Magnetism in Moiré Materials

Allan MacDonald , University of Texas

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 creating artificial crystals with lattice constants on the 10 nm scale. Recent progress in fabricating two-dimensional material devices has made it possible to use moiré patterns to design quantum metamaterials in which electrons exhibit strongly-correlated and topologically non-trivial properties that are rare in naturally occuring crystals. Since the miniband widths in both graphene and TMD moiré materials can be made small compared to interaction energy scales (by mechanisms [1,2] that differ), these materials can be used both for quantum simulation and for quantum design. 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 this talk I will focus on magnetism in moiré materials, which is sometimes similar to that found in atomic scale crystals and sometimes unusual. In many cases the magnetic order is purely orbital – opening the door to electrical manipulation of magnetic states. Orbital magnetic order combined with non-trivial topology in single-particle bands [3] helps to make quantum anomalous Hall effects common and gives rise to the fractional quantum anomalous Hall effect. The role of band topology is natural in graphene moirés, where it derives from the interesting band topology of graphene monolayers, but has been an unexpected bonus [3] in the case of TMD moires where it derives from the layer degree of freedom.
[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).

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