Figure 1

(Color online) (a) Crystal structure overlapped with the isosurface of the electron density occupying the cage conduction band (CCB). Red, yellow, and blue spheres represent Al, Ca, and O atoms, respectively. The gray frame indicates the cubic unit cell containing twelve cages, and the lattice constant (cubic symmetry) is $\sim 1.2\mathrm{nm}$. One of the cages has a free space with an inner diameter of $\sim 0.4\mathrm{nm}$. The isosurface, colored light green, was obtained by ab initio density functional theory calculations using the VASP code (Ref. 33). The Fermi level is located in CCB and is primarily composed of $s$-like electrons trapped in the empty cage. (b) Electronic structure. There are two types of conduction bands. One conduction band is constituted of a cage framework and another (CCB) is composed of three-dimensionally connected empty cages. The band gap between the valence band and framework conduction band is $\sim 7.5\mathrm{eV}$, and the cage conduction band is located $\sim 2\mathrm{eV}$ below the frame conduction band (Ref. 4).Reuse & Permissions

Figure 2

Heat capacities of sample A under zero magnetic field (solid circles) and under the magnetic field of $0.1\mathrm{T}$ (open circles). The broken line is given by $C_p=\beta T^3+\gamma T$, as discussed in the text. The solid curve is the theoretical curve associated with the BCS theory, as reported in Ref. 24. The inset shows $C_p$ versus $T^2$ plots of samples A (solid circles), B (open squares), C (solid triangles), and C12A7 (crosses, Ref. 18). The lines were obtained by least squares fitting of the data between 0.3 and $3\mathrm{K}$ to $C_p=\beta T^3+\gamma T$.Reuse & Permissions