Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators

Abstract

Topological insulators (TIs) having intrinsic or proximity-coupled s-wave superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i) We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition is a surface phase transition after which MZMs appear. The second transition is the well-known vortex phase transition. We find that the surface transition appears because of the competition between the superconducting gap and the local $\mathcal{T}$-breaking gap on the surface. (ii) We present numerical evidence that shows strong variation of the critical doping for the vortex phase transition as the center of the vortex is moved toward or away from the hinges of the sample. We believe our work provides new phenomenology that can help identify HOTIs, as well as illustrating a promising platform for the realization of MZMs.

arXiv comment6+4 pages, 4 figures, published version including Suppl.Mat

References in corpus (64)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological quantum matter with symmetries
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• 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
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Evidence for Majorana bound state in an iron-based superconductor
• Observation of topological superconductivity on the surface of an iron-based superconductor
• Experimental realization of an intrinsic magnetic topological insulator
• Topological protection of photonic mid-gap cavity modes
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Gapless surface Dirac cone in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi2Te4
• Majorana corner modes in a high-temperature platform
• Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2nTe3n+1
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Topological superconductivity on the surface of Fe-based superconductors
• Multiple topological states in iron-based superconductors
• High-Temperature Majorana Corner States
• Higher Order Topological Phases: A General Principle of Construction
• Weak-Pairing Higher Order Topological Superconductors
• Observation of half-integer level shift of vortex bound states in an iron-based superconductor
• Majorana Kramers pairs in higher-order topological insulators
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Minimal model for higher-order topological insulators and phosphorene
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Helical Hinge Majoranas in Iron-Based Superconductors
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Second-order Topological Superconductors with Mixed Pairing
• Magnetic second-order topological insulators and semimetals
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Topological states from topological crystals
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal
• Vortex Lines in Topological Insulator-Superconductor Heterostructures
• Phase tunable second-order topological superconductor
• Superconductivity in doped Dirac semimetals
• Quantum anomalous vortex and Majorana zero mode in iron-based superconductor Fe(Te,Se)
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Splitting the hinge mode of higher-order topological insulators
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Crystalline symmetry protected helical Majorana modes in the iron pnictides
• Detection of second-order topological superconductors by Josephson junctions
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Axion Insulator State with ferromagnetic ordering in CrI3/Bi2Se3/MnBi2Se4 Heterostructure
• Vortex Lattices in the Superconducting Phases of Doped Topological Insulators and Heterostructures
• Effect of Zeeman coupling on the Majorana vortex modes in iron-based topological superconductors
• Topological Vortex Phase Transitions in Iron-Based Superconductors

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• Classical higher-order topological insulators
• Higher-order Weyl Semimetals
• Altermagnetic Routes to Majorana Modes in Zero Net Magnetization
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Quantum Metric and Correlated States in Two-dimensional Systems
• Floquet generation of Second Order Topological Superconductor
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Hierarchy of higher-order topological superconductors in three dimensions
• Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Floquet Second Order Topological Superconductor based on Unconventional Pairing
• Vortex-line topology in iron-based superconductors with and without second-order topology
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Braiding higher-order Majorana corner states through their spin degree of freedom
• Unified characterization for higher-order topological phase transitions
• Chiral Majorana Hinge Modes in Superconducting Dirac Materials
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• High-temperature Majorana corner modes in a $d+i{d}^{\prime }$ superconductor heterostructure: Application to twisted bilayer cuprate superconductors
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Network model for higher-order topological phases
• Rotational symmetry breaking and partial Majorana corner states in a high-Tc superconductor based heterostructure
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Fragile topology in nodal-line semimetal superconductors
• Magnetic flux induced topological superconductivity in magnetic atomic rings
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Effects of disorder on the quantum transport properties in topologically nontrivial metal PbTaSe${}_2$
• Symmetry-protected gates of Majorana qubits in a high-$T_c$ superconductor platform
• Extended Haldane model -- a modern gateway to topological insulators
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Floquet first- and higher-order topological superconductors: A review
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators
• Altermagnetism Induced Bogoliubov Fermi Surfaces Form Topological Superconductivity