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