Intermolecular Overlap Geometry Gives Two Classes of Fulleride Superconductor: Electronic Structure of 38 K $T_c$ ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$

Superconductivity emerges for the $A15$ polymorph of the fulleride ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$ upon compression to a pressure of $\sim 4\mathrm{kbar}$. Using density functional theory we study the bonding in the $A15$ phase as a function of unit cell volume comparing it to that in the fcc polymorph. We find that, despite its smaller packing density, the bcc-derived $A15$ phase has both a substantially wider bandwidth for the partially occupied $t_{1u}$ band and a higher density of states at the Fermi level. This result can be traced to the striking differences in the nature of the interanion overlap in the $A15$ and fcc structures showing that the $A15$ ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$ phase is not simply yet another superconducting fulleride albeit with a very high $T_c$—the two sphere packings (body centered versus face centered) observed experimentally produce two electronically distinct classes of fulleride superconductors.

Figure 1

(a) Intermolecular ${\mathrm{C}}_{60}\mathrm{\text{−}}{\mathrm{C}}_{60}$ nearest-neighbor contacts viewed along the molecule center-to- molecule center directions for $A15$ and fcc structures. (b) Total energy per ${\mathrm{C}}_{60}$ as a function of volume, $V$, per ${\mathrm{C}}_{60}$ for fcc and $A15$ polymorphs of ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$, and a variant of the $A15$ phase with the ${\mathrm{C}}_{60}$ units rotated to reduce the number of atoms in the contact region. Labels indicate the experimental pressures at particular $V$ values. The vertical line indicates the $V$ below which the $A15$ phase becomes superconducting. The inset shows $T_c$ as a function of $V$ obtained from experiment [5].

Figure 2

The band structure (bottom panel) for the $t_{1u}$ bands for the $A15$ phase of ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$. The top panels show the eigenfunctions at the point of contact between ${\mathrm{C}}_{60}$’s at the bottom (left) and top (right) of the $t_{1u}$ band at the $M$ point.

Figure 3

(a) Density of states for the $A15$ phase of ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$ at lattice constants corresponding to ambient pressure and for a pressure of 7.2 kbar, i.e., in the region of the highest $T_c$, as shown in the inset in Fig. 1b. (b) Comparison of the DOS for the fcc (heavy line) and $A15$ structures (fine line) at the ambient pressure experimental lattice constants.

Figure 4

(a) Width of the $t_{1u}$ band as a function of volume, $V$ per ${\mathrm{C}}_{60}$ for both $A15$ and fcc polymorphs of ${\mathrm{Cs}}_3{\mathrm{C}}_{60}$. (b) Density of states at the Fermi energy versus $V$.