lambda (x)=N(x)V_{\mathrm{ep}}$.