Topological phases and surface flat bands in superconductors without inversion symmetry

Abstract

We examine different topological phases in three-dimensional non-centrosymmetric superconductors with time-reversal symmetry by using three different types of topological invariants. Due to the bulk boundary correspondence, a non-zero value of any of these topological numbers indicates the appearance of zero-energy Andreev surface states. We find that some of these boundary modes in nodal superconducting phases are dispersionless, i.e., they form a topologically protected flat band. The region where the zero-energy flat band appears in the surface Brillouin zone is determined by the projection of the nodal lines in the bulk onto the surface. These dispersionless Andreev surface bound states have many observable consequences, in particular, a zero-bias conductance peak in tunneling measurements. We also find that in the gapless phase there appear Majorana surface modes at time-reversal invariant momenta which are protected by a ${\mathbb{Z}}_2$ topological invariant.

8 pages, 5 figures; corrected typos; added references; updated figures

References in corpus (9)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topology of Andreev Bound States with Flat Dispersion
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Surface bound states and spin currents in non-centrosymmetric superconductors
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number

Cited by in corpus (210)

• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Topological superconductors: a review
• Symmetry and Topology in Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Dirac Line Nodes in Inversion Symmetric Crystals
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Topology of crystalline insulators and superconductors
• Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review
• Topological semi-metals with line nodes and drumhead surface states
• Majorana Fermions and Topology in Superconductors
• Bosonic Condensation and Disorder-Induced Localization in a Flat Band
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Dirac and Weyl Superconductors in Three Dimensions
• Flat bands in topological media
• Towards Three-Dimensional Weyl-SurfaceSemimetals in Graphene Networks
• Protected boundary states in gapless topological phases
• Scattering theory of topological insulators and superconductors
• Topological surface states in nodal superconductors
• Possible Topological Superconducting Phases of MoS${}_2$
• Superconductivity in the noncentrosymmetric half-Heusler compound LuPtBi : A possible topological superconductor
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Majorana Kramers Doublets in $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Types of topological surface states in nodal noncentrosymmetric superconductors
• Magnetic Field Driven Nodal Topological Superconductivity in Monolayer Transition Metal Dichalcogenides
• Bogoliubov Fermi surfaces: General theory, magnetic order, and topology
• Observation of half-quantum vortices in topological superfluid 3He
• Topological Lifshitz transitions
• Shockley model description of surface states in topological insulators
• Second-order Topological Superconductors with Mixed Pairing
• High-temperature surface superconductivity in rhombohedral graphite
• Nexus and Dirac lines in topological materials
• Topological Blount's theorem of odd-parity superconductors
• Weyl spin liquids
• Weyl and Dirac semimetals with Z_2 topological charge
• Majorana Flat Bands and Uni-directional Majorana Edge States in Gapless Topological Superconductors
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Possible pairing symmetries in SrPtAs with a local lack of inversion center
• Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points
• Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• Topological carbon materials: a new perspective
• Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides
• A Family Group of Two-dimensional Node-Line Semimetals
• Superconductivity in doped Dirac semimetals
• One-dimensional sawtooth and zigzag lattices for ultracold atoms
• Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines
• Hopf-link multi-Weyl-loop topological semimetals
• Topological Weyl Superconductor to Diffusive Thermal Hall Metal Crossover in the B-Phase of UPt${}_3$
• Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe${}_2$
• Dirac-Fermion-Induced Parity Mixing in Superconducting Topological Insulators
• Flat band in topological matter: possible route to room-temperature superconductivity
• Intrinsic Time-reversal-invariant Topological Superconductivity in Thin Films of Iron-based Superconductors
• Superconductivity in magnetic multipole states
• From Standard Model of particle physics to room-temperature superconductivity
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Topologically stable gapless phases in nonsymmorphic superconductors
• Chiral charge order in the superconductor 2H-TaS2
• Wannier representation of Floquet topological states
• Three-Dimensional Majorana Fermions in Chiral Superconductors
• Topological phase transitions in multi-component superconductors
• Two-dimensional topological nodal line semimetal in layered $X_{2}Y$ ($X$ = Ca, Sr, and Ba; $Y$ = As, Sb, and Bi)
• Emergent Horava gravity in graphene
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Theory of Tunneling Spectroscopy in Unconventional $p$-wave Magnet-Superconductor Hybrid Structures
