DiracWeyl

DiracWeyl is a term used in condensed matter physics to describe systems where low-energy electronic excitations realize Dirac and Weyl fermion physics within a single material or phase diagram. In a Dirac semimetal, low-energy excitations near a Dirac point behave as four-component Dirac fermions, described by a Dirac equation with time-reversal and inversion symmetry. If either inversion or time-reversal symmetry is broken, the Dirac point generically splits into a pair of Weyl nodes of opposite chirality, yielding a Weyl semimetal phase. The Weyl nodes act as monopoles of Berry curvature in momentum space and give rise to surface Fermi arcs and a chiral anomaly in transport. In a broader sense, a DiracWeyl system encompasses regimes where the same material exhibits Dirac-like and Weyl-like excitations under different symmetry or external perturbations, allowing a Dirac-to-Weyl transition.

Mathematical description: The Dirac Hamiltonian H_D = v_F (k · α) describes a four-component spinor; the Weyl Hamiltonian H_W = ± v_F (k · σ) describes two-component spinors with definite chirality. Symmetry considerations determine whether Dirac nodes remain protected or split into Weyl nodes. Experimental platforms include known Dirac semimetals such as Na3Bi and Cd3As2; lifting symmetries by magnetic order, strain, or external fields can drive a transition to a Weyl semimetal phase, observed via angle-resolved photoemission spectroscopy and magnetotransport experiments, including chiral anomaly signatures.

The term DiracWeyl thus captures the close relationship between these two emergent fermions in solid-state systems and the tunability of their topology.