  Using a generalized genetic algorithm, we propose four new sp3 carbon
allotropes with 5-6-7 (5-6-7-type Z-ACA and Z-CACB) or 4-6-8(4-6-8-type Z4-A3B1
and A4-A2B2) carbon rings. Their stability, mechanical and electronic
properties are systematically studied using first-principles method. We find
that all these four carbon allotropes show amazing stability in comparison with
recently proposed carbon phases. Both ZACA and Z-CACB are direct-band-gap
semiconductors with band gaps of 2.261 eV and 4.196 eV, respectively. Whereas
Z4-A3B1 and A4-A2B2 are indirect-band-gap semiconductors with band gaps of
3.105 eV and 3.271 eV, respectively. Their mechanical properties reveal that
all these four carbon allotropes are superhard materials comparable to diamond.
