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.

arXiv comment7+3 pages, 5 figures, some typos are corrected and new references are added

References in corpus (76)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators in Three Dimensions
• 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
• Unconventional sign-reversing superconductivity in LaFeAsO_(1-x)F_x
• Topological invariants of time-reversal-invariant band structures
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Periodic table for topological insulators and superconductors
• 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
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Evidence for Majorana bound state in an iron-based superconductor
• Observation of topological superconductivity on the surface of an iron-based superconductor
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Majorana corner modes in a high-temperature platform
• Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors
• Topological nature of FeSe${}_{0.5}$Te${}_{0.5}$ superconductor
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Time Reversal Invariant Topological Superconductivity and Majorana Kramers Pairs
• Topological superconductivity on the surface of Fe-based superconductors
• High-Temperature Majorana Corner States
• Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor
• Robust and clean Majorana zero mode in the vortex core of high-temperature superconductor (Li0.84Fe0.16)OHFeSe
• Weak-Pairing Higher Order Topological Superconductors
• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Majorana Kramers pairs in higher-order topological insulators
• Discovery of switchable weak topological insulator state in quasi-one-dimensional bismuth iodide
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Topological Characters in Fe(Te${}_{1-x}$Se${}_x$) thin films
• Helical Hinge Majoranas in Iron-Based Superconductors
• Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Higher-order topological odd-parity superconductors
• Second-order Topological Superconductors with Mixed Pairing
• Majorana modes in time-reversal invariant s-wave topological superconductors
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• In-plane Zeeman field induced Majorana corner and hinge modes in an $s$-wave superconductor heterostructure
• Time-Reversal Invariant Topological Superconductivity Induced by Repulsive Interactions in Quantum Wires
• Weak Topological Insulators and Composite Weyl Semimetals: $\beta$-Bi${}_4$X${}_4$ (X=Br, I)
• Majorana bound states in two-channel time-reversal-symmetric nanowire systems
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Refined symmetry indicators for topological superconductors in all space groups
• Topological and holonomic quantum computation based on second-order topological superconductors
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Quantized conductance of Majorana zero mode in the vortex of the topological superconductor (Li0.84Fe0.16)OHFeSe
• Proximity-induced Majorana hinge modes in antiferromagnetic topological insulators
• Proximity-induced Josephson $\pi$-Junctions in Topological Insulators
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Phase tunable second-order topological superconductor
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• All-electrically tunable networks of Majorana bound states
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Fractional Topological Superconductivity and Parafermion Corner States
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Three-dimensional superconductors with hybrid higher order topology
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals
• Detection of second-order topological superconductors by Josephson junctions
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Topological Vortex Phase Transitions in Iron-Based Superconductors
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors

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