Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal

Abstract

One-dimensional (1D) quasicrystals exhibit physical phenomena associated with the 2D integer quantum Hall effect. Here, we transcend dimensions and show that a previously inaccessible phase of matter --- the 4D integer quantum Hall effect --- can be incorporated in a 2D quasicrystal. Correspondingly, our 2D model has a quantized charge-pump accommodated by an elaborate edge phenomena with protected level crossings. We propose experiments to observe these 4D phenomena, and generalize our results to a plethora of topologically equivalent quasicrystals. Thus, 2D quasicrystals may pave the way to the experimental study of 4D physics.

8 pages, 3 figures, 4 appendices

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Cited by in corpus (151)

• Topological Photonics
• Topological Photonics
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• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Synthetic Dimension in Photonics
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological phase transition in non-Hermitian quasicrystals
• Topological quantum matter in synthetic dimensions
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• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Topological quantum matter with cold atoms
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Thouless pumping and topology
• Matter-wave diffraction from a quasicrystalline optical lattice
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Experimental band structure spectroscopy along a synthetic dimension
• Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
• Topological light-trapping on a dislocation
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Topological one-way fiber of second Chern number
• 4D spinless topological insulator in a periodic electric circuit
• Complex classes of periodically driven topological lattice systems
• Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation
• Measuring topological invariants from generalized edge states in polaritonic quasicrystals
• The 6D quantum Hall effect and 3D topological pumps
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Measurement of Chern numbers through center-of-mass responses
• Topological states on fractal lattices
• Anderson localization transitions with and without random potentials
• Four-Dimensional Higher-Order Chern Insulator and Its Acoustic Realization
• Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
• Revealing the topology of quasicrystals with a diffraction experiment
• Virtual Topological Insulators with Real Quantized Physics
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Integer and Fractional Quantum Hall Effect in a Strip of Stripes
• Topological states in quasicrystals
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• Higher-order topological pumping and its observation in photonic lattices
• High-order topological insulators from high-dimensional Chern insulators
• Topological superconductivity in quasicrystals
• Smart patterning for topological pumping of elastic surface waves
• Topological energy conversion through bulk or boundary of driven systems
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• Topological Gaps by Twisting
• Topological mechanics in quasicrystals
• Topological spin excitations in Harper-Heisenberg spin chains
• Quantum many-body topology of quasicrystals
• Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology
• Topological band structure via twisted photons in a degenerate cavity
• Layer-Dependent Topological Phase in a Two-Dimensional Quasicrystal and Approximant
• Local Topological Markers in Odd Dimensions
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Topological Sliding Moiré Heterostructure
• Realization of an atomic quantum Hall system in four dimensions
• Topologically nontrivial Andreev bound states
• Quantized Topological Anderson-Thouless Pump
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Topological Random Fractals
• Hubbard Models for Quasicrystalline Potentials
• Measuring second Chern number from non-adiabatic effects
• Dual gauge theory formulation of planar quasicrystal elasticity and fractons
• Four-dimensional topological lattices through connectivity
• Theory of quantum oscillations in quasicrystals: Quantizing spiral Fermi surfaces
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Classifying transport behavior via current fluctuations in open quantum systems
• Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
• Anomalous charge pumping in a one-dimensional optical superlattice
• Mean-field phases of an ultracold gas in a quasicrystalline potential
• Time Quasilattices in Dissipative Dynamical Systems
• Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays
• Projected Topological Branes
• Enhanced compressibility due to repulsive interaction in the Harper model
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
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• Semiclassical Dynamics, Berry Curvature and Spiral Holonomy in Optical Quasicrystals
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• Entangled multi-component 4D quantum Hall states from photonic crystal defects
• T-duality simplifies bulk-boundary correspondence: some higher dimensional cases
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• Second-order topological modes in two-dimensional continuous media
• Emergence of quasiperiodic Bloch wave functions in quasicrystals
• Colloquium: Synthetic quantum matter in non-standard geometries
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• Dimension transcendence and anomalous charge transport in magnets with moving multiple-$Q$ spin textures
• Superfluid Vortices in Four Spatial Dimensions
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Topological superconductivity in Fibonacci quasicrystals
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Quasiperiodic pairing in graphene quasicrystals
• Interacting Topological Insulators with Synthetic Dimensions
• Linking topological features of the Hofstadter model to optical diffraction figures
• Quantum percolation in quasicrystals using continuous-time quantum walk
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• Topological Lasing from Thouless Pumping in Bilayer Photonic Crystal
• Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Four-dimensional Floquet topological insulator with an emergent second Chern number
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• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
• Second Euler number in four dimensional synthetic matter
• Topological optical Raman superlattices
• Analytic non-Abelian gravitating solitons in the Einstein-Yang-Mills-Higgs theory and transitions between them
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• Nonadiabatic nonlinear non-Hermitian quantized pumping
• Hofstadter-Toda spectral duality and quantum groups
• Synthesizing the Quantum Spin Hall Phase for Ultracold Atoms in Bichromatic Chiral Optical Ladders
• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
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• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Quasiperiodic Quadrupole Insulators
• Topological charge and spin pumping in a semiconductor nanowire
• Asymmetric topological pumping in nonparaxial photonics
• Geometry induced quantum Hall effect and Hall viscosity
• Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems
• Fractional Quantum Hall States on CP2 Space
• Numerical calculation of the $k$-space second Chern number in four dimensions
• Two dimensional photonic quasicrystal edge states protected by second Chern number
• Localization and topological signatures under periodic twisting
• On the origin of energy gaps in quasicrystalline potentials
• Polarization-dependent topology in quantum emitter chains
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential