Hierarchy of higher-order topological superconductors in three dimensions

Abstract

After exploring much on two-dimensional higher-order topological superconductors (HOTSCs) hosting Majorana corner modes (MCMs) only, we propose a simple fermionic model based on a three-dimensional topological insulator proximized with $s$-wave superconductor to realize Majorana hinge modes (MHMs) followed by MCMs under the application of appropriate Wilson-Dirac perturbations. We interestingly find that the second-order topological superconductor, hosting MHMs, appears above a threshold value of the first type perturbation while the third-order topological superconducting phase, supporting MCMs, immediately arises incorporating infinitesimal perturbation of the second kind. Thus, a hierarchy of HOTSC phases can be realized in a single three-dimensional model. Additionally, the application of bulk magnetic field is found to be instrumental in manipulating the number of MHMs, leaving the number for MCMs unaltered. We analytically understand these above-mentioned numerical findings by resorting to the low energy model. We further characterize these topological phases with a distinct structure of the Wannier spectra. From the practical point of view, we manifest quantized transport signatures of these higher-order modes. Finally, we construct Floquet engineering to generate the hierarchy of HOTSC phases by kicking the same perturbations as considered in their static counterpart.

arXiv commentThis is the published version

References in corpus (91)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Quantized Electric Multipole Insulators
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Kwant: a software package for quantum transport
• Atomic quantum gases in periodically driven optical lattices
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• The Coexistence of Superconductivity and Topological Order in the Bi2Se3 Thin Films
• Chiral Topological Superconductor From the Quantum Hall State
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Experimental realization of a two-dimensional synthetic spin-orbit coupling in ultracold Fermi gases
• 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)
• Josephson supercurrent through a topological insulator surface state
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• High-Temperature Majorana Corner States
• Higher Order Topological Phases: A General Principle of Construction
• Weak-Pairing Higher Order Topological Superconductors
• An anomalous higher-order topological insulator
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• 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
• Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Helical Hinge Majoranas in Iron-Based Superconductors
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• Higher-order topological odd-parity superconductors
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Higher-order Floquet topological phases with corner and bulk bound states
• Coupled-wire construction of static and Floquet second-order topological insulators
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
• 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
• Topological and holonomic quantum computation based on second-order topological superconductors
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Hierarchy of higher-order Floquet topological phases in three dimensions
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Measurement-only quantum computation with Majorana corner modes
• Floquet generation of Second Order Topological Superconductor
• Higher Order Topological Insulator via Periodic Driving
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• All-electrically tunable networks of Majorana bound states
• Floquet higher order topological insulator in a periodically driven bipartite lattice
• Higher-order topological band structures
• Floquet higher-order topological insulators and superconductors with space-time symmetries
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Floquet second-order topological insulators in non-Hermitian systems
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Phonon-induced Floquet second-order topological phases protected by space-time symmetries
• Detection of second-order topological superconductors by Josephson junctions
• Time-induced second-order topological superconductors
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Higher-order topological superconductors based on weak topological insulators
• Vortex-line topology in iron-based superconductors with and without second-order topology
• Floquet Second Order Topological Superconductor based on Unconventional Pairing
• Transport spectroscopy of induced superconductivity in the three-dimensional topological insulator HgTe
• Tunable Fragile Topology in Floquet Systems
• High-$T_c$ Superconductor Fe(Se,Te) Monolayer: an Intrinsic, Scalable and Electrically-tunable Majorana Platform
• Majorana fermion exchange in strictly one dimensional structures
• Quadrupole spin polarization as signature of second-order topological superconductors
• Helical Majorana edge mode in a superconducting antiferromagnetic quantum spin Hall insulator
• Superconducting proximity in three dimensional Dirac materials: odd-frequency, pseudoscalar, pseudovector and tensor-valued superconducting orders
• Magnetic Flux Periodicity in Second Order Topological Superconductors
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Braiding and all quantum operations with Majorana modes in 1D

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• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Topological characterization and stability of Floquet Majorana modes in Rashba nanowire
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Generation of higher-order topological insulators using periodic driving
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Intrinsically Interacting Higher-Order Topological Superconductors
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Majorana corner states on the dice lattice
• Sublattice-sensitive Majorana Modes
• Non-Hermitian second-order topological superconductors
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• Higher-order topological and nodal superconducting transition-metal sulfides MS (M = Nb and Ta)
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Topologically localized insulators
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Edge and corner superconductivity in a 2D topological model
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Hierarchical Topological States in Thermal Diffusive Networks
• Higher-order topological superconductor phases in a multilayer system
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Adiabatic charge transport in extended SSH models
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Mixed-parity octupolar pairing and corner Majorana modes in three dimensions
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Fragile topology in nodal-line semimetal superconductors
• Finite-temperature topological invariant for higher-order topological insulators
• Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Extended Haldane model -- a modern gateway to topological insulators
• Topological energy pumping in a quasi-periodically driven four-level system
• Corner Flat Bands Induced by $d$-Density Wave and Partial Corner State Modification Due to Competition with $d$-Wave Superconductivity
• Floquet first- and higher-order topological superconductors: A review