  Dirac-like electronic states are the main engines powering the tremendous
advances in research of graphene, topological insulators and other materials
with these states. Zero effective mass, high carrier mobility and numerous
applications are some consequences of linear dispersion that distinguishes
Dirac states. Here we report a new class of linear electronic bands in
two-dimensional materials with zero effective mass and sharp band edges never
seen in solid state matter before, and predict stable materials with such
electronic structure utilizing symmetry group analysis and ab initio approach.
We make a full classification of completely linear bands in two-dimensional
materials and find that only two classes exist: Dirac fermions on one hand and
pyramidal-like and cootie catcher-like states on the other hand. The new class
supports zero effective mass and hence high carrier mobility similar to that of
graphene, anisotropic electronic properties like that of phosphorene, and
robustness of states with respect to electronic correlations.
