According to Wikipedia a metamaterial is any material engineered to have properties that are not readily realized in naturally occurring crystals. In practice the metamaterial notion has been employed mainly to design exotic properties for light wave in matter by patterning it on sub-optical wavelengths. The advent of two-dimensional materials in recent years has opened up an emerging opportunity to realize quantum metamaterials, in which many-particle matter waves wavesthat exhibit strongly-correlated and topologically non-trivial properties rare in naturally occurring crystals appear at will. For example, two-dimensional van der Waals crystals that are overlaid with a difference in lattice constant or a relative twist form a moiré pattern. In semiconductors and semimetals, the low-energy electronic properties of these systems are accurately described by Hamiltonians that have the periodicity of the moiré pattern –artificial crystals with lattice constants on the 10 nm scale. Over the past several years substantial progress has been made in the fabrication of these moiremetamaterials, especially ones based on graphene, hexagonal boron nitride, and transitional metal dichalocogenides(TMDs). Since the miniband widths in both graphene and TMD moiré materials can be made small comparted to interaction energy scales, for different reasons [1,2] in the two cases, the birth of moiré materials has opened up a new platform to study strongly correlated electrons and excitions, a platform that can be used both for simulation and for design and has been surprisingly rich. An important property of moiré materials is that their band filling factors can be tuned over large ranges without introducing chemical dopants, simply by using electrical gates.

 

In addition to realizing Mott insulators, density waves, a variety of different types of magnets, and superconductors –states of matter that are familiar from the study of strongly correlated atomic scale crystals –moirematerials have emerged as perhaps the best platform uncovered to date for studies of topologically non-trivial matter, especially strongly interacting topologically non-trivial matter. The role of band topology is natural in graphene moires, where it derives from the interesting band topology of graphene monolayers, but has been an unexpected bonus [3] in the case of TMD moireswhere it derives from twists in the layer degree of freedom. I will discuss the latest developments in this evolving story.

 

[1] R. Bistritzer, and A.H.MacDonald, Proceedings of the National Academy of Sciences 26, 12233 ( 2011).

[2] F. Wu, T. Lovorn, E. Tutuc, and A.H.MacDonald, Phys. Rev. Lett. 121, 026402 (2018).

[3] F. Wu, T. Lovorn, E. Tutuc, I. Martin, and A.H.MacDonald, Phys. Rev. Lett. 122, 086402 (2019).