Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor

Abstract

We perform self-consistent studies of two-dimensional (2D) $s$-wave topological superconductivity (TSC) with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations. In particular, we examine the effects of a nonmagnetic impurity in detail and show that the nature of the spin-polarised midgap bound state varies significantly depending on the material parameters. Most notably, a nonmagnetic impurity in a 2D $s$-wave topological superconductor can act like a magnetic impurity in a conventional $s$-wave superconductor, leading to phase transitions of the ground state as the impurity potential is varied. Furthermore, by solving for the spin-dependent Hartree potential self-consistently along with the superconducting order parameter, we demonstrate that topological charge density waves can coexist with TSC at half filling just as in a conventional $s$-wave superconductor.

arXiv comment11 pages, 11 figures

References in corpus (66)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Conventional superconductivity at 203 K at high pressures
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• New Perspectives for Rashba Spin-Orbit Coupling
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Majorana fermions in a tunable semiconductor device
• Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x)
• The Kernel Polynomial Method
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Fermi surface nesting and the origin of Charge Density Waves in metals
• Large bulk resistivity and surface quantum oscillations in the topological insulator Bi2Te2Se
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Controlling many-body states by the electric-field effect in a two-dimensional material
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Single particle Green's functions and interacting topological insulators
• Josephson supercurrent through a topological insulator surface state
• Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a $p_x+i{p}_y$ superconductor
• Observation of half-height magnetization steps in Sr2RuO4
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Edge modes, edge currents, and gauge invariance in $p_x+i{p}_y$ superfluids and superconductors
• Spectral Properties of Quasiparticle Excitations Induced by Magnetic Moments in Superconductors
• Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3
• Two energy gaps and Fermi surface 'arcs' in NbSe2
• Direct Evidence for the Dirac-Cone Topological Surface States in Ternary Chalcogenide TlBiSe2
• Proximity effect at the superconductor - topological insulator interface
• Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials
• Local Electronic Structure of a Single Magnetic Impurity in a Superconductor
• Electrochemical synthesis and superconducting phase diagram of Cu_xBi2Se3
• Topological superconductivity and unconventional pairing in oxide interfaces
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Local Electronic Structure of Defects in Superconductors
• Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions
• Direct Observation of the Topological Surface States in Lead-Based Ternary Telluride Pb(Bi1-xSbx)2Te4
• Universal impurity-induced bound state in topological superfluids
• Efficient Numerical Self-consistent Mean-field Approach for Fermionic Many-body Systems by Polynomial Expansion on Spectral Density
• A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors
• Vortex states and Majorana fermions in spin-orbit coupled semiconductor-superconductor hybrid structures
• The Anderson prescription for surfaces and impurities
• Discovery of several large families of Topological Insulator classes with backscattering-suppressed spin-polarized single-Dirac-cone on the surface
• Numerical construction of a low-energy effective Hamiltonian in a self-consistent Bogoliubov-de Gennes approach of superconductivity
• Manifestation of chirality in the vortex lattice in a two-dimensional topological superconductor
• Probing vortex Majorana fermions and topology in semiconductor-superconductor heterostructures
• Critical Temperature Enhancement of Topological Superconductors: A Dynamical Mean Field Study
• Formation of magnetic impurities and pair-breaking effect in a superfluid Fermi gas
• Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number
• Orbital angular momentum in a nonchiral topological superconductor
• Impurity Effects on Bound States in the Vortex Core of Topological S-wave Superconductor
• Electronic structure and spontaneous internal field around non-magnetic impurities in spin-triplet chiral p-wave superconductors
• Topological s-wave pairing superconductivity with spatial inhomogeneity: Mid-gap-state appearance and robustness of superconductivity
• Current patterns and magnetic impurities in time-reversal breaking superconductor

Cited by in corpus (9)

• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Topological superconductivity in quasicrystals
• Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe${}_2$ with spin orbit coupling
• Ultracold atoms in a square lattice with spin-orbit coupling: Charge order, superfluidity, and topological signatures
• Delocalisation of Majorana quasiparticles in plaquette--nanowire hybrid system
• Accurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• Gapless superconductivity and its real-space topology in quasicrystals
• Interplay between pairing and correlations in spin-polarized bound states