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The electronic structures of two mixed valence insulators YbB$_6$ andYbB$_12$ are studied by using the local density approximation (LDA)supplemented with the Gutzwiller method and dynamic mean field theory (DMFT).YbB$_6$ is found to be a moderately correlated Z$_2$ topological insulator,similar to SmB$_6$ but having much larger bulk band gap. Notably, YbB$_12$ isrevealed to be in a new novel quantum state, strongly correlated topologicalcrystalline Kondo insulator, which is characterized by its non-zero mirrorChern number. The surface calculations find odd (three) and even (four) numberof Dirac cones for YbB$_6$ and YbB$_12$, respectively.

Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides