Helical Majorana surface states of strongly disordered topological superconductors with time-reversal symmetry

Abstract

Noncentrosymmetric superconductors with strong spin-orbit coupling and the B phase of ${}^3$He are possible realizations of topological superconductors with time-reversal symmetry. The nontrivial topology of these time- reversal invariant superconductors manifests itself at the material surface in the form of helical Majorana modes. In this paper, using extensive numerical simulations, we investigate the stability and properties of these Majorana states under strong surface disorder, which influences both bulk and surface states. To characterize the effects of strong disorder, we compute the level spacing statistics and the local density of states of both two- and three-dimensional topological superconductors. The Majorana surface states, which are located in the outermost layers of the superconductor, are protected against weak disorder, due to their topological characteristic. Sufficiently strong disorder, on the other hand, partially localizes the surface layers, with a more pronounced effect on states with energies close to the gap than on those with energies close to zero. In particular, we observe that for all disorder strengths and configurations there always exist two extended states at zero-energy that can carry thermal current. At the crossover from weak to strong disorder the surface state wave functions and the local density of states show signs of critical delocalization. We find that at this crossover the edge density of states of two-dimensional topological superconductors exhibits a zero-energy divergence, reminiscent of the Dyson singularity of quasi-one-dimensional dirty superconductors.

arXiv comment9 pages, 7 figures

References in corpus (50)

• Topological Insulators
• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Anderson Transitions
• Periodic table for topological insulators and superconductors
• Search for Majorana fermions in superconductors
• Heavy fermion superconductivity and magnetic order in non-centrosymmetric $CeP{t}_{3}Si$
• Superconductivty without inversion symmetry: MnSi versus CePt_3Si
• Topological Superconductivity and Superfluidity
• Topological Superconductivity in CuxBi2Se3
• 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 -
• Majorana Fermions in Semiconductor Nanowires: Fundamentals, Modeling, and Experiment
• S-wave/spin-triplet order in superconductors without inversion symmetry: Li${}_2$Pd${}_3$B and Li${}_2$Pt${}_3$B
• Topology of Andreev Bound States with Flat Dispersion
• Classification of Topological Insulators and Superconductors
• Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
• Spin Triplet Superconducting State due to Broken Inversion Symmetry in Li_2Pt_3B
• Topological phases and surface flat bands in superconductors without inversion symmetry
• Quasiparticle localization in superconductors with spin-orbit scattering
• Protected boundary states in gapless topological phases
• Types of topological surface states in nodal noncentrosymmetric superconductors
• Unconventional superconductivity in weakly correlated, non-centrosymmetric $\mathrm{M}{\mathrm{o}}_3\mathrm{A}{\mathrm{l}}_2\mathrm{C}$
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Structure and physical properties of the noncentrosymmetric superconductor Mo3Al2C
• Delocalization in coupled one-dimensional chains
• Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators
• Cross-Correlated Responses of Topological Superconductors and Superfluids
• Surface bound states and spin currents in non-centrosymmetric superconductors
• Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number
• Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
• Andreev bound states and tunneling characteristics of a non-centrosymmetric superconductor
• Localization and delocalization in dirty superconducting wires
• The fate of topological-insulator surface states under strong disorder
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions
• A new superconductor derived from topological insulator heterostructure
• Edge currents as a signature of flat bands in topological superconductors
• Spin current in topologically trivial and nontrivial noncentrosymmetric superconductors
• Dirac Fermions and Superconductivity in Homologous Structures (AgxPb1-xSe)5(Bi2Se3)3m,m = 1,2
• Theory of quasiparticle scattering interference on the surface of topological superconductors
• Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
• Stability of flat-band edge states in topological superconductors without inversion center
• Interface currents in topological superconductor-ferromagnet heterostructures
• Helical spin texture of surface states in topological superconductors
• Scattering theory of topological invariants in nodal superconductors
• Disorder effects on thermal transport on the surface of topological superconductors by the self-consistent Born approximation

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• Interaction-driven first-order and higher-order topological superconductivity
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• Control of Edge Currents at a Ferromagnet - Triplet Superconductor Interface by Multiple Helical Majorana Modes
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