Majorana multipole response: General theory and application to wallpaper groups

Abstract

Whereas identification of Cooper pair symmetry is the first and crucial step in the investigation of unconventional superconductors, only a few have been established so far because of its own difficulties. To solve this problem, we develop a theory for identification of pairing symmetry using knowledge of topological superconductivity. Establishing the multipole theory of emergent Majorana fermions in time-reversal-invariant topological superconductors, we discover a one-to-one correspondence between the electromagnetic response of Majorana fermions and Cooper pair symmetry. The emergent Majorana fermions host magnetic structures that share the same irreducible representation with Cooper pairs under crystalline symmetry. We furthermore reveal that Majorana fermions in high-spin or nonsymmorphic superconductors may exhibit magnetic octupole responses, which give a direct evidence of these exotic superconducting states. Electric responses of multiple Majorana Kramers pairs are also clarified. Our theory provides the fundamentals for identification of unconventional Cooper pairings through surface-spin-sensitive measurements as well as that for manipulation of Majorana fermions by external electromagnetic fields.

arXiv comment26 pages, 2 figures

References in corpus (100)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological quantum chemistry
• Topological superconductors: a review
• The (High Quality) Topological Materials In The World
• Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator
• Catalogue of Topological Electronic Materials
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topological Superconductivity in CuxBi2Se3
• Topological classification of crystalline insulators through band structure combinatorics
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Topology of crystalline insulators and superconductors
• High-throughput calculations of magnetic topological materials
• Majorana Fermions and Topology in Superconductors
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Spin-Rotation Symmetry Breaking in the Superconducting State of CuxBi2Se3
• Quantitative mappings between symmetry and topology in solids
• Dirac and Weyl Superconductors in Three Dimensions
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Distinguishing a Majorana zero mode using spin resolved measurements
• Topological classification with additional symmetries from Clifford algebras
• Topological odd-parity superconductors
• Multiple topological states in iron-based superconductors
• Thermodynamic evidence for nematic superconductivity in Cu${}_x$Bi${}_2$Se${}_3$
• Observation of superconductivity in 3D Dirac semimetal Cd3As2 crystal
• Superconductivity in the topological semimetal YPtBi
• Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3
• Topological spin-current in non-centrosymmetric superconductors
• Odd-Parity Pairing and Topological Superconductivity in a Strongly Spin-Orbit Coupled Semiconductor
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Unconventional Superconductivity at Mesoscopic Point-contacts on the 3-Dimensional Dirac Semi-metal Cd${}_3$As${}_2$
• Superconductivity in the noncentrosymmetric half-Heusler compound LuPtBi : A possible topological superconductor
• Detecting the Majorana fermion surface state of ${}^3$He-B through spin relaxation
• Topological superconductivity in Dirac semimetals
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Topology of nonsymmorphic crystalline insulators and superconductors
• Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
• Pairing of j=3/2 fermions in half-Heusler superconductors
• Superconductivity in the antiperovskite Dirac-metal oxide Sr${}_3$SnO
• Topological Crystalline Materials - General Formulation, Module Structure, and Wallpaper Groups -
• Weak Antilocalization Effect and Noncentrosymmetric Superconductivity in a Topologically Nontrivial Semimetal LuPdBi
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Topological Blount's theorem of odd-parity superconductors
• Refined symmetry indicators for topological superconductors in all space groups
• Crossed surface flat bands of Weyl semimetal superconductors
• Topological states from topological crystals
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Superconductivity in non-centrosymmetric YPtBi under pressure
• Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Superconductivity in doped Dirac semimetals
• UPt${}_3$ as a Topological Crystalline Superconductor
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Topological Materials Discovery By Large-order symmetry indicators
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Quantum impurity spin in Majorana edge fermions
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Symmetry indicators for topological superconductors
• Tomography of pairing symmetry from magnetotunneling spectroscopy -- a case study for quasi-1D organic superconductors
• Magnetic Field Response and Chiral Symmetry of Time Reversal Invariant Topological Superconductors
• Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces
• Theory of magnetotunneling spectroscopy in spin triplet p-wave superconductors
• Topological Crystalline Materials of $J=3/2$ Electrons: Antiperovskites, Dirac points, and High Winding Topological Superconductivity
• $Z_4$ Topological Superconductivity in UCoGe
• Two-dimensional topological materials discovery by symmetry-indicator method
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Surface electronic state of superconducting topological crystalline insulator
• Topological Nonsymmorphic Crystalline Superconductors
• Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors
• The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
• Majorana multipole response of topological superconductors
• Anisotropic magnetic responses of topological crystalline superconductors
• Quadrupole spin polarization as signature of second-order topological superconductors
• Surface transport coefficients for three-dimensional topological superconductors
• Topological Crystalline Superconductivity in Dirac Semimetal Phase of Iron-based Superconductors
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Variants of the symmetry-based indicator
• Majorana Doublets, Flat Bands, and Dirac Nodes in s-Wave Superfluids
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Topological crystalline superconductors with linearly and projectively represented $C_n$ symmetry
• Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Magnetic tilting and emergent Majorana spin connection in topological superconductors

Cited by in corpus (9)

• Topological enhancement of non-normality in non-Hermitian skin effects
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Spin Susceptibility of a J=3/2 Superconductor
• Majorana multipole response with magnetic point group symmetry
• Majorana Spin Current Generation by Dynamic Strain
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Euler band topology in superfluids and superconductors
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors