Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus

Abstract

We propose a realization of a quantum Hall effect (QHE) in a second-order topological insulator (SOTI) in three dimensions (3D), which is mediated by hinge states on a torus surface. It results from the nontrivial interplay of the material structure, Zeeman effect, and the surface curvature. In contrast to the conventional 2D- and 3D-QHE, we show that the 3D-SOTI QHE is not affected by orbital effects of the applied magnetic field and exists in the presence of a Zeeman term only, induced e.g. by magnetic doping. To explain the 3D-SOTI QHE, we analyze the boundary charge for a 3D-SOTI and establish its universal dependence on the Aharonov-Bohm flux threading through the torus hole. Exploiting the fundamental relation between the boundary charge and the Hall conductance, we demonstrate the universal quantization of the latter, as well as its stability against random disorder potentials and continuous deformations of the torus surface.

arXiv comment17 pages, 9 figures

References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Quantized Electric Multipole Insulators
• Magnetic-field-induced quantized anomalous Hall effect in intrinsic magnetic topological insulator MnBi${}_2$Te${}_4$
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Trajectory of Anomalous Hall Effect toward the Quantized State in a Ferromagnetic Topological Insulator
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Hedgehog Spin-texture and Berry's Phase tuning in a Magnetic Topological Insulator
• High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels
• Precise quantization of anomalous Hall effect near zero magnetic field
• Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Large magnetic gap at the Dirac point in a Mn-induced Bi${}_2$Te${}_3$ heterostructure
• Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2
• Engineering Corner States from Two-Dimensional Topological Insulators
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Giant Anisotropic Magnetoresistance in a Quantum Anomalous Hall Insulator
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Observation of the zero Hall plateau in a quantum anomalous Hall insulator
• Fractional Topological Superconductivity and Parafermion Corner States
• Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance
• Evolution of Magnetic Interactions in Sb-substituted MnBi2Te4
• High-order topological insulators from high-dimensional Chern insulators
• Origins of electronic bands in antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Majorana and parafermion corner states from two coupled sheets of bilayer graphene
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Fractional boundary charges in quantum dot arrays with density modulation
• From fractional boundary charges to quantized Hall conductance
• Topological invariants to characterize universality of boundary charge in one-dimensionalinsulators beyond symmetry constraints
• Quadrupole spin polarization as signature of second-order topological superconductors
• Infrared study of the multiband low-energy excitations of the topological antiferromagnet MnBi${}_2$Te${}_4$
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Hinge states in a system of coupled Rashba layers
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Universality of Boundary Charge Fluctuations
• Fractional boundary charges with quantized slopes in interacting one- and two-dimensional systems
• Universal properties of boundary and interface charges in multichannel one-dimensional models without symmetry constraints
• Universality of Abelian and non-Abelian Wannier functions in one dimension
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators

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