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

TL;DR

This paper demonstrates that a 2D quasicrystal can host a 4D quantum Hall effect, revealing new topological phases and edge phenomena, and proposes experimental methods to observe these higher-dimensional effects.

Contribution

It introduces a 2D quasicrystal model that exhibits a 4D quantum Hall effect, bridging dimensions and expanding the scope of topological matter research.

Findings

Realization of 4D quantum Hall effect in 2D quasicrystals

Quantized charge-pumping with protected edge states

Proposal for experimental observation of 4D phenomena

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.