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We discuss topological electronic states described by the Dirac Hamiltonian plus an additional one in three dimensions. When the additional Hamiltonian is an element of an Abelian group, electronic states become topologically nontrivial even in the absence of the fundamental symmetries such as the time-reversal symmetry and the particle-hole one. Such symmetry-breaking topological states are characterized by the Chern number defined in the two-dimensional partial Brillouin zone. The topological insulators in Zeeman fields are an example of the symmetry-breaking topological electric state. We show the crossover from the topological insulating phase to the topological semimetal one in strong Zeeman fields.

We discuss the surface impedance (Z = R - iX) of a normal-metal/superconductor proximity structure taking into account the spin-dependent potential at the junction interface. Because of the spin-mixing transport at the interface, odd-frequency spin-triplet s-wave Cooper pairs penetrate into the normal metal and cause the anomalous response to electromagnetic fields. At low temperature, the local impedance at a surface of the normal metal shows the nonmonotonic temperature dependence and the anomalous relation R > X. We also discuss a possibility of observing such anomalous impedance in experiments.