Motivated by recent discoveries of superconductivity in lightly doped multilayer graphene systems, we present a low-energy model to study superconductivity in two-dimensional materials whose Fermi surface consists of two valleys at $\pm \mathit{K}$ 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.

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• Edge states
• Impurities in superconductors
• Spin-singlet pairing
• Spin-triplet pairing
• Superconducting order parameter
• Graphene