• Time reversal invariant topological superconductivity in correlated non-centrosymmetric systems
• Proximity effect with noncentrosymmetric superconductors
• Edge currents as a signature of flat bands in topological superconductors
• Fragile surface zero-energy flat bands in three-dimensional chiral superconductors
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Experimental consequences of Bogoliubov Fermi surfaces
• Superconductivity without inversion and time-reversal symmetries
• Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals
• Topological Fermi arcs in superfluid ${}^3$He
• Scanning tunneling spectroscopy of layers of superconducting 2H-TaSe${}_{\text{2}}$: Evidence for a zero bias anomaly in single layers
• Route to Topological Superconductivity via Magnetic Field Rotation
• Double helix nodal line superconductor
• The Topological Relation Between Bulk Gap Nodes and Surface Bound States : Application to Iron-based Superconductors
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Paramagnetically induced gapful topological superconductors
• Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio
• Surface electronic state of superconducting topological crystalline insulator
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Singlet-Quintet Mixing in Spin-Orbit Coupled Superconductors with j=3/2 Fermions
• Majorana surface modes of nodal topological pairings in spin-$\frac{3}{2}$ semi-metals
• Andreev-Majorana bound states in superfluids
• Two-dimensional topological superconductivity with antiferromagnetic insulators
• Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Majorana Flat Bands in s-Wave Gapless Topological Superconductors
• Spin response and topology of a staggered Rashba superconductor
• Flat bands as a route to high-temperature superconductivity in graphite
• Theory of quasiparticle scattering interference on the surface of topological superconductors
• Tunneling spectroscopy of topological superconductors
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Gate-induced Dirac cones in multilayer graphenes
• Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor La${}_7$Ni${}_3$
• Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization
• Generalized Berry phase for a bosonic Bogoliubov system with exceptional points
• Majorana fermions in s-wave noncentrosymmetric superconductor with Rashba and Dresselhaus (110) spin-orbit couplings
• Observation of Dirac surface states in the noncentrosymmetric superconductor BiPd
• Stability of flat-band edge states in topological superconductors without inversion center
• Spin Berry phase in the Fermi arc states
• Coexistence of nontrivial topological properties and strong ferromagnetic fluctuations in $A_2$Cr${}_3$As${}_3$ ($A$=Na, K, Rb and Cs)
• Interface currents in topological superconductor-ferromagnet heterostructures
• Magnetically robust topological edge states and flat bands
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Gapless topological Fulde-Ferrell superfluidity induced by in-plane Zeeman field
• Zeeman field induced topological phase transitions in triplet superconductors
• Spin Currents and Spontaneous Magnetization at Twin Boundaries of Noncentrosymmetric Superconductors
• Quantum oscillations and a non-trivial Berry phase in the noncentrosymmetric superconductor BiPd
• Josephson Effect in Noncentrosymmetric Superconductor Junctions
• Surface transport coefficients for three-dimensional topological superconductors
• Symmetry-Preserving Quadratic Lindbladian and Dissipation Driven Topological Transitions in Gaussian States
• Theory of tunneling spectroscopy for chiral topological superconductors
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Classification of crystalline topological semimetals with an application to Na${}_3$Bi
• Topology and zero energy edge states in carbon nanotubes with superconducting pairing
• Anomalous thermodynamic power laws near topological transitions in nodal superconductors
• Helical spin texture of surface states in topological superconductors
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Superconducting properties of the non-centrosymmetric Superconductors TaXSi (X= Re, Ru)
• Rashba Sandwiches with Topological Superconducting Phases
• Weyl Phases in Point-Group Symmetric Superconductors
• Topological Superconductivity in Multifold Fermion Metals
• Platform for nodal topological superconductors in monolayer molybdenum dichalcogenides
• Topological phase transitions of Thouless charge pumping realized in helical organic molecules with long-range hoppings
• Nature and symmetry of the order parameter of the noncentrosymmetric superconductor Li2Pt3B
• Majorana vortex-bound states in three-dimensional nodal noncentrosymmetric superconductors
• Unconventional superconductivity and Surface pairing symmetry in Half-Heusler Compounds
• Giant surface Edelstein effect in $d$-wave superconductors
• Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry
• Probing Majorana Flat Bands in Nodal $d_{x^2-y^2}$-wave Superconductors with Rashba Spin-Orbit Coupling
• Scattering theory of topological invariants in nodal superconductors
• Surface instability in nodal noncentrosymmetric superconductors
• Stability of flat zero-energy states at the dirty surface of a nodal superconductor
• Dirac and Weyl fermions: from Gor'kov equations to Standard Model (in memory of Lev Petrovich Gorkov)
• Edge currents as a probe of the strongly spin-polarized topological noncentrosymmetric superconductors
