The 6D quantum Hall effect and 3D topological pumps

Abstract

Modern technological advances allow for the study of systems with additional synthetic dimensions. Using such approaches, higher-dimensional physics that was previously deemed to be of purely theoretical interest has now become an active field of research. In this work, we derive from first principles using a semiclassical equation of motions approach, the bulk response of a six-dimensional Chern insulator. We find that in such a system a quantized bulk response appears with a quantization originating from a six-dimensional topological index -- the 3rd Chern number. Alongside this novel six-dimensional response, we rigorously describe the lower even-dimensional Chern-like responses that can occur due to nonvanishing 1st and 2nd Chern numbers in sub-spaces of the six-dimensional space. Last, we propose how to realize such a bulk response using three-dimensional topological charge pumps in cold atomic systems.

arXiv comment12 pages + 13 pages of supporting material, 2 figures, published version

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Cited by in corpus (55)

• Topological quantum matter in synthetic dimensions
• Topological Non-Hermitian skin effect
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Experimental observation of temporal pumping in electro-mechanical waveguides
• 4D spinless topological insulator in a periodic electric circuit
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• Landau-Zener Transition in Topological Acoustic Pumping
• Edge States and Topological Pumping in Stiffness Modulated Elastic Plates
• Many-Body Topological and Skin States without Open Boundaries
• Topolectrical-circuit realization of 4D hexadecapole insulator
• Topological states in quasicrystals
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Exploring 2D synthetic quantum Hall physics with a quasi-periodically driven qubit
• A comprehensive review on developments of synthetic dimensions
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Exploring Topology of 1D Quasiperiodic Metastructures through Modulated LEGO Resonators
• High-order topological insulators from high-dimensional Chern insulators
• Tensor Berry connections and their topological invariants
• Ground-state quantum geometry in superconductor-quantum dot chains
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Symmetry and topology of hyperbolic Haldane models
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Many-Body Localization with Quasiperiodic Driving
• Topological Sliding Moiré Heterostructure
• Realization of an atomic quantum Hall system in four dimensions
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Enhanced higher harmonic generation from nodal topology
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Four-dimensional topological lattices through connectivity
• Observation of flat-band and band transition in the synthetic space
• Six-dimensional time-space crystalline structures
• Josephson effect in a Fibonacci quasicrystal
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Second-order topological modes in two-dimensional continuous media
• Entangled multi-component 4D quantum Hall states from photonic crystal defects
• Topological superconductivity in Fibonacci quasicrystals
• Dimensional crossover of the integer quantum Hall plateau transition and disordered topological pumping
• Anisotropic non-linear optical response of nodal loop materials
• Topological Electromagnetic Effects and Higher Second Chern Numbers in Four-Dimensional Gapped Phases
• Floquet simulators for topological surface states in isolation
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
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• Two-dimensional Thouless pumping in time-space crystalline structures
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• Four-dimensional Floquet topological insulator with an emergent second Chern number
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• Evaluation of real-space second Chern number using the kernel polynomial method
• Hopf Semimetals
• Numerical calculation of the $k$-space second Chern number in four dimensions