Graphical abstract template · Graphene research · Moiré
Twisted bilayers and moiré superlattices
Twisted bilayer graphene and graphene on hBN in six panels: tear-and-stack assembly, the moiré pattern and its period, the two layers in 3D, the magic angle of 1.1°, the moiré of graphene on hBN from the 1.8 % lattice mismatch, and the moiré seen by STM.
Updated 9 cited papers45 editable layers
At a glance
- Category
- Graphene research
- Method
- Moiré
- Starting materials
- Exfoliated graphene flakes and hBN on a polymer stamp
- Product
- Twisted bilayers at a set angle, and aligned graphene on hBN
- Key result
- Lattices, stacking maps and STM images computed by LabCanvas from the lattice constants and the twist; the tear-and-stack sizes and angle are drawn, not to scale
- Figure
- 1920 × 1080 px (16:9), 45 editable layers, 6 generated objects
Step by step
- Tear and stackSuccessive transfers with accurate rotational alignment built Bernal bilayers and aligned double-bilayer devices (Kim et al. 2016) and bilayer moiré crystals with twist angles controlled below 1° (Kim et al. 2017); in hBN-assisted tear-and-stack the angle is fixed when the stack is assembled (Varma Sangani et al. 2020; Zhang et al. 2026)
- The moiré patternTwo honeycomb lattices, one turned by θ, give AA, AB and BA stacking regions repeating with the period L = a / (2 sin(θ/2))
- Two layersThe layers drawn apart in 3D at graphite’s 3.35 Å spacing, one turned by θ
- Magic angleAt the magic angles the moiré bands of a twisted bilayer become flat (Bistritzer & MacDonald 2011); bilayers twisted to about 1.1° became superconducting (Cao et al. 2018)
- Graphene on hBNhBN’s lattice constant of 2.504 Å against graphene’s 2.460 Å (Liu et al. 2022) gives a moiré even when the layers are aligned
- Seen by STMSTM images the moiré of graphene on hBN, whose wavelength follows the twist and the 1.8 % mismatch (Yankowitz et al. 2012)
Strengths
- The twist is a new control knob for the bands
- Tear-and-stack fixes the angle at assembly (Zhang et al. 2026)
- hBN gives flat, clean substrates
Limitations
- Small angles relax and vary across a device
- Exact angles are hard to reach and to keep
Uses
- Superconducting and flat-band states
- Moiré superlattice devices
- Talks on twistronics
Papers this template follows
- Bistritzer & MacDonald, “Moiré bands in twisted double-layer graphene”, PNAS 2011. doi:10.1073/pnas.1108174108primary
- Cao et al., “Unconventional superconductivity in magic-angle graphene superlattices”, Nature 2018. doi:10.1038/nature26160primary
- Kim et al., “van der Waals heterostructures with high accuracy rotational alignment”, Nano Lett. 2016. doi:10.1021/acs.nanolett.5b05263primary
- Kim et al., “Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene”, Proc. Natl Acad. Sci. USA 2017. doi:10.1073/pnas.1620140114primary
- Yankowitz et al., “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride”, Nat. Phys. 2012. doi:10.1038/nphys2272primary
- Varma Sangani et al., “Facile deterministic cutting of 2D materials for twistronics using a tapered fibre scalpel”, Nanotechnology 2020. doi:10.1088/1361-6528/ab8b93further reading
- Zhang et al., “Dynamic twisting and imaging of moiré crystals”, Sci. Adv. 2026. doi:10.1126/sciadv.aeg5362further reading
- Liu et al., “Influence of hexagonal boron nitride on electronic structure of graphene”, Molecules 2022. doi:10.3390/molecules27123740further reading
- Hunt et al., “Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure”, Science 2013. doi:10.1126/science.1237240further reading
Computed by LabCanvas after Bistritzer & MacDonald, PNAS 2011 (doi:10.1073/pnas.1108174108), Cao et al., Nature 2018, Kim et al., Nano Lett. 2016, Yankowitz et al., Nat. Phys. 2012, Liu et al., Molecules 2022, and the papers in the details.
How templates are written and checked: editorial guidelines.
Questions
What does the “Twisted bilayers and moiré superlattices” template show?
Twisted bilayer graphene and graphene on hBN in six panels: tear-and-stack assembly, the moiré pattern and its period, the two layers in 3D, the magic angle of 1.1°, the moiré of graphene on hBN from the 1.8 % lattice mismatch, and the moiré seen by STM.
What are the steps shown in “Twisted bilayers and moiré superlattices”?
1. Tear and stack: Successive transfers with accurate rotational alignment built Bernal bilayers and aligned double-bilayer devices (Kim et al. 2016) and bilayer moiré crystals with twist angles controlled below 1° (Kim et al. 2017); in hBN-assisted tear-and-stack the angle is fixed when the stack is assembled (Varma Sangani et al. 2020; Zhang et al. 2026). 2. The moiré pattern: Two honeycomb lattices, one turned by θ, give AA, AB and BA stacking regions repeating with the period L = a / (2 sin(θ/2)). 3. Two layers: The layers drawn apart in 3D at graphite’s 3.35 Å spacing, one turned by θ. 4. Magic angle: At the magic angles the moiré bands of a twisted bilayer become flat (Bistritzer & MacDonald 2011); bilayers twisted to about 1.1° became superconducting (Cao et al. 2018). 5. Graphene on hBN: hBN’s lattice constant of 2.504 Å against graphene’s 2.460 Å (Liu et al. 2022) gives a moiré even when the layers are aligned. 6. Seen by STM: STM images the moiré of graphene on hBN, whose wavelength follows the twist and the 1.8 % mismatch (Yankowitz et al. 2012).
What are the starting materials and the product?
Starting materials: Exfoliated graphene flakes and hBN on a polymer stamp. Product: Twisted bilayers at a set angle, and aligned graphene on hBN.
Which papers is “Twisted bilayers and moiré superlattices” based on?
Bistritzer & MacDonald, “Moiré bands in twisted double-layer graphene”, PNAS 2011 (doi:10.1073/pnas.1108174108); Cao et al., “Unconventional superconductivity in magic-angle graphene superlattices”, Nature 2018 (doi:10.1038/nature26160); Kim et al., “van der Waals heterostructures with high accuracy rotational alignment”, Nano Lett. 2016 (doi:10.1021/acs.nanolett.5b05263); Kim et al., “Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene”, Proc. Natl Acad. Sci. USA 2017 (doi:10.1073/pnas.1620140114); Yankowitz et al., “Emergence of superlattice Dirac points in graphene on hexagonal boron nitride”, Nat. Phys. 2012 (doi:10.1038/nphys2272); Varma Sangani et al., “Facile deterministic cutting of 2D materials for twistronics using a tapered fibre scalpel”, Nanotechnology 2020 (doi:10.1088/1361-6528/ab8b93); Zhang et al., “Dynamic twisting and imaging of moiré crystals”, Sci. Adv. 2026 (doi:10.1126/sciadv.aeg5362); Liu et al., “Influence of hexagonal boron nitride on electronic structure of graphene”, Molecules 2022 (doi:10.3390/molecules27123740); Hunt et al., “Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure”, Science 2013 (doi:10.1126/science.1237240).
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