• Topological flat bands in optical checkerboard-like lattices
• Quasidisorder Induced Topology
• String and conventional order parameters in the solvable modulated quantum chain
• Finite temperature geometric properties of the Kitaev honeycomb model
• Theory of tunneling conductance of anomalous Rashba metal / superconductor junctions
• Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface
• Superconductivity in noncentrosymmetric NbReSi investigated by muon spin rotation and relaxation
• Toward simulation of topological phenomenas with one-, two- and three-dimensional quantum walks
• Evolution of edge states in topological superfluids during the quantum phase transition
• Constructing Landau framework for topological order: Quantum chains and ladders
• Probing nodeless superconductivity in LaMSi (M = Ni, Pt) using muon-spin rotation and relaxation
• Edge instabilities of topological superconductors
• Topological nodal line in superfluid ${}^3$He and the Anderson theorem
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Conductance oscillations and zero-bias anomaly in a single superconducting junction to a three-dimensional $B{i}_{2}T{e}_3$ topological insulator
• Strong antisymmetric spin-orbit coupling and superconducting properties: The case of noncentrosymmetric LaPtSi
• Inter-orbital p- and d-wave pairings between $d_{xz/yz}$ and $d_{xy}$ orbitals in Sr${}_2$RuO${}_4$
• Sensitivity of quantum walks to boundary of two-dimensional lattices: approaches from the CGMV method and topological phases
• Fermionic boundary modes in two-dimensional noncentrosymmetric superconductors
• Topology of quantum vacuum
• Dynamical bulk-edge correspondence for nodal lines in parameter space
• Nodal topology in $d$-wave superconducting monolayer FeSe
• Appearance of flat surface bands in three-dimensional topological insulators in a ferromagnetic exchange field
• Topological Quantum Critical Points in Strong Coupling limits: Global Symmetries and Strongly Interacting Majorana Fermions
• Superconductivity from piezoelectric interactions in Weyl semimetals
• Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures
• Surface density of states and tunneling spectroscopy of a spin-3/2 superconductor with Bogoliubov Fermi Surfaces
• Generating Giant Spin Currents Using Nodal Topological Superconductors
• Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields
• Topological multiband s-wave superconductivity in coupled multifold fermions
• Intrinsic topological superconductivity with exactly flat surface bands in the quasi-one-dimensional A${}_2$Cr${}_3$As${}_3$ (A=Na, K, Rb, Cs) superconductors
• Controllable simulation of topological phases and edge states with quantum walk
• Orbital hybridized topological Fulde-Ferrel superfluidity in a noncentrosymmetric optical lattice
• Tunneling conductance in superconducting junctions with $p$-wave unconventional magnets breaking time-reversal symmetry
• Anatomy of a periodically driven p-wave superconductor
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Universal hard-edge statistics of non-Hermitian random matrices
• Disentanglement, disorder lines, and Majorana edge states in a solvable quantum chain
• Topological nodal superconducting phases and topological phase transition in the hyperhoneycomb lattice
• Non-Abelian topological superconductivity in maximally twisted double-layer spin-triplet valley-singlet superconductors
• On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices
• Topological quantum phase transitions in the spin-singlet superconductor with Rashba and Dresselhaus (110) spin-orbit couplings
• Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems
• Two-dimensional Paired Topological Superfluids of Rydberg Fermi Gases
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
• Manifestation of a topological gapless phase in a two-dimensional chiral symmetric system through Loschmidt echo
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates
• Brane order and quantum magnetism in modulated anisotropic ladders
• Boundary states in the chiral symmetric systems with a spatial symmetry
• Complete zero-energy flat bands of surface states in fully gapped chiral noncentrosymmetric superconductors
• Graphite on graphite
• Emergent topology in thin films of nodal line semimetals
• ${}^3$He-R: A Topological $s^{\pm }$ Superfluid with Triplet Pairing
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Multi-locational Majorana Zero Modes
• Cartesian Nodal Lines and Magnetic Kramers Weyl Nodes in Spin-Split Antiferromagnets
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• Weakly Anisotropic Noncentrosymmetric Superconductors with Radial Line Nodes and Thermodynamical Anomalies
• Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators
• Manipulation of Majorana wave packets at surfaces of nodal noncentrosymmetric superconductors
• Unconventional Pairings and Radial Line Nodes in Inversion Symmetry Broken Superconductors
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Inversion symmetry breaking and criticality in free fermionic lattices
• Equivalence class of Emergent Single Weyl fermion lattice models in 3 dimensions: gapless superconductors and superfluids versus chiral fermions
• Majorana flat bands at structured surfaces of nodal noncentrosymmetric superconductors
• Nodal Line Topological Superfluid and Multiply Protected Majorana Fermi Arc in a Three-Dimensional Time-Reversal-Invariant Superfluid Model