Weak-Pairing Higher Order Topological Superconductors

Abstract

Conventional topological superconductors are fully gapped in the bulk but host gapless Majorana modes on their boundaries. We instead focus on a new class of superconductors, second-order topological superconductors, that have gapped, topological surfaces and gapless Majorana modes instead on lower-dimensional boundaries, i.e., corners of a two-dimensional system or hinges for a three-dimensional system. Here we propose two general scenarios in which second-order topological superconductivity can be realized spontaneously with weak-pairing instabilities. First, we show that $p_x+i{p}_y$-wave pairing in a (doped) Dirac semimetal in two dimensions with four mirror symmetric Dirac nodes realizes second-order topological superconductivity. Second, we show that $p+id$ pairing on an ordinary spin-degenerate Fermi sruface realizes second-order topological superconductivity as well. In the latter case we find that the topological invariants describing the system can be written using simple formulae involving only the low-energy properties of the Fermi surfaces and superconducting pairing. In both cases we show that these exotic superconducting states can be intrinsically realized in a metallic system with electronic interactions. For the latter case we also show it can be induced by proximity effect in a heterostructure of cuprate and topological superconductors.

14 pages, 6 figures; typos corrected; references added

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• Higher-order bulk-boundary correspondence for topological crystalline phases
• Higher Order Topological Phases: A General Principle of Construction
• Topological Superconductivity in Two-Dimensional Altermagnetic Metals
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• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Helical Hinge Majoranas in Iron-Based Superconductors
• Higher-order topological insulators in amorphous solids
• Higher-order topological odd-parity superconductors
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Band Representations and Topological Quantum Chemistry
• Second-order Topological Superconductors with Mixed Pairing
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• 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
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• 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
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Braiding Majorana corner modes in a second-order topological superconductor
• 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 phases on fractal lattices
• Second-order topological phases protected by chiral symmetry
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Antiunitary symmetry protected higher order topological phases
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Phase tunable second-order topological superconductor
• Floquet generation of Second Order Topological Superconductor
• Higher-Order Topological Dirac Superconductors
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
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• Symmetry indicators of band topology
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
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• Three-dimensional superconductors with hybrid higher order topology
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• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Dual topology in Jacutingaite Pt${}_2$HgSe${}_3$
• Higher Order Bosonic Topological Phases in Spin Models
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• Helical Liquids in Semiconductors
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• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
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• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Geometric orbital magnetization in adiabatic processes
• Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Rotation Symmetry-Protected Topological Phases of Fermions
• High-$T_c$ Superconductor Fe(Se,Te) Monolayer: an Intrinsic, Scalable and Electrically-tunable Majorana Platform
• Aspects of topological superconductivity in 2D systems: noncollinear magnetism, skyrmions, and higher-order topology
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Dirty higher-order Dirac semimetal: Quantum criticality and bulk-boundary correspondence
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Quadrupole spin polarization as signature of second-order topological superconductors
• Strain engineered higher order topological phases for spin-3/2 Luttinger fermions
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
• 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
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• Boundary Topological Superconductors
• Density-driven higher-order topological phase transitions in amorphous solids
• Chiral Majorana Hinge Modes in Superconducting Dirac Materials
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
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• A Dirac fermion model associated with second order topological insulator
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• Network model for higher-order topological phases
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• Interaction-driven first-order and higher-order topological superconductivity
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Higher-order topological superconductivity in monolayer WTe${}_2$ from repulsive interactions
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Hierarchical Topological States in Thermal Diffusive Networks
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Characterization of higher-order topological superconductors using Bott indices
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Higher-order topological superconductor phases in a multilayer system
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• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
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• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
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• Engineering Majorana corner modes from two-dimensional hexagonal crystals
• Euler band topology in superfluids and superconductors
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• Network model for magnetic higher-order topological phases
• Extended Haldane model -- a modern gateway to topological insulators
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes
• Majorana bound states with chiral magnetic textures
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases