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We study topological states of matter in quasicrystals, which do not rely on crystalline order. In the absence of a band-structure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of the topological crystalline insulator.
INTRODUCTION With the substantial and increasing demands of consumer electronics in today’s society, electronic waste has become one of the fastest growing segments of environmental pollution (1–3). Therefore, the next generation of electronics with environment-friendly features, such as water dissolvability and recyclability, is in high demand.
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