The physical description of all materials is rooted in quantum mechanics, which describes how atoms bond and electrons interact at a fundamental level. Although these quantum effects can in many cases be approximated by a classical description at the macroscopic level, in recent years there has been growing interest in material systems where quantum effects remain manifest over a wider range of energy and length scales. Such quantum materials include superconductors, graphene, topological insulators, Weyl semimetals, quantum spin liquids, and spin ices. Many of them derive their properties from reduced dimensionality, in particular from confinement of electrons to two-dimensional sheets. Moreover, they tend to be materials in which electrons cannot be considered as independent particles but interact strongly and give rise to collective excitations known as quasiparticles. In all cases, however, quantum-mechanical effects fundamentally alter properties of the material. This Review surveys the electronic properties of quantum materials through the prism of the electron wavefunction, and examines how its entanglement and topology give rise to a rich variety of quantum states and phases; these are less classically describable than conventional ordered states also driven by quantum mechanics, such as ferromagnetism.
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B.K. acknowledges financial support by the European Research Council under Advanced Grant No. 669550 (Com4Com) and by the German Science Foundation (DFG) in the Collaborative Research Center TRR80. J.E.M. was supported by the Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under Contract No. DE-AC02-05CH11231, and the National Science Foundation under grant DMR-1507141.
The authors declare no competing financial interests.
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