One-dimensional ${\mathbb{Z}}_4$ topological superconductor

Abstract

We describe the mean-field model of a one-dimensional topological superconductor with two orbitals per unit cell. Time-reversal symmetry is absent, but a nonsymmorphic symmetry, involving a translation by a fraction of the unit cell, mimics the role of time-reversal symmetry. As a result, the topological superconductor has ${\mathbb{Z}}_4$ topological phases, two which support Majorana bound states and two which do not, in agreement with a prediction based on K-theory classification [K. Shiozaki et al., Phys. Rev. B 93, 195413 (2016)]. As with the Kitaev chain, the presence of Majorana bound states gives rise to the $4\pi$-periodic Josephson effect. A random matrix with nonsymmorphic time-reversal symmetry may be block diagonalized, and every individual block has time-reversal symmetry described by one of the Gaussian orthogonal, unitary or symplectic ensembles. We show how this is manifested in the energy level statistics of a random system in the ${\mathbb{Z}}_4$ class as the spatial period of the nonsymmorphic symmetry is varied from much less than to of the order of the system size.

8 pages, 4 figures, plus supplementary 11 pages

References in corpus (60)

• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Helical liquids and Majorana bound states in quantum wires
• Classification of topological quantum matter with symmetries
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Random Matrix Theories in Quantum Physics: Common Concepts
• Periodic table for topological insulators and superconductors
• Localization of interacting fermions at high temperature
• Topological superconductors: a review
• Prediction and observation of the first antiferromagnetic topological insulator
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Introduction to topological superconductivity and Majorana fermions
• Majorana fermions in chains of magnetic atoms on a superconductor
• Dirac Semimetals in Two Dimensions
• Experimental realization of an intrinsic magnetic topological insulator
• Antiferromagnetic topological insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -
• Topology of crystalline insulators and superconductors
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Hourglass Fermions
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Fractional ac Josephson effect in p- and d-wave superconductors
• Random-matrix theory of Majorana fermions and topological superconductors
• Topological Superconductivity in a Planar Josephson Junction
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Two-dimensional platform for networks of Majorana bound states
• Parity qubits and poor man's Majorana bound states in double quantum dots
• Majorana fermions in superconducting nanowires without spin-orbit coupling
• Remarks on the tight-binding model of graphene
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological non-symmorphic crystalline insulators
• Majorana fermions in superconducting helical magnets
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Topological tight-binding models from non-trivial square roots
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Topological and geometrical aspects of band theory
• Möbius Kondo Insulators
• Roadmap towards Majorana qubits and nonabelian physics in quantum dot-based minimal Kitaev chains
• Equivalent topological invariants for one-dimensional Majorana wires in symmetry class D
• Signatures of topological phase transitions in mesoscopic superconducting rings
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Möbius topological superconductivity in UPt${}_3$
• $Z_4$ Topological Superconductivity in UCoGe
• Phase-induced topological superconductivity in a planar heterostructure
• Orbital embedding and topology of one-dimensional two-band insulators
• Three-phase Majorana zero modes at tiny magnetic fields
• Space group constraints on weak indices in topological insulators
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Topological domain wall states in a non-symmorphic chiral chain
• Topological aspects of $\pi$ phase winding junctions in superconducting wires
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Pfaffian invariant identifies magnetic obstructed atomic insulators

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