Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians

Abstract

We discover novel topological effects in the one-dimensional Kitaev chain modified by long-range Hamiltonian deformations in the hopping and pairing terms. This class of models display symmetry-protected topological order measured by the Berry/Zak phase of the lower band eigenvector and the winding number of the Hamiltonians. For exponentially-decaying hopping amplitudes, the topological sector can be significantly augmented as the penetration length increases, something experimentally achievable. For power-law decaying superconducting pairings, the massless Majorana modes at the edges get paired together into a massive non-local Dirac fermion localised at both edges of the chain: a new topological quasiparticle that we call topological massive Dirac fermion. This topological phase has fractional topological numbers as a consequence of the long-range couplings. Possible applications to current experimental setups and topological quantum computation are also discussed.

RevTex4 file, color figures, close to published version

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Exponential Protection of Zero Modes in Majorana Islands
• Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
• Kitaev chains with long-range pairing
• Majorana modes and $p$-wave superfluids for fermionic atoms in optical lattices
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain

Cited by in corpus (87)

• Long-range interacting quantum systems
• Multipartite entanglement in topological quantum phases
• Topological properties of a dense atomic lattice gas
• Majorana nanowires for topological quantum computation
• Probing the role of long-range interactions in the dynamics of a long-range Kitaev Chain
• Extended Kitaev chain with longer-range hopping and pairing
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Long-range topological insulators and weakened bulk-boundary correspondence
• Characterization of topological states via dual multipartite entanglement
• Out-of-equilibrium phase diagram of long-range superconductors
• Topological Quantum Liquids with Long-Range Couplings
• Chiral Topological Superconductors Enhanced by Long-Range Interactions
• Topological phonon polaritons in one-dimensional non-Hermitian nanoparticle chains
• Majorana bound states in semiconducting nanostructures
• Criticality of Spin Systems with Weak Long-Range Interactions
• Entanglement entropy in the Long-Range Kitaev chain
• Dynamical Quantum Phase Transitions in Extended Transverse Ising Models
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Disordered Kitaev chain with long-range pairing: Loschmidt echo revivals and dynamical phase transitions
• Floquet Majorana zero and $\pi$ modes in planar Josephson junctions
• Dynamical quantum phase transition from a critical quantum quench
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• One-dimensional quantum many body systems with long-range interactions
• Edge states of the long-range Kitaev chain: an analytical study
• Singular dynamics and emergence of nonlocality in long-range quantum models
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain
• Current transport properties and phase diagram of a Kitaev chain with long-range pairing
• Topological superconductivity and Majorana states in low-dimensional systems
• Universal dynamical scaling of long-range topological superconductors
• Edge and bulk localization of Floquet topological superconductors
• Self-organized topological insulator due to cavity-mediated correlated tunneling
• Long-range Kitaev Chains via Planar Josephson Junctions
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Quantum dynamics on a lossy non-Hermitian lattice
• Edge insulating topological phases in a two-dimensional long-range superconductor
• Multipartite-Entanglement Tomography of a Quantum Simulator
• Correlations, long-range entanglement and dynamics in long-range Kitaev chains
• Critical phase boundaries of static and periodically kicked long-range Kitaev chain
• Staircase to Higher-Order Topological Phase Transitions
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Dynamical generation of Majorana edge correlations in a ramped Kitaev chain coupled to nonthermal dissipative channels
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Detecting topological phase transitions through entanglement between disconnected partitions in a Kitaev chain with long-range interactions
• Scaling laws for non-Hermitian skin effect with long-range couplings
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Topological footprints of the 1D Kitaev chain with long range superconducting pairings at a finite temperature
• Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with $d$-wave superconductors
• Topological quantum optical states in quasiperiodic cold atomic chains
• Phase diagram of the disordered Kitaev chain with long range pairing connected to external baths
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• End-to-end correlations in the Kitaev chain
• Softening of Majorana edge states by long-range couplings
• Effective Long-Range Pairing and Hopping in Topological Nanowires Weakly Coupled to $s$-Wave Superconductors
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• Dynamic generation of nonequilibrium superconducting states in Kitaev chain
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
• Quench dynamics of entanglement spectrum and topological superconducting phases in a long-range Hamiltonian
• Sublogarithmic behaviour of the entanglement entropy in fermionic chains
• Transformer Wave Function for Quantum Long-Range models
• Universal cooling dynamics toward a quantum critical point
• Effects of Peierls phases in open linear chains
• Topological physics in quantum critical systems
• Information geometric analysis of long range topological superconductors
• First- and second-order quantum phase transitions in the long-range unfrustrated antiferromagnetic Ising chain
• Emerging topological characterization in non-equilibrium states of quenched Kitaev chains
• Polynomial description of inhomogeneous topological superconducting wires
• Diagonal Entropy and Topological Phase Transitions in Extended Kitaev Chains
• Efimov Effect in Long-range Quantum Spin Chains
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch
• On the complex behaviour of the density in composite quantum systems
• Band twisting and resilience to disorder in long-range topological superconductors
• Impurity flat band states in the diamond chain
• Universal Bound States in Long-range Spin Chains with an Impurity
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping
• Electrical, thermal and thermoelectric transport in open long-range Kitaev chain
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Multipartite entanglement in quantum phase transitions
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Topologically nontrivial multicritical points
• Asymptotic behavior of correlation functions of one-dimensional polar-molecules on optical lattices
• Charge current and phase diagram of the disordered open longer-range Kitaev chain
• Universal Relations in Long-range Quantum Spin Chains
• Transport in extended Kitaev chain with time reversal symmetry breaking and long-range interaction