the bands are not at ε$_{F}$ ). The magnetic spin susceptibility χ is given by Fixed-spin-moment calculations were conducted to produce an energy-vs.-moment E ( M ) curve, result- ing in a susceptibility of χ = 2 . 93 µ 2 B eV $^{$_{−}$1}$, or 3 . 76 × 10 $_{−}$6 emu/mol. This is the exchange-enhanced susceptibility in the Stoner theory, and can be writ- ten as where S ≡ χ/χ$_{0}$ is the Stoner enhancement fac- tor, I is the Stoner parameter, and the bare Pauli susceptibility χ$_{0}$ is equal to µ 2 $_{B}$N ( ε$_{F}$ ). Janak has shown how to calculate I within density functional theory, 31 which must be equivalent (within a minor approximation he used) to our approach of using fixed-spin-moment calculations. With our calculated values we obtain S = 2 . 75, which translates to I = 0 . 60 eV. Some interpreta- tion of this value of Stoner I should be noted. First, ε$_{F}$ falls where most of the states are Si-derived, so for simplicity we neglect Al (and Na, which is ion- ized). Second, we note that there are two Si atoms in the primitive cell. Thus to get an “atomic value” of I$_{Si}$ , we should use a value of N ( ε$_{F}$ ) / 2 per Si atom. The result then is very roughly I$_{Si}$ ∼ 1 eV. This value can be compared to the atomic value for Al (next to Si in the periodic table) in the elemental metal, which is I$_{Al}$ = 0.6 eV. 31 It seems, therefore, that Si in NaAlSi is considerably more “magneti- cally inclined” than is Al in aluminum. However, the Stoner enhancement overall is not large, indicating relatively modest magnetic enhancement and rather conventional magnitude of magnetic interactions. Isostructural and isovalent NaAlGe is not super- conducting (above 1.6 K, at least), so it should be instructive to compare its electronic structure to that of NaAlSi. Using its experimental lattice parameters, 23 we have calculated the band structure of NaAlGe, and compared it with that of NaAlSi on a rather fine scale in Fig. 7. The band structures are very similar, the one difference being that the band along Γ-M near M does not cross ε$_{F}$ in NaAlGe. The free-electron band is also identical. The classes of materials that contain relatively high temperature superconductors 36 continues to expand. Superconductors derived from doped 2D semiconductors pose many of the most interesting issues in superconductivity today. The cuprates and the Fe-pnictides (and -chalcogenides) are strongly magnetic, and comprise one end of the spectrum (though they are themselves quite different). On Supposing the tiny bit of FS along Γ-M cannot account for the difference in superconducting behav- iors, the factors relevant for electron-phonon cou- pling will be the difference in mass (Ge is more than twice as heavy as Si) and the difference in elec- tronic character, which can affect force constants and electron-phonon matrix elements. A real pos- sibility is that the pairing mechanism is electronic rather than phononic. In three dimensions purely electronic pairing mechanisms have been attracting serious study (by Sham and collaborators 32,33 for ex- ample), but 2D semimetals introduce new features that deserve detailed study. Another possibility is that these pockets are im- portant, and that superconductivity arises from an enhancement of electron-phonon coupling in these tiny electron pockets from low frequency electronic response, either interband transitions or plasma os- cillations, or both. A model in which the elec- tronic response of a 2D electronic superlattice plays a central role in the mechanism has been previously studied 34,35 using a model of parallel conducting sheets separated by a dielectric spacer. This model may be useful as a starting point for understanding NaAlSi. V. DISCUSSION B. Magnetic susceptibility χ = ∂M ∂H = ( ∂ $^{2}$E/∂M$^{2}$) $^{$_{−}$1}$. χ = Sχ$_{0}$ ≡ χ$_{0}$ 1 − IN ( ε$_{F}$ ) , 7 C. Comparison to NaAlGe FIG. 7: (Color online.) Blowup of the band structures of NaAlSi and NaAlGe near ε F .