We study the instabilities of a particle-hole symmetric Weyl metal with both electron and hole Fermi surfaces (FSs) around the Weyl points. For a repulsive interaction we find that the leading instability is towards a longitudinal spin-density-wave $\left({\mathrm{SDW}}_z\right)$ order. Besides, there exist three degenerate subleading instabilities: a charge-density-wave (CDW) instability, and two transverse spin-density-wave $\left({\mathrm{SDW}}_{x,y}\right)$ instabilities. For an attractive interaction the leading instabilities are towards two pair-density-wave (PDW) orders which pair the two FSs separately. Both the PDW and ${\mathrm{SDW}}_z$ order parameters fully gap out the FSs, while the CDW and ${\mathrm{SDW}}_{x,y}$ ones leave line nodes on both FSs. For the ${\mathrm{SDW}}_z$ and the PDW states, the surface Fermi arc in the metallic state evolves to a chiral Fermi line which passes the projection of the Weyl points and traverses the full momentum space. For the CDW state, the line node projects to a “drumhead” band localized on the surface, which can lead to a topological charge polarization. We verify the surface states by computing the angular-resolved photoemission spectroscopy data.

• Received 7 May 2016
• Revised 18 July 2016

DOI:https://doi.org/10.1103/PhysRevB.94.075115