Magnetic response of Majorana Kramers pairs with an order-two symmetry

Abstract

We study an intrinsic relation between the topology of bulk electronic states and magnetic responses of Majorana Kramers pairs, Kramers pairs of Majorana fermions, on a surface of time-reversal-invariant topological superconductors. Majorana Kramers pairs respond to an applied magnetic field anisotropically due to the interplay between time-reversal and crystal symmetries. In this paper, we propose a systematic procedure to determine such surface magnetic responses in systems with an order-two symmetry. From the analysis of topological invariants associated with an order-two symmetry, it is found that magnetic responses are classified into four types, which are attributed to different topological invariants and exhibit distinguishable, characteristic magnetic responses. For a Kramers pair of Majorana fermions protected by ${\mathbb{Z}}_2$ topological invariants, we clarify that types of magnetic responses are determined only from Fermi--surface topology and symmetry of Cooper pairs. Finally, we apply our theory to the topological nonsymmorphic crystalline superconducting state in UCoGe, which exhibits a biaxially anisotropic magnetic response.

25 pages, 13 figures

References in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• 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
• Superconductivity on the border of weak itinerant ferromagnetism in UCoGe
• Topology of crystalline insulators and superconductors
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• 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
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Topological field theory and thermal responses of interacting topological superconductors
• Topological Blount's theorem of odd-parity superconductors
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Microscopic theory of spin transport at the interface between the superconductor and a ferromagnetic insulator
• Quantum impurity spin in Majorana edge fermions
• Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors
• Anisotropic magnetic responses of topological crystalline superconductors
• Quantum Criticality in the Ferromagnetic Superconductor UCoGe under Pressure and Magnetic Field
• Quadrupole spin polarization as signature of second-order topological superconductors
• Odd-frequency pairing and Ising spin susceptibility in time-reversal invariant superfluids and superconductors
• Majorana multipole response: General theory and application to wallpaper groups
• Phase diagram of UCoGe
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Topological crystalline superconductors with linearly and projectively represented $C_n$ symmetry
• Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe

Cited by in corpus (9)

• Majorana multipole response: General theory and application to wallpaper groups
• Electric Multipoles of Double Majorana Kramers Pairs
• Crystal-symmetry-protected gapless vortex-line phases in superconducting Dirac semimetals
• Majorana multipole response with magnetic point group symmetry
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Nuclear spin relaxation rate of nonunitary Dirac and Weyl superconductors
• Superconducting Gap Structures in Wallpaper Fermion Systems
• Euler band topology in superfluids and superconductors
• Double-twisted surface spectrum from hybridized Majorana Kramers pairs and wallpaper fermions