Topological Phases of Inhomogeneous Superconductivity

Abstract

We theoretically consider the effect of a spatially periodic modulation of the superconducting order parameter on the formation of Majorana fermions induced by a one-dimensional system with magnetic impurities brought into close proximity to an $s$-wave superconductor. When the magnetic exchange energy is larger than the inter-impurity electron hopping we model the effective system as a chain of coupled Shiba states. While in the opposite regime, the effective system is accurately described by a quantum wire model. Upon including a spatially modulated superconducting pairing, we find, for sufficiently large magnetic exchange energy, the system is able to support a single pair of Majorana fermions with one Majorana fermion on the left end of the system and one on the right end. When the modulation of superconductivity is large compared to the magnetic exchange energy, the Shiba chain returns to a trivially gapped regime while the quantum wire enters a new topological phase capable of supporting two pairs of Majorana fermions.

9 pages, 3 figures

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• Majorana braiding with thermal noise
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• Topological properties of helical Shiba chains with general impurity strength and hybridization
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Cited by in corpus (47)

• Majorana Kramers pairs in higher-order topological insulators
• Floquet Majorana and Para-Fermions in Driven Rashba Nanowires
• Majorana Fermions in Magnetic Chains
• Majorana bound states in semiconducting nanostructures
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Topological properties of chains of magnetic impurities on a superconducting substrate: Interplay between the Shiba band and ferromagnetic wire limits
• One-dimensional quantum many body systems with long-range interactions
• Yu-Shiba-Rusinov qubit
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Low-field Topological Threshold in Majorana Double Nanowires
• Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra
• Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors
• Nodal Andreev Spectra in Multi-Majorana Three-Terminal Josephson Junctions
• Majorana quasiparticles of inhomogeneous Rashba chain
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Asymptotic behavior of impurity-induced bound states in low-dimensional topological superconductors
• How to measure the Majorana polarization of a topological planar Josephson junction
• Effects of the electrostatic environment on superlattice Majorana nanowires
• Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions
• Realizing Topological Superconductivity with Superlattices
• Magnetic field effects on a nanowire with inhomogeneous Rashba spin-orbit coupling: Spin properties at equilibrium
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Controlling topological superconductivity by magnetization dynamics
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Majorana bound state engineering via efficient real-space parameter optimization
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Supercurrent as a Probe for Topological Superconductivity in Magnetic Adatom Chains
• Friedel oscillations and Majorana zero modes in inhomogeneous superconductors
• Majorana bound states in magnetic impurity chains: effects of $d$-wave pairing
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Quasiparticle focusing of bound states in two-dimensional $s$-wave superconductors
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Effect of Van Hove singularities on Shiba states in two-dimensional $s$-wave superconductors
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Majorana-magnon interactions in topological Shiba chains
• Dynamical Shiba states by precessing magnetic moments in an s-wave superconductor
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
• Dynamical torques from Shiba states in $s$-wave superconductors
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. I. Continuum description
• Subgap states at ferromagnetic and spiral-ordered magnetic chains in two-dimensional superconductors. II. Topological classification
• RKKY interaction at helical edges of topological superconductors
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Spectral properties of Andreev crystals
• Spin-dependent tunneling between individual superconducting bound states
• Topological superconducting phase in a non-Hermitian Kitaev chain with staggered pairing imbalance