  Motivated by recent discoveries of superconductivity in lightly-doped
multilayer graphene systems, we present a low-energy model to study
superconductivity in 2D materials whose Fermi surface consists of two valleys
at $\pm \vec{K}$-points. We assume a triplet odd-valley superconducting order
with a pair potential that is isotropic in each valley but has a different sign
in the two different valleys. Our theory predicts the emergence of an almost
flat band of edge states centered at zero energy for certain edge orientations.
As a result, a prominent experimental signature of this type of
superconductivity is the presence of a large zero-energy peak in the local
density of states near specific edges.
  The results of the effective low-energy theory are confirmed by numerically
analyzing a specific microscopic tight-binding realization of odd-valley
superconductivity, f-wave superconductivity on a honeycomb lattice in a ribbon
geometry. Our work provides a test for odd-valley superconductivity through
edge spectroscopy.
