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arXiv · 1302.2647

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

Yaacov E. Kraus·Zohar Ringel·Oded Zilberberg
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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.

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Yaacov E. Kraus, Zohar Ringel, Oded Zilberberg. 2013-11-25. Four-Dimensional Quantum Hall Effect in a Two-Dimensional Quasicrystal. https://doi.org/10.1103/physrevlett.111.226401

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