Abstract
Majorana Kramers pairs emerged on surfaces of time-reversal-invariant topological crystalline superconductors show the Ising anisotropy to an applied magnetic field. We clarify that crystalline symmetry uniquely determines the direction of the Majorana Ising spin for given irreducible representations of pair potential, deriving constraints to topological invariants. Besides, necessary conditions for nontrivial topological invariants protected by the n-fold rotational symmetry are shown.
Highlights
Topological superconductors are fully or partially gapped systems hosting gapless states on their surfaces [1,2,3,4] as Andreev bound states [5,6,7,8]
A1u, A2u, B2u, and Eu (y) pair potentials, Majorana zero modes vanish for a specific direction of magnetic field, i.e., the Majorana zero modes respond to the field as a Ising spin
The obtained result is the detailed classification in the class-DIII superconductors in one spatial dimension
Summary
Topological superconductors are fully or partially gapped systems hosting gapless states on their surfaces [1,2,3,4] as Andreev bound states [5,6,7,8]. The gapless surface states behave as Majorana fermions, which are self-conjugate particles and protected by the topological invariant associated to (broken) symmetries. Applying an external magnetic field is a one way to destruct Majorana fermions in time-reversal-invariant (DIII [10,11,12]) topological superconductors since a magnetic field breaks time-reversal symmetry. One finds the direction of Majorana Ising spin and summarizes it in tables (Appendix C).
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