Topological phases combining superconductivity and magnetism

Mario Cuoco

In this talk I will present different routes to generate and manipulate topological phases due to the interplay between superconductivity and magnetism. The search for new variants of semimetals (SMs) recently highlighted the interplay of Dirac fermions physics and magnetism. Indeed, antiferromagnetic (AFM) SMs can be obtained where both time and inversion are broken while their combination is kept [1,2] or due to chiral- [2] and time-symmetry [2,3] combined with non-symmorphic transformations [2]. Here, we discuss materials, i.e. transition metal oxide systems, that can exhibit AFM-SM phase due to orbitally directional double- exchange effects [4, 2]. In this context, the impact of s-wave spin-singlet pairing on AFM-SMs with Dirac points or nodal loops at the Fermi level [5] is generally shown to convert the semimetal into various types of nodal topological superconductors. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the AFM-superconducting state that set out the occurrence of a large variety of electronic topological transitions [4].
Finally, I will focus on various quantum platforms marked by spin-singlet or spin-triplet pairing interfaced with non-trivial magnetic patterns and discuss the nature of the emerging topological phases [6,7,8]. The coexistence of ferromagnetism or antiferromagnetism with spin-triplet superconductivity is also analysed and discussed with respect to relevant materials cases.

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