Moiré Patterns in Two-Dimensional Materials
Tuesday, May 16, 2017 - 2:50pm - 3:30pm
Murphy 130
Allan MacDonald (The University of Texas at Austin)
According to Wikipedia a moiré pattern (/mwɑːrˈeɪ/; French: [mwaˈʁe]) is a large scale interference pattern that is produced when an opaque regular pattern with transparent gaps is overlaid on another similar pattern. A moiré pattern appears only when the regular patterns are rotated by a small twist angle relative to each other or have different, but similar pitches. Moiré patterns are ubiquitous in two-dimensional van der Waals materials with regular patterns formed by two-dimensional crystals and differences in pitch established by differences between lattice constants. I will discuss some electronic properties of two-dimensional semiconductor, gapless semiconductor, and semimetal systems in which moiré patterns have been established.
In these three classes of materials many electronic properties depend on states localized in a small region of momentum space, allowing quantum mechanics to be formulated in terms of envelope function continuum models in which the underlying two-dimensional lattices no longer explicitly appear. In semiconductors and semimetals moiré patterns give rise [1] to a periodic modulation of continuum model Hamiltonians, and commensurability between the moiré pattern and the underlying crystal plays no role. For a given pair of two-dimensional crystals, the moiré pattern can be used to add periodic modulation with an experimentally adjustable unit cell area to a uniform continuum model two-dimensional Hamiltonian. I will discuss some examples [2,3] of new physics that can be explored using van der Waals material moiré patterns.
[1] Moire bands in twisted double-layer graphene, R. Bistritzer and A.H. MacDonald, PNAS 108, 12233 (2011).
[2] Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride, Ashley M. DaSilva, Jeil Jung, and A.H. MacDonald, Phys. Rev. Lett. 117, 036802 (2016).
[3] Topological Exciton Bands in Moiré Heterojunctions, Fengcheng Wu, Timothy Lovorn, and A.H. MacDonald, Phys. Rev. Lett. 118, 147401 (2017).
In these three classes of materials many electronic properties depend on states localized in a small region of momentum space, allowing quantum mechanics to be formulated in terms of envelope function continuum models in which the underlying two-dimensional lattices no longer explicitly appear. In semiconductors and semimetals moiré patterns give rise [1] to a periodic modulation of continuum model Hamiltonians, and commensurability between the moiré pattern and the underlying crystal plays no role. For a given pair of two-dimensional crystals, the moiré pattern can be used to add periodic modulation with an experimentally adjustable unit cell area to a uniform continuum model two-dimensional Hamiltonian. I will discuss some examples [2,3] of new physics that can be explored using van der Waals material moiré patterns.
[1] Moire bands in twisted double-layer graphene, R. Bistritzer and A.H. MacDonald, PNAS 108, 12233 (2011).
[2] Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride, Ashley M. DaSilva, Jeil Jung, and A.H. MacDonald, Phys. Rev. Lett. 117, 036802 (2016).
[3] Topological Exciton Bands in Moiré Heterojunctions, Fengcheng Wu, Timothy Lovorn, and A.H. MacDonald, Phys. Rev. Lett. 118, 147401 (2017).