Semi-Dirac fermion
Class of fermionic quasiparticles
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In condensed matter physics, semi-Dirac fermions are a class of quasiparticles that can exhibit both massless (like light) and massive (like conventional particles) behavior depending on the direction of propagation[1]. More precisely, they disperse linearly along a given direction in momentum space, and quadratically in the orthogonal direction.[2] This exotic electronic structure can emerge at the critical point of a topological phase transition from semimetal to insulator wherein two Dirac cones coalesce, giving rise to a semi-Dirac point. Note that the Berry phases annihilate, resulting in topologically trivial quasiparticles. The fundamental anisotropy leads to a variety of unique properties and novel phenomena.[3][4] These excitations have been experimentally observed in a wide range of physical contexts from cold atoms trapped in optical lattices,[5] to the nodal line semi-metal zirconium silicon sulfide (ZrSiS), which is the first unambiguous detection in solids.[6] Different approaches have been taken to generalizations, such as considering arbitrary numbers of quadratically and linearly dispersing dimensions,[7] or replacing the quadratic term with an arbitrary even power law.[8] For the latter, an interacting microscopic model has been proposed as the first theoretical realization of the higher-order quartic semi-Dirac fermions in two-dimensions.[9]
There are also type-II semi-Dirac fermions, which were proposed as a model to explain the coexisting non-trivial topological, and semi-Dirac, behavior in titanium/vanadium oxide heterostructures.[10] These excitations occur at the merger of three Dirac cones, leaving a finite Berry phase and the associated topological properties. The critical spectrum possesses semi-Dirac character in the sense that it is linear and parabolic along the principal axes, but displays a different admixture of momentum components for an arbitrary direction of motion. Moreover the system remains semimetallic following the transition, with both Dirac and type-II semi-Dirac properties appearing at different Fermi levels. Long-range Coulomb interactions have been shown to drive the system to this electronic phase[11].
