Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Abstract

According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1°and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1°, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with fourfold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors ±1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.moiré crystal | graphene | twisted bilayer | moiré band | Hofstadter butterfly M oiré patterns form when nearly identical two-dimensional (2D) crystals are overlaid with a small relative twist angle (1-4). The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5-12). In bilayer graphene, this ratio is small when twist angles exceed about 2°(10, 13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5). At smaller twist angles, electronic properties become increasingly complex. Theory (14, 15) has predicted that extremely flat bands appear at a series of magic angles, the largest of which is close to 1°. Flat bands in 2D electron systems, for example the Landau level bands that appear in the presence of external magnetic fields, allow for physical properties that are dominated by electron-electron interactions, and have been friendly territory for the discovery of fundamentally new states of matter. Here we report transport and scanning probe microscopy (SPM) studies of bilayer graphene moiré crystals with carefully controlled small-twist angles (STA), below 1°. We find that conductivity minima emerge in transport at neutrality, and at anomalous satellite densities that correspond to ±8 additional electrons in the moiré crystal unit cell, and that the conductivity minimum at neutrality is not weakened by a transverse electric field applied between the layers. Our observations can be explained only by strong electronic correlations. MethodsOur STA bilayer graphene samples are fabricated by sequential graphene and hexagonal boron-nitride (hBN) flake pick-up steps using a hemispherical handle substrate (16) that allows an individual flake to be detached from a substrate while leaving flakes in its immediate proximity intact. To...

Topological Exciton Bands in Moiré Heterojunctions

“…For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].In this Letter, we study the influence of moiré patterns on collective excitations, focusing on the important case of excitons in the transition metal dichalcogenide (TMD) 2D semiconductors [7,8] like MoS 2 and WS 2 . Exciton features dominate the optical response of these materials because electron-hole pairs are strongly bound by the Coulomb interaction [9][10][11][12].…”

“…For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].…”

Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials

“…Utilising this technique, Cao et al 44 This is the authors' version, pre-peer reviewed, of the following article: R. Frisenda et al "Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials" Chemical Society Reviews (2017) DOI: 10.1039/C7CS00556C Which has been published in final form at: http://pubs.rsc.org/en/content/articlelanding/2017/cs/c7cs00556c 25 and Kim et al 43 reported on h-BN-encapsulated twisted bilayer graphene devices with twist angles equal or smaller than 2º, where insulating states induced by strong interlayer interactions via superlattice modulation were observed. The technique was taken to the current limit by Kim et al 45 where the sub-degree twist angle regime was explored with a resolution better than 0.2º. This is the authors' version, pre-peer reviewed, of the following article: R. Frisenda et al "Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials" Chemical Society Reviews (2017) DOI: 10.1039/C7CS00556C Which has been published in final form at: http://pubs.rsc.org/en/content/articlelanding/2017/cs/c7cs00556c 26 …”

Scanning Probe Microscopy of Topological Structure Induced Electronic States of Graphene

“…By stacking graphene layers together, the properties of monolayer graphene could be tuned due to the evolution of 2D character and the Dirac fermion behavior. A strongly correlated system may be created and allow to study exotic many‐body quantum phases, as demonstrated in the magic‐angle‐twisted bilayer graphene . Li et al found that the band structure of bilayer graphene is sensitive to the stacking orientation, which alters the interlayer coupling between the two graphene sheets .…”