Perfectly localized Majorana corner modes in fermionic lattices

Abstract

Focusing on examples of Majorana zero modes on the corners of a two-dimensional lattice, we introduce a method to find parameter regions where the Majorana modes are perfectly localized on a single site. Such a limit allows us to study the dimerization structure of the sparse bulk Hamiltonian that results in the higher-order topology of the system. Furthermore, such limits typically provide an analytical understanding of the system energy scales. Based on the dimerization structure we extract from the two-dimensional model, we identify a more general stacking procedure to construct Majorana zero modes in arbitrary corners of a $d$-dimensional hypercube, which we demonstrate explicitly in $d\le 3$.

arXiv comment12 pages, 12 figures

References in corpus (39)

• Topological Insulators
• Unpaired Majorana fermions in quantum wires
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• 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
• Topolectrical circuit realization of topological corner modes
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological classification of crystalline insulators through band structure combinatorics
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Observation of second-order topological insulators in sonic crystals
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Minimal model for higher-order topological insulators and phosphorene
• Boundary Green functions of topological insulators and superconductors
• Edge modes in band topological insulators
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Topological and holonomic quantum computation based on second-order topological superconductors
• Braiding Majorana corner modes in a second-order topological superconductor
• Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
• All-electrically tunable networks of Majorana bound states
• Higher-order topological band structures
• Fractional Topological Superconductivity and Parafermion Corner States
• Intrinsic Time-reversal-invariant Topological Superconductivity in Thin Films of Iron-based Superconductors
• Majorana bound states in semiconducting nanostructures
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Braiding higher-order Majorana corner states through their spin degree of freedom
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Corner states, hinge states and Majorana modes in SnTe nanowires
• Topological Superconducting Vortex From Trivial Electronic Bands
• Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction

Cited by in corpus (1)

• Higher-order topological superconductors characterized by Fermi level crossings