Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals

Abstract

We propose that three-dimensional layered octagonal quasicrystals can host magnetic-field-tunable Möbius insulators and various higher-order topological insulators (HOTIs), enabled by the interplay of quasicrystalline symmetry and magnetic order. By constructing a minimal model based on stacked Ammann-Beenker tilings with magnetic exchange coupling and octagonal warping, we demonstrate that an A-type antiferromagnetic (AFM) configuration yields a topological phase protected by an effective time-reversal symmetry $\mathcal{S}=\mathcal{T}{\tau }_{1/2}$. Breaking $\mathcal{S}$ via an in-plane magnetic field induced canting of the AFM order while preserving a nonsymmorphic glide symmetry ${\mathcal{G}}_n={\tau }_{1/2}{\mathcal{M}}_n$ leads to Möbius-twisted surface states, realizing a Möbius insulator in an aperiodic 3D system. Furthermore, we show that the quasicrystal with a general magnetic configuration supports multiple HOTI phases characterized by distinct hinge mode configurations that can be switched by rotating the magnetic field. A low-energy effective theory reveals that these transitions are driven by mass kinks between adjacent surfaces. Our work establishes a platform for realizing symmetry-protected topological phases unique to quasicrystals and highlights the tunability of hinge and surface states via magnetic control.

References in corpus (54)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Prediction and observation of the first antiferromagnetic topological insulator
• Intrinsic magnetic topological insulators in van der Waals layered MnBi${}_2$Te${}_4$-family materials
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Experimental realization of a topological crystalline insulator in SnTe
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Model Hamiltonian for Topological Insulators
• Topological axion states in magnetic insulator MnBi${}_2$Te${}_4$ with the quantized magnetoelectric effect
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Antiferromagnetic topological insulators
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Gapless surface Dirac cone in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Topological Electronic Structure and Its Temperature Evolution in Antiferromagnetic Topological Insulator MnBi2Te4
• Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2nTe3n+1
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling
• Natural van der Waals heterostructural single crystals with both magnetic and topological properties
• Higher-Order Topological Insulators in Quasicrystals
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Engineering Corner States from Two-Dimensional Topological Insulators
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Topological phases without crystalline counterparts
• Higher-order topological insulators in amorphous solids
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Projectively enriched symmetry and topology in acoustic crystals
• Acoustic Möbius insulators from projective symmetry
• Higher-Order topological insulator in a dodecagonal quasicrystal
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Topological states in quasicrystals
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Quasicrystalline second-order topological semimetals
• Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Properties of the Ammann-Beenker tiling and its square approximants