One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems

Abstract

We describe nonsymmorphic four-band tight-binding models in one dimension with Kramers degeneracy, and propose topolectric-circuit realizations of their topological phases. We begin with a representative model in the nonsymmorphic AII class with symmorphic time-reversal symmetry and nonsymmorphic charge-conjugation and chiral symmetries, resulting in a ${\mathbb{Z}}_2$ invariant. We also provide a Bogoliubov-de Gennes model in the nonsymmorphic D class with symmorphic charge-conjugation symmetry and nonsymmorphic time-reversal and chiral symmetries, which supports a ${\mathbb{Z}}_4$ classification. To compute these invariants, we extend an open-path winding-number formulation previously used for non-Kramers-degenerate nonsymmorphic ${\mathbb{Z}}_2$ phases to Kramers-degenerate four-band systems. We propose topolectric circuit implementations of nonsymmorphic systems, beginning with a comparison between the symmorphic Su-Schrieffer-Heeger and nonsymmorphic charge-density-wave models. We then extend this methodology to topolectric realizations of the AII and ${\mathbb{Z}}_4$ models, finding that the impedance response reproduces the predicted phase boundaries and associated zero energy modes. Finally, we analyze disorder in the ${\mathbb{Z}}_4$ model and find that, although disorder breaks the nonsymmorphic symmetries, certain domain-wall zero modes in the minimal nearest-neighbor model remain pinned at zero energy because the disorder has no first-order coupling to the soliton subspace; longer-range terms satisfying relevant symmetries lift this emergent property.

21 pages, 16 figures

References in corpus (35)

• Non-Abelian Anyons and Topological Quantum Computation
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Topological Crystalline Insulators
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Introduction to topological superconductivity and Majorana fermions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Antiferromagnetic topological insulators
• Topology of crystalline insulators and superconductors
• Realization of a minimal Kitaev chain in coupled quantum dots
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• Time-Reversal-Invariant $Z_4$ Fractional Josephson Effect
• Topolectric circuits: Theory and construction
• Topological and geometrical aspects of band theory
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• A comprehensive review on topological superconducting materials and interfaces
• Observation of symmetry protected zero modes in topolectrical circuits
• One-dimensional topological insulators with noncentered inversion symmetry axis
• Möbius topological superconductivity in UPt${}_3$
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Topological features of ground states and topological solitons in generalized Su-Schrieffer-Heeger models using generalized time-reversal, particle-hole, and chiral symmetries
• Orbital embedding and topology of one-dimensional two-band insulators
• Majorana zero modes in gate-defined germanium hole nanowires
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• One-dimensional non-interacting topological insulators with chiral symmetry
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Topological superconductivity in proximity to type-II superconductors
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Solitons in binary compounds with stacked two-dimensional honeycomb lattices