Topology of Andreev bound states with flat dispersion

2011/02/08 by Masatoshi Sato, Yukio Tanaka, Keiji Yada +1 · 8 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Andreev reflection #Bound state #Combinatorics #Condensed matter physics #Fermion #Invariant (physics) #MAJORANA #Magnetic field #Mathematical analysis #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Superconductivity #Topological Materials and Phenomena #Topology (electrical circuits) #Upper and lower bounds #Zeeman effect #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevb.83.224511

published as Phys. Rev. B 83, 224511 (2011) · 56 pages, 11 figures, references are added

arxiv created 2011/02/08 · openalex publication_date 2011/06/23 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Theory of dispersionless Andreev bound states on surfaces of time-reversal-invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. We then summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss the (i) d_xy-wave superconductor, (ii) p_x-wave superconductor, and (iii) noncentrosymmetric superconductors. In the last example, we find a peculiar time-reversal-invariant Majorana fermion. The time-reversal-invariant Majorana fermion shows an unusual response to the Zeeman magnetic field, which can be used to identify it experimentally.

Citations

• Theory of topological spin current in noncentrosymmetric superconductors
• Superconductivity without Inversion Symmetry: MnSi versusCePt3Si
• Symmetries of Pairing Correlations in Superconductor–Ferromagnet Nanostructures
• Quantum field-theoretical methods in transport theory of metals
• Classification of topological insulators and superconductors in three spatial dimensions
• Theory of pairing symmetry inside the Abrikosov vortex core
• Topological Stability of Majorana Zero Modes in Superconductor–Topological Insulator Systems
• Quantum Spin Hall Effect in Graphene
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Andreev bound states and tunneling characteristics of a noncentrosymmetric superconductor
• Tunneling conductance of normal metal/dx2−y2-wave superconductor junctions in the presence of broken time-reversal symmetry states near interfaces
• Time Reversal Polarization and a Z₂ Adiabatic Spin Pump
• Phenomenological theory of zero-energy Andreev resonant states
• Chain of Majorana States from Superconducting Dirac Fermions at a Magnetic Domain Wall
• Fault-tolerant quantum computation by anyons
• Effect of zero-energy bound states on macroscopic quantum tunneling in high-Tcsuperconductor junctions
• Theory of charge transport in diffusive normal metal/unconventional singlet superconductor contacts
• Quantum impurity spin in Majorana edge fermions
• Topological quantum computation

Cited by

• Helical spin texture of surface states in topological superconductors
• Edge states and topological phases in non-Hermitian systems
• Anomalous proximity effect of planar topological Josephson junctions
• Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model
• Topological Ising superconductivity in two-dimensional p-wave magnet
• Tunneling spectroscopy and Majorana modes emergent from topological gapless phases in high-Tccuprate superconductors
• Topological Origin of Andreev Flatland in UTe₂: Implication for Josephson STM Measurements
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology

Related

• Topological Superconductivity and Surface Andreev Bound States in Doped Semiconductors: Application to CuxBi2Se3
• Index-theoretic route to the subgap Andreev bands and topological response in Josephson junctions
• Symmetry Protected and Topologically Protected Crossed Andreev Reflection
• Oscillating-charged Andreev Bound States and Their Appearance in UTe₂
• Time-reversal symmetric topological superconductivity in Machida-Shibata lattices