Non-Abelian braiding of Dirac fermionic modes using topological corner states in higher-order topological insulator

Abstract

We numerically demonstrate that the topological corner states residing in the corners of higher-order topological insulator possess non-Abelian braiding properties. Such topological corner states are Dirac fermionic modes other than Majorana zero-modes. We claim that Dirac fermionic modes protected by nontrivial topology also support non-Abelian braiding. An analytical description on such non-Abelian braiding is conducted based on the vortex-induced Dirac-type fermionic modes. The braiding operator for Dirac fermionic modes is also analytically derivated and compared with the Majorana zero-modes. Experimentally, such non-Abelian braiding operation on Dirac fermionic modes is proposed to be testified through topological electric circuit.

arXiv comment6 pages, 3 figues

References in corpus (48)

• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Quantized Electric Multipole Insulators
• 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
• Topolectrical circuit realization of topological corner modes
• Observation of a phononic quadrupole topological insulator
• Acoustic higher-order topological insulator on a Kagome lattice
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Topolectrical circuits
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Novel Topological Phase with Zero Berry Curvature
• Electron fractionalization in two-dimensional graphenelike structures
• Observation of second-order topological insulators in sonic crystals
• Topological properties of linear circuit lattices
• Topological Quantum Computation Based on Chiral Majorana Fermions
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Higher-order bulk-boundary correspondence for topological crystalline phases
• A Short Introduction to Topological Quantum Computation
• Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates
• Topolectrical-circuit octupole insulator with topologically protected corner states
• 4D spinless topological insulator in a periodic electric circuit
• Topological nodal states in circuit lattice
• Topological circuits of inductors and capacitors
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Non-Abelian braiding of light
• Topological Anderson Insulator in electric circuits
• Gapped Topological Kink States and Topological Corner States in Graphene
• Quasi-one-dimensional Quantum Anomalous Hall Systems as New Platforms for Scalable Topological Quantum Computation
• Majorana Braiding Dynamics on Nanowires
• Fractional Charge and Spin States in Topological Insulator Constrictions
• Z2 invariant protected bound states in topological insulators
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Fractional Fermions with Non-Abelian Statistics
• Double-frequency Aharonov-Bohm effect and non-Abelian braiding properties of Jackiw-Rebbi zero-mode
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions

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• Higher-order topological phases in crystalline and non-crystalline systems: a review
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• Unveiling non-Abelian statistics of vortex Majorana bound states in iron-based superconductors using fermionic modes
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• Hierarchical Topological States in Thermal Diffusive Networks
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• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Non-Abelian operation through scattering between chiral Dirac edge modes
• Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes