K₄ Carbon Modifications by Modulating Phonon Eigenvectors

The number of carbon allotropes is ever increasing with a variety of novel network topologies. Among several that were recently proposed, the K₄ structure draws particular attention due to its similarities with diamond, but it is a chiral periodic graph. However, the proposed K₄ was shown to be dynamically unstable. As a result, despite the fact that such a graph is uncommon in the allotropes of elements, the graph of K₄ is disregarded as a potential structure for elemental carbon. Herein, by means of first principles calculations, we have attempted stabilizing such a chiral graph for carbon by modulating phonon eigenvectors associated with imaginary phonon frequencies that were responsible for the structure instability. This has led us to generate six novel stable carbon allotropes, with 4- and a mix of 3,4-connected carbon atoms, that have the history of chiral K₄. The newly predicted carbon allotropes retain chirality, exhibit lower symmetry than K₄ carbon, and show improved thermodynamic stability. Among these, the thermodynamic stability increases as the ratio of 3:4 connectedness decreases. Analysis of the electronic structure suggests that the 3-connected K₄ net would prefer to be colored with elements of three valence electrons. The computed band gap suggests that all the six novel K₄ modifications predicted are semiconductors with band gaps ranging from 0.72 to 5.14 eV. In addition, the calculated elastic stiffness constants indicates that the K₄ carbon modifications are mechanically stable.