There is currently intensive effort searching for topological phases beyond the framework of the K-theoretical classification. Such topological phases outside the K-theoretical classification are called unstable topological phases. In this talk, we discuss two topics about unstable topological phases realized in spin-orbit-free systems, i.e., systems with the SU(2) spin rotation symmetry. In the first part, we present theoretical models of spin-orbit-free topological insulators in class AI, which have n surface Dirac cone protected by time-reversal and n-fold rotation symmetries. Our models are generalizations of Fu’s model of a spinless topological crystalline insulator, in which orbital degrees of freedom play the role of pseudospins. In the second part, we extend the concept of spin-orbit-free topological insulators to superconductors in class CI. By defining a topological invariant and constructing a theoretical model, we show that spin-orbit-free topological superconducting phases are realized in a class of s±-wave superconductors. In closing, we discuss the application to iron-based superconductors.
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