Protected Weyl semimetals within 2D chiral classes

Weyl semimetals in three dimensions can exist independently of any symmetryapart from translations. Conversely, in two dimensions, Weyl semimetals arebelieved to require additional symmetries including crystalline symmetries toexist. In this study, we demonstrate that a 2D Weyl semimetal phase can existin systems with Hamiltonians possessing internal symmetries, such as timereversal ${\cal T}$, charge conjugation ${\cal C}$ , and their combined chiralsymmetry ${\cal S} = {\cal CT}$, only. Starting from a minimal-dimension DiracHamiltonian, we establish the presence of a stable Weyl semimetal phase in eachof the five chiral classes: AIII, BDI, CII, DIII, and CI in two dimension.Similar to 3D Weyl semimetals where Weyl points possess nontrivial topologicalcharges (Chern number), the Weyl points in WSMs within the 2D chiral classesare characterized by the $Z$ winding numbers. In accordance with thebulk-boundary correspondence, protected Fermi arc edge states emerge,connecting the projections of Weyl points that carry opposite topologicalcharges. Unlike the surface states in 3D WSMs, the edge states of WSMs within2D chiral classes are completely dispersionless and are always at the zeroenergy due to the protecting chiral symmetry.