Four superhard carbon allotropes: First-principle study
  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. 
Chaoyu He, L. Z. Sun, C. X. Zhang, K. W. Zhang, Xiangyang Peng,   Jianxin Zhong
cond-mat.mtrl-sci