Multifaceted properties of Andreev bound states: Interplay of symmetry and topology

Abstract

Andreev bound states ubiquitously emerge as a consequence of nontrivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties as Majorana fermions and odd-frequency pairing. A unified concept behind Andreev bound states originates from a soliton state in the one-dimensional Dirac equation with mass domain wall, and the interplay of ABSs with symmetry and topology enriches their physical characteristics. We make an overview of Andreev bound states with a special focus on superfluid ${}^3$He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity, and the anomalous magnetic response. The marriage of the superfluid ${}^3$He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with Andreev bound states.

26 pages, 4 figures

References in corpus (53)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Topology of crystalline insulators and superconductors
• Fulde-Ferrell-Larkin-Ovchinnikov State in Heavy Fermion Superconductors
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Theory of the proximity effect in junctions with unconventional superconductors
• Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Topological field theory and thermal responses of interacting topological superconductors
• Evidence for broken time-reversal symmetry in the superconducting phase of URu${}_2$Si${}_2$
• Tunneling of anyonic Majorana excitations in topological superconductors
• An Index Theorem for the Majorana Zero Modes in Chiral P-Wave Superconductors
• Phase Diagram and Spectroscopy of FFLO states of two-dimensional d-wave superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Strongly interacting Majorana fermions
• Role of the Majorana Fermion and the Edge Mode in Chiral Superfluidity near a p-Wave Feshbach Resonance
• Odd-frequency superconducting states with different types of Meissner response: Problem of coexistence
• Surface Majorana Cone of the Superfluid ${}^3$He B Phase
• Colossal thermomagnetic response in the exotic superconductor URu2Si2
• Majorana surface states of superfluid 3He A- and B-phases in a slab
• Quantum impurity spin in Majorana edge fermions
• Surface Specific Heat of ${}^3$He and Andreev Bound States
• Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
• Self-consistent multiple complex-kink solutions in Bogoliubov-de Gennes and chiral Gross-Neveu systems
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Vortex state in a Fulde-Ferrell-Larkin-Ovchinnikov superconductor based on the quasiclassical theory
• Field-Orientation Dependence of Low-Energy Quasiparticle Excitations in the Heavy-Electron Superconductor UBe13
• Superconducting doped topological materials
• Topological Fermi arcs in superfluid ${}^3$He
• Anomalous Attenuation of Transverse Sound in 3He
• Edge Current due to Majorana Fermions in Superfluid ${}^3$He A- and B-Phases
• Superfluid 3He in a restricted geometry with a perpendicular magnetic field
• Quasiparticle Excitations and Evidence for Superconducting Double Transitions in Monocrystalline U0.97Th0.03Be13
• Vortex Core Structure in Neutral Fermion Superfluids with Population Imbalance
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Consequences of bulk odd-frequency superconducting states for the classification of Cooper pairs
• Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates
• Odd-frequency pairing effect on the superfluid density and the Pauli spin susceptibility in spatially nonuniform spin-singlet superconductors
• Spin triplet nematic pairing symmetry and superconducting double transition in U${}_{1-x}$Th${}_x$Be${}_{13}$
• Majorana edge modes of superfluid 3He A-phase in a slab
• Spin imbalance effect on Larkin-Ovchinnikov-Fulde-Ferrel state
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Emergent Odd-Frequency Superconducting Order Parameter near Boundaries in Unconventional Superconductors
• Magnetization profile and core level spectroscopy in a multiply quantized vortex of imbalanced Fermi superfluids

Cited by in corpus (20)

• Andreev Bound States and Their Signatures
• Theory of Majorana zero modes in unconventional superconductors
• Superconducting phenomena in systems with unconventional magnets
• Enhancing the Josephson diode effect with Majorana bound states
• Josephson effect and odd-frequency pairing in superconducting junctions with unconventional magnets
• Non-Hermitian phase-biased Josephson junctions
• Orientation-dependent transport in junctions formed by $d$-wave altermagnets and $d$-wave superconductors
• Josephson diode effect with Andreev and Majorana bound states
• Radial Fulde-Ferrell-Larkin-Ovchinnikov state in a population-imbalanced Fermi gas
• Emergent pair symmetries in systems with poor man's Majorana modes
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Soliton defects and topological $4\pi$-periodic superconductivity from an orbital magnetic field effect in edge Josephson junctions
• Odd-frequency pairing due to Majorana and trivial Andreev bound states
• Coexistence of topological and nontopological Fermi-superfluid phases
• Kibble-Zurek Dynamics & Statistics of Topological Defects in Chiral Superfluid ${}^3$He Films
• Engineering subgap states in superconductors by the symmetry of altermagnetism
• Collective modes in Fulde-Ferrell-Larkin-Ovchinnikov superconductors: The role of long-range Coulomb interaction and signatures in density response
• Detecting Topological Phase Transition in Superconductor-Semiconductor Hybrids by Electronic Raman Spectroscopy
• The Josephson effect in Fibonacci superconductors
• Giant and robust Josephson diode effect in multiband topological nanowires