Crystal structure search and electronic properties of alkali-doped phenanthrene and picene

Alkali-doped aromatic compounds have shown evidence of metallic and superconducting phases whose precise nature is still mysterious. In potassium and rubidium-doped phenanthrene, superconducting temperatures around 5 K have been detected, but such basic elements as the stoichiometry, crystal structure, and electronic bands are still speculative. We seek to predict the crystal structure of ${\mathrm{M}}_3$-phenanthrene (M = K, Rb) using ab initio evolutionary simulation in conjunction with density functional theory (DFT), and find metal but also insulator phases with distinct structures. The original $P{2}_1$ herringbone structure of the pristine molecular crystal is generally abandoned in favor of different packing and chemical motifs. The metallic phases are frankly ionic with three electrons acquired by each molecule. In the nonmagnetic insulating phases the alkalis coalesce reducing the donated charge from three to two per phenanthrene molecule. A similar search for ${\mathrm{K}}_3$-picene yields an old and a new structure, with unlike potassium positions and different electronic bands, but both metallic retaining the face-to-edge herringbone structure and the $P{2}_1$ symmetry of pristine picene. Both the new ${\mathrm{K}}_3$-picene and the best metallic ${\mathrm{M}}_3$-phenanthrene are further found to undergo a spontaneous transition from metal to antiferromagnetic insulator when spin polarization is allowed, a transition which is not necessarily real, but which underlines the necessity to include correlations beyond DFT. Features of the metallic phases that may be relevant to phonon-driven superconductivity are underlined.

Figure 1

(a) DFT-PBE total energy per dimolecular cell of over 1500 structures of ${\mathrm{K}}_3{\mathrm{C}}_{14}{\mathrm{H}}_{10}$ $({\mathrm{K}}_3$-PA) with 54 atoms/cell. (b) Total energy evolution with increasing generation number.

Figure 2

Crystal structures of the ${\mathrm{M}}_3$-PA low energy structures, obtained assuming two PA molecules and six K or Rb atoms per cell. PS is the previous $P{2}_1$ symmetry herringbone structure of de Andres et al. [11], chosen as reference. Structure EA1 (metallic) is a first evolution of PS; EA2 (insulating) and EA3 (metallic) are the two lowest energy structural polymorphs. All have a lower $P_1$ symmetry, but differ by arrangement and shape details of the phenanthrene molecules, and by the positions of the alkalis. Note that approximately defined molecular planes are nearly orthogonal in EA2, but have turned parallel in EA3, which represents our best candidate metallic (possibly superconducting) phase.

Figure 3

Cell volume and enthalpy of the most stable ${\mathrm{K}}_3$-PA and ${\mathrm{Rb}}_3$-PA candidate structures. After a DFT-PBE genetic search, the lowest energy structures were refined with vdW functionals or with increasing pressure.

Figure 4

DFT-PBE electronic band structure of various ${\mathrm{K}}_3$-PA crystal structures. Among the two best structures EA2 and EA3, EA2 is a nonmagnetic band insulator, where the two uppermost filled bands have molecular LUMO character, the lowest unfilled bands a LUMO+1 character, and the filled band emphasized in red is a shared orbital within the six alkali atoms in the cell. EA3 instead is the best metallic structure with partly degenerate LUMO+1 half-filled bands at Fermi level, not unlike those calculated for La-PA [20]. In analogy to that case, the near degeneracy at Fermi can be reduced or lifted by a slight intracell atomic displacement (here of the K atoms) which takes the system to a semimetallic state. The insulating antiferromagnetic electronic structure obtained by allowing spin polarization in metallic EA3 is also shown.

Figure 5

Electron density portrait ${\left|\Psi \left(r\right)\right|}^2$ of the filled orbital shown as a red band in Fig. 4 for the EA2 nonmagnetic insulating structure of ${\mathrm{K}}_3$-PA. Coordinates were chosen to emphasize the shared nature of this orbital between the six clustered K atoms.

Figure 6

Top view of the EA3 structure of ${\mathrm{K}}_3$-PA. K atoms are aligned in a slightly deformed straight line with a ${\mathrm{K}}_1$–${\mathrm{K}}_2$–${\mathrm{K}}_3$ angle of ${174}^{\circ }$. An increased zigzag deformation reducing this angle to ${162}^{\circ }$ transforms the metal into a semimetal. The distance between the phenanthrene molecular centers is about 5.5 Å, that between the K and center of the nearest benzene ring of PA 2.7 Å. The PA molecules, although not strictly planar, approximately lie on parallel planes, in contrast with the herringbone structure of pristine phenanthrene and of structure EA1.

Figure 7

The three best structures B, C, D of ${\mathrm{K}}_3$-picene. All structures are herringbone with $P{2}_1$ symmetry as in pristine molecular picene. D basically coincides with a previously proposed structure [36], whereas in C alternating lines of potassium atoms are shifted relative to one another, forming a zigzag network. C and D have basically the same total energy.

Figure 8

Volume (a) and enthalpy (b) of four relevant structures A–D of ${\mathrm{K}}_3$-PC using different functionals and at different pressures. Structure D is closest to an earlier established structure in Ref. [36]. The two best structures C and D are nearly degenerate in energy and differ by the fractional shift of one alkali line relative to the other line in the unit cell. Note that here vdW corrections are more important than in ${\mathrm{M}}_3$-PA, on account of the larger molecular size. A hydrostatic pressure of about 10 kbars (blue line) has here a similar effect to vdW-DF (cyan and red lines).

Figure 9

Electronic band structure of structures C and D of ${\mathrm{K}}_3$-PC in the nonmagnetic (left) and antiferromagnetic state (right). Structure C has narrower bands, and gains 40 meV per dimolecular cell upon antiferromagnetic ordering, while in the broader-band crystal structure D the gain is about 20 meV. The energy lowering in the antiferromagnetic insulators signals the importance of correlations, more than a real magnetic instability of the metallic state [39].