One-dimensional alkali-doped ${\mathrm{C}}_{60}$ chains encapsulated in BN nanotubes

We study the energetics, electronic structures, and electron-phonon couplings of a one-dimensional potassium-doped ${\mathrm{C}}_{60}$ chain encapsulated in a boron nitride nanotube using the framework of the density-functional theory. We demonstrate that the reaction of potassium doping is exothermic and the resulting material is one-dimensional metal where conducting electrons are only in the ${\mathrm{C}}_{60}$ chain. Interestingly, the Fermi-level density of states has a peculiar pressure dependence and can be larger than those in the three-dimensional alkali-doped fullerene compounds, indicating the possibility of various phase transitions. We also discuss the electron-phonon couplings and the possibility of superconductivity.

Figure 1

Geometry of ${\mathrm{K}}_3$C${}_{60}$@BN(10,10): (a) top view and (b) side view. Tube radius for nitrogen atoms (blue circle) is approximately 0.03 Å longer than that for boron atoms (yellow circle).

Figure 2

Reaction energies, $\Delta E$, of ${\mathrm{K}}_x$C${}_{60}$@BN(10,10).

Figure 3

Electronic band structures of (a) BN(10,10) and ${\mathrm{K}}_x$C${}_{60}$@BN(10,10) with (b) $x=0$, (c) $x=1$, (d) $x=2$, and (e) $x=3$. Details of the band structures around the Fermi level are shown for (f) $x=0$, (g) $x=1$, (h) $x=2$, and (i) $x=3$ (solid lines), where, for comparison, we also plot the band structures of ${\mathrm{K}}_x$C${}_{60}$ that has the same geometry with ${\mathrm{K}}_x$C${}_{60}$@BN(10,10) (dashed curve). Valence-band top or Fermi level (dotted line) are set to be zero.

Figure 4

Densities of states at the Fermi level, $N(E_F)$, as a function of lattice constant, $l$, for ${\mathrm{K}}_x$C${}_{60}$ with (a) $x=1$, (b) $x=2,$ and (c) $x=3$. Densities of states, $N(E)$, around the Fermi level at $l=9.86$ Å are shown in the inset.