Boundary Topological Superconductors

Abstract

For strongly anisotropic time-reversal invariant (TRI) insulators in two and three dimensions, the band inversion can occur respectively at all TRI momenta of a high symmetry axis and plane. Although these classes of materials are topologically trivial as the strong and weak $Z_2$ indices are all trivial, they can host an even number of unprotected helical gapless edge states or surface Dirac cones on some boundaries. We show in this work that when the gapless boundary states are gapped by $s_{\pm }$-wave superconductivity, a boundary time-reversal invariant topological superconductor (BTRITSC) characterized by a $Z_2$ invariant can be realized on the corresponding boundary. Since the dimension of the BTRITSC is lower than the bulk by one, the whole system is a second-order TRI topological superconductor. When the boundary of the BTRITSC is further cut open, Majorana Kramers pairs and helical gapless Majorana modes will respectively appear at the corners and hinges of the considered sample in two and three dimensions. Furthermore, a magnetic field can gap the helical Majorana hinge modes of the three-dimensional second-order TRI topological superconductor and lead to the realization of a third-order topological superconductor with Majorana corner modes. Our proposal can potentially be realized in insulator-superconductor heterostructures and iron-based superconductors whose normal states take the desired inverted band structures.

7+3 pages, 5 figures, some typos are corrected and new references are added

References in corpus (11)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Classification of topological insulators and superconductors in three spatial dimensions
• Reflection symmetric second-order topological insulators and superconductors
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Quantized conductance of Majorana zero mode in the vortex of the topological superconductor (Li0.84Fe0.16)OHFeSe
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor

Cited by in corpus (10)

• Higher-order topological superconductors based on weak topological insulators
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Braiding higher-order Majorana corner states through their spin degree of freedom
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Sublattice-sensitive Majorana Modes
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes