The pseudo-relativistic physics that gives 2D graphene its fascinating properties can also be found in 3D materials known as Dirac semimetals. The common feature of such systems is the existence of Dirac points in momentum space, at which the conduction and valence bands meet. Here, the electronic band dispersion is linear, and so the electrons behave like relativistic particles. Benjamin Wieder and colleagues have now predicted a new class of Dirac semimetal that would feature double Dirac points.
In bulk materials, Dirac points are a consequence of symmetry and topology in the electronic structure. The Dirac points of Dirac semimetals are fourfold degenerate and, in certain cases, strain can be used to tune the system to behave either as a trivial or topological insulator. Using tight-binding models, Wieder et al. showed that seven of the 230 space groups can host a double Dirac point that would be eightfold degenerate. Such systems could be tuned into either a trivial or a topological insulator phase by applying strain along two different directions, providing a unique platform for topological band structure engineering.
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Fleet, L. Lead a double life. Nature Phys 12, 528 (2016). https://doi.org/10.1038/nphys3792