Cubic Dirac fermions in quasi-one-dimensional transition-metal chalcogenide semimetals immune to Peierls distortion

A Cubic Dirac Fermion in condensed-matter physics refers to a band crossing in periodic solids that has 4-fold degeneracy with cubic dispersions in certain directions. Such a crystalline symmetry induced fermion is composed of 6 Weyl fermions where 3 have left-handed and 3 have right-handed chirality, and constitutes one of the ``new fermions'' that have no counterpart in high-energy physics. However, no prediction has yet pointed to a plausible example of a material candidate hosting such a cubically-dispersed Dirac semimetal (CDSM). Here we establish the design principles for CDSM finding that only 2 out of 230 space groups possess the required symmetry elements. Adding the required band occupancy criteria, we conduct a material search using density functional band theory identifying a group of quasi-one-dimensional molybdenum chalcogenide compounds A(MoX)$_{\mathrm{3}}$ (A $=$ Na, K, Rb, In, Tl; X $=$ S, Se, Te) with space group P6$_{\mathrm{3}}$/m as ideal CDSM candidates. Studying the stability of the A(MoX)$_{\mathrm{3}}$ family towards a Peierls distortion reveals a few candidates such as Rb(MoTe)$_{\mathrm{3}}$ and Tl(MoTe)$_{\mathrm{3}}$ that are resilliant to Peierls distortion, thus retaining the metallic character.