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.

This is the published version

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Cited by in corpus (41)

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• 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
• Sublattice-sensitive Majorana Modes
• Majorana corner states on the dice lattice
• Non-Hermitian second-order topological superconductors
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Higher-order topological and nodal superconducting transition-metal sulfides MS (M = Nb and Ta)
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• 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
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Edge and corner superconductivity in a 2D topological model
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Controlling Majorana modes by $p$-wave pairing in two-dimensional $p+id$ topological superconductors
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• 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
• Finite-temperature topological invariant for higher-order topological insulators
• Fragile topology in nodal-line semimetal superconductors
• 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