Quantum impurity coupled to Majorana edge fermions

Abstract

We study a quantum impurity coupled to the edge states of a two-dimensional helical topological superconductor, i.e., to a pair of counterpropagating Majorana fermion edge channels with opposite spin polarizations. For an impurity described by the Anderson impurity model, we show that the problem maps onto a variant of the interacting resonant two-level model which, in turn, maps onto the ferromagnetic Kondo model. Both magnetic and non-magnetic impurities are considered. For magnetic impurities, the bosonization and numerical renormalization group analyses show that the system flows to a fixed point with residual ln 2 entropy and we find characteristically anisotropic static and dynamic impurity magnetic susceptibilities. For non-magnetic impurities, the system flows to a fixed point with no residual entropy and we find diamagnetic response at low temperatures. We comment on the Schrieffer-Wolff transformation for problems with non-standard conduction band continua and on the issues related to the differences in describing the impurities by either Anderson or Kondo impurity models.

13 pages, 10 figures

References in corpus (14)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• The numerical renormalization group method for quantum impurity systems
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Interaction Effects in Topological Superconducting Wires Supporting Majorana Fermions
• Majorana edge states in interacting one-dimensional systems
• Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials
• Quantum impurity spin in Majorana edge fermions
• Phase lapses in transmission through interacting two-level quantum dots
• Topological superfluids with time reversal symmetry
• A quantum criticality perspective on the charging of narrow quantum-dot levels

Cited by in corpus (13)

• Spin and Majorana polarization in topological superconducting wires
• Majorana-Klein hybridization in topological superconductor junctions
• Non-Abelian Braiding of Chiral Majorana Fermions by Quantum Dots
• Majorana modes and complex band structure of quantum wires
• Transport through Majorana nanowires attached to normal leads
• Transport in a hybrid normal-topological superconductor Kondo model
• Transport Signatures of Majorana Quantum Criticality Realized by Dissipative Resonant Tunneling
• Probing Majorana zero modes by measuring transport through an interacting magnetic impurity
• Two-impurity helical Majorana problem
• RKKY interaction at helical edges of topological superconductors
• Mixed-Valence Transition on a Quantum-Dot Coupled to Superconducting and Spin-Polarized Leads
• Electrical transport through a quantum dot side-coupled to a topological superconductor
• Spin-polarized zero-bias peak from a single magnetic impurity at an s-wave superconductor: first-principles study