Yaacov E. Kraus, Zohar Ringel, Oded Zilberberg
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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http://arxiv.org/abs/1302.2647
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