title: Four-dimensional quantum Hall effect in a two-dimensional quasicrystal.
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.
authors: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
authors: Yaacov E
authors: YE
authors: Kraus
authors: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel and Theoretical Physics, Oxford University, 1, Keble Road, Oxford OX1 3NP, United Kingdom.
authors: Zohar
authors: Z
authors: Ringel
authors: Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel and Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland.
authors: Oded
authors: O
authors: Zilberberg