We study the interaction effect in a three-dimensional Dirac semimetal and find that two competing orders, charge-density-wave orders and nematic orders, can be induced to gap the Dirac points. Applying a magnetic field can further induce an instability towards forming these ordered phases. The charge-density-wave phase is similar to that of a Weyl semimetal, while the nematic phase is unique for Dirac semimetals. Gapless zero modes are found in the vortex core formed by nematic order parameters, indicating the topological nature of nematic phases. The nematic phase can be observed experimentally using scanning tunneling microscopy.

• Received 7 April 2015
• Revised 2 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.041108