Topological Nonsymmorphic Crystalline Superconductors

Abstract

Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes", at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors". We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide symmetry. Furthermore, we generalize the classification of topological nonsymmorphic crystalline superconductors to the classes with time reversal symmetry, including the DIII and BDI classes, in two dimensions. Our theory provides a guidance to search for new topological superconducting materials with nonsymmorphic crystal structures.

In this new version, we update the topological classification and show several model studies for systems in symmetry class D, BDI and DIII

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Cited by in corpus (23)

• Topological superconductivity on the surface of Fe-based superconductors
• Topology of nonsymmorphic crystalline insulators and superconductors
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• Topologically stable gapless phases in nonsymmorphic superconductors
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Floquet topological phase transitions in a periodically quenched dimer
• Möbius topological superconductivity in UPt${}_3$
• $Z_4$ Topological Superconductivity in UCoGe
• Crystalline Kitaev spin liquids
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Dirac lines and loop at the Fermi level in the Time-Reversal Symmetry Breaking Superconductor LaNiGa${}_2$
• Topological Superconductivity Induced by Magnetic Texture Crystals
• Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders
• Topological Gapless Phases in Non-Symmorphic Antiferromagnets
• Nodal Brillouin Zone Boundary from Folding a Chern Insulator
• Majorana multipole response: General theory and application to wallpaper groups
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Generic phase diagram for Weyl superconductivity in mirror-symmetric superconductors
• Equivalence and superposition of real and imaginary quasiperiodicities
• Topological superconductor candidates PdBi${}_2$Te${}_4$ and PdBi${}_2$Te${}_5$ from a generic ab initio strategy
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Inversion-symmetric Electron Gases as New Platforms for Topological Planar Josephson Junctions