  We show that a recently predicted layered phase of lithium monoboride, Li2B2,
combines the key mechanism for strong electron-phonon coupling in MgB2 (i.e.,
interaction of covalent B sigma bands with B bond-stretching modes) with the
dominant coupling mechanism in CaC6 (i.e., interaction of free-electron-like
interlayer states with soft intercalant modes). Yet, surprisingly, the
electron-phonon coupling in Li2B2 is calculated to be weaker than in either
MgB2 or CaC6. We demonstrate that this is due to the accidental absence of B pi
states at the Fermi level in Li2B2. In MgB2, the pi electrons play an indirect
but important role in strengthening the coupling of sigma electrons. Doping
Li2B2 to restore pi electrons at the Fermi level is expected to lead to a new
superconductor that could surpass MgB2 in Tc.
