Pairing Obstructions in Topological Superconductors

Abstract

The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor, we show that the wave function of an individual Cooper pair decays exponentially with separation in the trivial phase and polynomially in the topological phase. For the position-space Majorana representation, we show that the topological phase is characterized by a nonzero Majorana polarization, which captures an irremovable and quantized separation of Majorana Wannier centers from the atomic positions. We apply our results to diagnose second-order topological superconducting phases in two dimensions. Our work establishes a vantage point for the generalization of Topological Quantum Chemistry to superconductivity.

arXiv comment6 pages, 3 figures, accepted manuscript, supplement included

References in corpus (54)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Maximally localized Wannier functions: Theory and applications
• Helical liquids and Majorana bound states in quantum wires
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Spin and Majorana polarization in topological superconducting wires
• Weak-Pairing Higher Order Topological Superconductors
• Wannier Center Sheets in Topological Insulators
• Majorana Kramers pairs in higher-order topological insulators
• Topology of Disconnected Elementary Band Representations
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Second-order Topological Superconductors with Mixed Pairing
• Fractional corner charges in spin-orbit coupled crystals
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Smooth gauge for topological insulators
• Refined symmetry indicators for topological superconductors in all space groups
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Symmetry indicators for topological superconductors
• Fragile topological phases in interacting systems
• Two-dimensional topological materials discovery by symmetry-indicator method
• Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• Variants of the symmetry-based indicator
• Towards a Particle-Number Conserving Theory of Majorana Zero Modes in p+ip Superfluids

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• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
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• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Abundant surface-semimetal phases in three-dimensional obstructed atomic insulators
• Topological obstructed atomic limit by annihilating Dirac fermions
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Topological phases of amorphous matter
• Phase-Space Approach to Wannier Pairing and Bogoliubov Orbitals in Square-Octagon Lattices
• Breakdown of the symmetry constraint in a Floquet topological insulator
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Analysis of the singular band structure occurring in one-dimensional topological normal and superfluid fermionic systems: A pedagogical description