# Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Double layer Graphene

Tuning the twist angle between lattice directions of a stack of neighboring atomic layers leads to formation of moiré superlattices (observed, for example, with scanning probe techniques) and spatial modulation of interlayer coupling. The most known example of twisted graphene double layer (*tDLG*), sketched in Fig. 1a, manifests peculiar interaction between the layers in the range of twist angles from 0° to 30°, giving rise to a variety of interesting phenomena. At small twist angles the electrons slow down due to velocity renormalization and for *a magic angle *~ 1.1^{° }the electronic bands become flat in the whole superlattice Brillouin mini-zone, leading to strong electron - electron correlations and superconductivity. Large angle *tDLG*has been less investigated. Interestingly, at exactly 30° twist, *tDLG *is a quasicrystal, because of irrational sqrt(3) relation between the lattice vectors of the two layers. Moreover, the concept of moiré superlattice for large angle *tDLG *may be questioned because the superlattice has only few atoms and its principal vectors are comparable in size to the principal vectors of single layer graphene lattice itself (Fig. 1b). Secondly, the bands crossing for large angle *tDLG *should occur at the energy close to single layer graphene van Hove singularity at ** M **point of its Brillouin zone. Motivated by these considerations and few published reports on large angle

*tDLG*we performed a detailed study of this system combining experimental microscopy methods and theoretical modeling.

The Gorbachev’sgroup at the University of Manchester fabricated several high purity state of the art devices with few micrometer sized

*tDLG*with the twist angle ranging from 22° to 30°. For such twist angles the moiré real space superlattice is too small to observe with scanning probe microscopy, while the superlattice vectors in the reciprocal space are on the contrary large, so that the twist angles were measured by low energy electron diffraction from a micron sized spot (µLEED) at the Nanospectroscopy beamline of Elettra with precision of ~0.1°, which is important if one wants to be sure that the model system for simulation the band structure corresponds to the real device. Detailed electronic structure of the devices was measured by angle resolved photoemission microscopy (µARPES) at the Specromicroscopy beamline of Elettra and the electron dispersion maps were simulated by Mycha-Kruczyńskiat the University of Bath using the measured twist angles and photoelectron attenuations as the only input parameters for the modeling of µARPES results, which are briefly summarized below.

Extensive modification of the electronic structure in each device not only at the intersection of the bands of the two graphene layers, well known as “bands anti-crossing”, but also across wider energy range were observed (Fig.1 c). Our analysis demonstrates that the appearance of additional minigaps above the energy of the bands’ anti-crossing can be explained by intervalley interaction, i.e. coupling of electrons of different valleys of the same graphene layer via the moiré potential induced by the other layer (Fig. 1b). These two types of interactions manifest themselves in several van Hove singularity peaks present in the density of electronic states (Fig. 1d) in twisted graphene double layer and prove that the that the concept of moiré lattice is still a valid in such small real space superlattice. Interestingly, for the twist angles > 21.8° the intervalley interaction occurs at the energies above band anti-crossings as shown by the arrows in Fig. 1c. Finally, we observe that, as the twist angle approaches 30°, as for the device with 29.7° twist, the twelve-fold symmetry leads to appearance of possible secondary Dirac points ~ 2.4 eV below the Dirac point of a single layer graphene (Fig. 1e and 1f).

**Figure 1**. a) Sketch of a* tDLG* device. b) Moiré superlattice and its principal vectors in inverse space constructed from µARPES map at the energy of Dirac points **K _{1}**,

**K**of the top layer and

_{2}**K**of the bottom layer with green scale bar of 0.5 Å

_{1}’^{-1}. On the right the simulated warped Dirac cones at lower energy schematically describing the interaction between K

_{1}and K

_{2}valleys of top layer graphene. c) Measured (left) and simulated (right) spectra along

**K**

_{2}-K_{1}**-**

**K**

_{1}’**-**

**K**path for three devices with 29.7° (top), 26.5° (middle) and 22.6° (bottom) twist angles. With the arrows showing minigaps schematically described by intervalley interaction in (b). d) Calculated (bottom) density of states and measured (top) angle-integrated spectrum for 29.7°

_{2}*tdLG*device. Note that single layer graphene van Hove singularity is the main peak at 3 eV. e) Constant energy map at 2.4 eV below Dirac point and (f)spectrum across secondary Dirac point indicated by blue arrows.

It has been shown in a previous study that it is possible to dope graphene sufficiently to move the chemical potential to the ** M **point van Hove singularity, and so it might be feasible to explore large-angle

*tDLG*in a similar regime. This suggests large-angle

*tdLG*as a platform in which the interaction effects at van Hove singularities of different origin (in-plane nearest-neighbor coupling, interlayer Dirac cone anticrossing, moiré-induced intralayer intervalley coupling) and competition between them could be explored.

**This research was conducted by the following research team:**

*Matthew J. Hamer*^{1,2}*, Alessio Giampietri*^{3}*, Viktor Kandyba*^{3}*, Francesca Genuzio*^{3}*, Tevfik O. Menteş*^{3}*, Andrea Locatelli*^{3}*, **Roman V. Gorbachev*^{1,2,4}_{, }*Alexei Barinov*^{3 }and *Marcin Mycha-Kruczyński*^{5,6}

^{1 }Department of Physics, University of Manchester, Manchester, UK

^{2 }National Graphene Institute, University of Manchester, Manchester, UK

^{3 }Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy

^{4 }Henry Royce Institute, Manchester, UK

^{5 }Department of Physics, University of Bath, Bath, UK

^{6 }Centre for Nanoscience and Nanotechnology, University of Bath, Bath, UK

**Contact persons:**

Alexei Barinov -

Marcin Mucha-Kruczynski -

### Reference

M. J. Hamer, A. Giampietri, V. Kandyba, F. Genuzio, T. O. Menteş, A. Locatelli,R. V. Gorbachev, A. Barinovand M. Mycha-Kruczyński, "*Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Bilayer Graphene*”, ACS Nano 16, 1954-1962 (2022), DOI:10.1021/acsnano.1c06439