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

2013/02/28 by Yaacov E. Kraus, Zohar Ringel, Oded Zilberberg · 6 citations
Materials Science · Physics and Astronomy · #2D Materials and Applications #Charge (physics) #Computer science #Condensed matter physics #Electron #Enhanced Data Rates for GSM Evolution #Fractional quantum Hall effect #Integer (computer science) #Physics #Quantum #Quantum Hall effect #Quantum mechanics #Quantum spin Hall effect #Quasicrystal #Quasicrystal Structures and Properties #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.other #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.111.226401

published as Phys. Rev. Lett. 111, 226401 (2013) · 8 pages, 3 figures, 4 appendices

arxiv created 2013/11/25 · openalex publication_date 2013/11/25 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Topological field theory of time-reversal invariant insulators
• Periodic table for topological insulators and superconductors
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Imaging topological edge states in silicon photonics
• Topological insulators and superconductors
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• SimulatingZ2topological insulators with cold atoms in a one-dimensional optical lattice
• Topological Insulators
• Non-Abelian anyons and topological quantum computation

Cited by

• Quasicrystalline Analogue of the Haldane Model
• Ergodic edge modes in the 4D quantum Hall effect
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• T-Duality Simplifies Bulk–Boundary Correspondence: Some Higher Dimensional Cases
• Integer and fractional quantum Hall effect in a strip of stripes
• Topological gap labeling with third Chern numbers in three-dimensional quasicrystals