Interacting Majorana modes at surfaces of noncentrosymmetric superconductors
arXiv:1911.01889 · doi:10.1103/PhysRevB.101.024519
Abstract
Noncentrosymmetric superconductors with line nodes are expected to possess topologically protected flat zero-energy bands of surface states, which can be described as Majorana modes. We here investigate their fate if residual interactions beyond BCS theory are included. For a minimal square-lattice model with a plaquette interaction, we find string-like integrals of motion that form Clifford algebras and lead to exact degeneracies. These degeneracies strongly depend on whether the numbers of sites in the and directions are even or odd, and are robust against disorder in the interactions. We show that the mapping of the Majorana model onto two decoupled spin compass models [Kamiya et al., Phys. Rev. B 98, 161409 (2018)] and extra spectator degrees of freedom only works for open boundary conditions. The mapping shows that the three-leg and four-leg Majorana ladders are integrable, while systems of larger width are not. In addition, the mapping maximally reduces the effort for exact diagonalization, which is utilized to obtain the gap above the ground states. We find that this gap remains open if one dimension is kept constant and even, while the other is sent to infinity, at least if that dimension is odd. Moreover, we compare the topological properties of the interacting Majorana model to those of the toric-code model. The Majorana model has long-range entangled ground states that differ by fluxes through the system on a torus. The ground states exhibit string condensation similar to the toric code but the topological order is not robust. While the spectrum is gapped - due to spontaneous symmetry breaking inherited from the compass models - states with different values of the fluxes end up in the ground-state sector in the thermodynamic limit. Hence, the gap does not protect these fluxes against weak perturbations.
arXiv comment14 pages + references, 7 figures, minor update
References in corpus (65)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Unpaired Majorana fermions in quantum wires
- 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
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Periodic table for topological insulators and superconductors
- Comments on the Sachdev-Ye-Kitaev model
- Search for Majorana fermions in superconductors
- Heavy fermion superconductivity and magnetic order in non-centrosymmetric
- Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state
- Topological phases of fermions in one dimension
- Symmetry protection of topological order in one-dimensional quantum spin systems
- On the Integrability of the Rabi Model
- Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
- Superconductivty without inversion symmetry: MnSi versus CePt_3Si
- Riemannian symmetric superspaces and their origin in random matrix theory
- Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
- Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
- High-temperature surface superconductivity in topological flat-band systems
- Fermion zero modes on vortices in chiral superconductors
- Quantum orders in an exact soluble model
- Topology of Andreev Bound States with Flat Dispersion
- Classification of Topological Insulators and Superconductors
- Bipartite entanglement and entropic boundary law in lattice spin systems
- Flat bands in topological media
- Topological phases and surface flat bands in superconductors without inversion symmetry
- Superconductivity in the topological semimetal YPtBi
- One-Dimensional Symmetry Protected Topological Phases and their Transitions
- Fermions, strings, and gauge fields in lattice spin models
- Protected boundary states in gapless topological phases
- Topological Classification and Stability of Fermi Surfaces
- Protected Qubits and Chern Simons theories in Josephson Junction Arrays
- Topological surface states in nodal superconductors
- Superconductivity in the noncentrosymmetric half-Heusler compound LuPtBi : A possible topological superconductor
- Beyond Triplet: Unconventional Superconductivity in a Spin-3/2 Topological Semimetal
- Anomalous Andreev bound state in non-centrosymmetric superconductors
- Types of topological surface states in nodal noncentrosymmetric superconductors
- Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
- Surface density of states and topological edge states in non-centrosymmetric superconductors
- The Quantum Compass Model on the Square Lattice
- Generalized Elitzur's Theorem and Dimensional Reduction
- Topologically protected flat zero-energy surface bands in non-centrosymmetric superconductors
- Effective action for Superconductors and BCS-Bose crossover
- Inflated nodes and surface states in superconducting half-Heusler compounds
- Superconductivity in non-centrosymmetric YPtBi under pressure
- Strongly interacting Majorana fermions
- Unconventional superconductivity in YPtBi and related topological semimetals
- Directional Ordering of Fluctuations in a Two-dimensional Compass Model
- Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
- Symmetry Breaking in Coupled SYK or Tensor Models
- Quantum Ising chains with boundary fields
- Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
- Edge currents as a signature of flat bands in topological superconductors
- Majorana-Hubbard model on the square lattice
- Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
- The origin of holomorphic states in Landau levels from non-commutative geometry, and a new formula for their overlaps on the torus
- Symmetry properties and spectra of the two-dimensional quantum compass model
- Helical spin texture of surface states in topological superconductors
- Surface Majorana fermions and bulk collective modes in superfluid 3He-B
- Phase diagrams of Majorana-Hubbard ladders
- Surface instability in nodal noncentrosymmetric superconductors
- Majorana stripe order on the surface of a three-dimensional topological insulator