Electronic correlation effects in superconducting picene from ab initio calculations

We show, by means of ab initio calculations, that electron-electron correlations play an important role in potassium-doped picene (K${}_x$-picene), recently characterized as a superconductor with $T_c=18\text{K}$. The inclusion of exchange interactions by means of hybrid functionals reproduces the correct gap for the undoped compound and predicts an antiferromagnetic state for $x=3$, where superconductivity has been observed. These calculations, which do not require us to assume a value for the interaction strength, indirectly suggest that these materials should have a sizable ratio between the effective Coulomb repulsion $U$ and the bandwidth. This is fully compatible with simple estimates of this ratio. Using these values of $U$ in a simple effective Hubbard model, an antiferromagnetic state is indeed stabilized. Our results highlight the similarity between potassium-doped picene and alkali-doped fulleride superconductors.

Figure 1

Schematic arrangement of two inequivalent picene molecules ($A$ and $B$) along the $a$,$b$ planar molecular axes in (a) pristine and (b) doped molecular crystals.

Figure 2

Results for pristine picene: Panel (a) presents the PBE band structure; panel (b) shows the density of states calculated with PBE, HSE, and B3LYP functionals. The energies are plotted along lines in the Brillouin zone connecting points $\Gamma =(0,0,0)$, $X=(\frac{1}{2},0,0)$, $M=(\frac{1}{2},\frac{1}{2},0)$, $L=(\frac{1}{2},0,\frac{1}{2})$. The zero of the energy is at the Fermi level.

Figure 3

Results for ${\mathrm{K}}_3$-picene restricted to the energy region close to the Fermi level: (a) shows the PBE band structure, while (b) presents the density of states calculated with PBE (nonmagnetic), compared with HSE both in nonmagnetic and AFM states (b). The energies are plotted along lines in the Brillouin zone connecting points $\Gamma =(0,0,0)$, $X=(\frac{1}{2},0,0)$, $M=(\frac{1}{2},\frac{1}{2},0)$, $L=(\frac{1}{2},0,\frac{1}{2})$. The zero of energy is at the Fermi level.