Scattering theory of topological insulators and superconductors

Abstract

The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require knowledge of all states below the Fermi energy. Here, we propose a way to calculate the topological invariant employing solely its scattering matrix at the Fermi level without knowledge of the full spectrum. Since the approach based on scattering matrices requires much less information than the Hamiltonian-based approaches (surface versus bulk), it is numerically more efficient. In particular, is better-suited for studying disordered systems. Moreover, it directly connects the topological invariant to transport properties potentially providing a new way to probe topological phases.

11 pages, 7 figures, 1 table, 3 ancilla videos. v2: updated figures and references. v3: added appendix (published version). v4: fixed typos, updated references

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Cited by in corpus (135)

• Classification of topological quantum matter with symmetries
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• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Random-matrix theory of Majorana fermions and topological superconductors
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• Generating Many Majorana Modes via Periodic Driving: A Superconductor Model
• Topological index for periodically driven time-reversal invariant 2D systems
• Boundary Green functions of topological insulators and superconductors
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• K-Theory and Pseudospectra for Topological Insulators
• Network Models of Photonic Floquet Topological Insulators
• Measurement of a topological edge invariant in a microwave network
• Topological tight-binding models from non-trivial square roots
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Majorana nanowires for topological quantum computation
• Aperiodic Weak Topological Superconductors
• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
• Complex classes of periodically driven topological lattice systems
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Topological equivalence of crystal and quasicrystal band structures
• Resonantly Tunable Majorana Polariton in a Microwave Cavity
• Anomalous bulk-edge correspondence in continuous media
• Scattering matrix invariants of Floquet topological insulators
• Phase tunable second-order topological superconductor
• Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models
• Topology vs. Anderson localization: non-perturbative solutions in one dimension
• Scattering theory of topological phases in discrete-time quantum walks
• Local invariants identify topology in metals and gapless systems
• Localization, delocalization, and topological phase transitions in the one-dimensional split-step quantum walk
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Photonic ${\mathbb{Z}}_2$ topological Anderson insulators
• Detecting topological invariants in chiral symmetric insulators via losses
• Simulation and Detection of Photonic Chern Insulators in One-Dimensional Circuit Quantum Electrodynamics Lattice
• Floquet Weyl Phases in a Three Dimensional Network Model
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Revealing a topological connection between stabilities of Fermi surfaces and topological insulators/superconductors
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• Phase spectroscopy of topological invariants in photonic crystals
• Amorphous topological matter: theory and experiment
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Three-dimensional topological magnon systems
• Coherent error threshold for surface codes from Majorana delocalization
• Topological invariant for generic 1D time reversal symmetric superconductors in class DIII
• Phase-induced topological superconductivity in a planar heterostructure
• Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions
• Reconfigurable Microwave Photonic Topological Insulator
• Localisation, delocalisation, and topological transitions in disordered 2D quantum walks
• Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Computing a logarithm of a unitary matrix with general spectrum
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Extended topological group structure due to average reflection symmetry
• Fractionalization and topology in amorphous electronic solids
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Exact edge, bulk and bound states of finite topological systems
• Thermal metal-insulator transition in a helical topological superconductor
• Topology and localization of a periodically driven Kitaev model
• Quantum criticality at the Chern-to-normal insulator transition
• Finite volume calculation of $K$-theory invariants
• Surface codes, quantum circuits, and entanglement phases
• Dirac surface states in magnonic analogs of topological crystalline insulators
• Probing topology in nonlinear topological materials using numerical $K$-theory
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
• Effects of non-equilibrium noise on a quantum memory encoded in Majorana zero modes
• Counter-propagating edge states in Floquet topological insulating phases
• Density of states, transport, and topology in disordered Majorana nanowires
• Local Chern Marker for Periodic Systems
• Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class
• Quality factor for zero-bias conductance peaks in Majorana nanowire
• Generalization of spectral bulk-boundary correspondence
• Majorana bound state engineering via efficient real-space parameter optimization
• Local formula for the $Z_2$ invariant of topological insulators
• Anomalous Floquet topological crystalline insulators
• On the topological character of three-dimensional Nexus triple point degeneracies
• Metal--topological-insulator transition in the quantum kicked rotator with Z2 symmetry
• Single-point spin Chern number in a supercell framework
• Scattering theory of topological invariants in nodal superconductors
• Topological states on uneven (Pb,Sn)Se (001) surfaces
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Optical interface states protected by synthetic Weyl points
• Network model for higher-order topological phases
• Quantitative K-Theory Related to Spin Chern Numbers
• The invisible Majorana bound state at the helical edge
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Simulating Floquet topological phases in static systems
• Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble
• Anomalous levitation and annihilation in Floquet topological insulators
• A Bipartite Kronig-Penney Model with Dirac Potential Scatterers
• Topological superconductivity in a magnetic-texture coupled Josephson junction
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Extended Majorana zero modes in a topological superconducting-normal T-junction
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Transport properties of an interacting Majorana chain
• Band alignment effect in the topological photonic alloy
• Universal phase diagram of topological superconductors subjected to magnetic flux
• Floquet-Weyl and Floquet-topological-insulator phases in a stacked two-dimensional ring-network lattice
• Scattering theory of delicate topological insulators
• Topological reflection matrix
• Multiple Andreev reflections in two-dimensional Josephson junctions with broken time-reversal symmetry
• Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems
• Signature of edge states in resonant wave scattering
• Scattering theory of higher order topological phases
• Topological phases of amorphous matter
• Topological zero-modes of the spectral localizer of trivial metals
• Boiling Quantum Vacuum: Thermal Subsystems from Ground-State Entanglement
• Renormalization-group-inspired neural networks for computing topological invariants
• Pumped heat and charge statistics from Majorana braiding
• 3D Network Model for Strong Topological Insulator Transitions
• Dimensional reduction and scattering formulation for even topological invariants
• Fluctuations and Correlations of Local Topological Order Parameters in Disordered Two-dimensional Topological Insulators
• Improved performance in quantum transport calculations: A divide-and-conquer method based on S-matrices
• Topological insulators and geometry of vector bundles
• Floquet-Anderson localization in the Thouless pump and how to avoid it
• Identifying biases of the Majorana scattering invariant
• Effect of Disorder on the Conductance of (non-) Topological SN Junctions
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators
• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons
• Magnetic doping-induced second-order and first-order topological phase transition inthe photonic alloy
• Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
• Scattering description of edge states in Aharonov-Bohm triangle chains
• Network model for magnetic higher-order topological phases
• Quantum Hall Effect without Chern Bands
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Synthetic gauge field and pseudospin-orbit interaction in a stacked two-dimensional ring-network lattice
• Real-space formulation of the Chern invariant and topological phases in a disordered Chern insulator
• Topological power pumping in quantum circuits
• Stability of Majorana bound states in the presence of spin-flip scattering