  Coherence effects by the impurity scattering of Caroli--de Gennes--Matricon
(CdGM) modes in a vortex for nodal topological superconductors have been
studied. The coherence effects reflect a topological number defined on a
particular momentum space avoiding the superconducting gap nodes. First, we
analytically derived the eigenvalue and eigenfunction of the CdGM modes,
including the zero-energy modes, in a nodal topological superconducting state
without impurities, where we focused on a possible superconducting state of
UPt$_3$ as an example. Then, we studied impurity effects on the CdGM modes by
introducing the impurity self-energy, which are dominated by the coherence
factor depending on the eigenfunction of the CdGM modes. For the zero-energy
CdGM modes, the coherence factor vanishes in a certain momentum range, which is
guaranteed by topological invariance characterized by the one-dimensional
winding number.
