Maximized electron interactions at the magic angle in twisted bilayer graphene.

The electronic properties of heterostructures of atomically thin van der Waals crystals can be modified substantially by moiré superlattice potentials from an interlayer twist between crystals1,2. Moiré tuning of the band structure has led to the recent discovery of superconductivity3,4 and correlated insulating phases5 in twisted bilayer graphene (TBG) near the 'magic angle' of twist of about 1.1 degrees, with a phase diagram reminiscent of high-transition-temperature superconductors. Here we directly map the atomic-scale structural and electronic properties of TBG near the magic angle using scanning tunnelling microscopy and spectroscopy. We observe two distinct van Hove singularities (VHSs) in the local density of states around the magic angle, with an energy separation of 57 millielectronvolts that drops to 40 millielectronvolts with high electron/hole doping. Unexpectedly, the VHS energy separation continues to decrease with decreasing twist angle, with a lowest value of 7 to 13 millielectronvolts at a magic angle of 0.79 degrees. More crucial to the correlated behaviour of this material, we find that at the magic angle, the ratio of the Coulomb interaction to the bandwidth of each individual VHS (U/t) is maximized, which is optimal for electronic Cooper pairing mechanisms. When doped near the half-moiré-band filling, a correlation-induced gap splits the conduction VHS with a maximum size of 6.5 millielectronvolts at 1.15 degrees, dropping to 4 millielectronvolts at 0.79 degrees. We capture the doping-dependent and angle-dependent spectroscopy results using a Hartree-Fock model, which allows us to extract the on-site and nearest-neighbour Coulomb interactions. This analysis yields a U/t of order unity indicating that magic-angle TBG is moderately correlated. In addition, scanning tunnelling spectroscopy maps reveal an energy- and doping-dependent three-fold rotational-symmetry breaking of the local density of states in TBG, with the strongest symmetry breaking near the Fermi level and further enhanced when doped to the correlated gap regime. This indicates the presence of a strong electronic nematic susceptibility or even nematic order in TBG in regions of the phase diagram where superconductivity is observed.

Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions.

The possibility of confining interlayer excitons in interfacial moiré patterns has recently gained attention as a strategy to form ordered arrays of zero-dimensional quantum emitters and topological superlattices in transition metal dichalcogenide heterostructures. Strain is expected to play an important role in the modulation of the moiré potential landscape, tuning the array of quantum dot-like zero-dimensional traps into parallel stripes of one-dimensional quantum wires. Here, we present real-space imaging of unstrained zero-dimensional and strain-induced one-dimensional moiré patterns along with photoluminescence measurements of the corresponding excitonic emission from WSe2/MoSe2 heterobilayers. Whereas excitons in zero-dimensional moiré traps display quantum emitter-like sharp photoluminescence peaks with circular polarization, the photoluminescence emission from excitons in one-dimensional moiré potentials shows linear polarization and two orders of magnitude higher intensity. These results establish strain engineering as an effective method to tailor moiré potentials and their optoelectronic response on demand.

Author Correction: Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Bent Ferroelectric Domain Walls as Reconfigurable Metallic-Like Channels.

Use of ferroelectric domain-walls in future electronics requires that they are stable, rewritable conducting channels. Here we demonstrate nonthermally activated metallic-like conduction in nominally uncharged, bent, rewritable ferroelectric-ferroelastic domain-walls of the ubiquitous ferroelectric Pb(Zr,Ti)O3 using scanning force microscopy down to a temperature of 4 K. New walls created at 4 K by pressure exhibit similar robust and intrinsic conductivity. Atomic resolution electron energy-loss spectroscopy confirms the conductivity confinement at the wall. This work provides a new concept in "domain-wall nanoelectronics".

Visualization of moiré superlattices.

Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity1,2, magnetism3, topological edge states4,5, exciton trapping6 and correlated insulator phases7. However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix.

Piezoelectric enhancement under negative pressure.

Enhancement of ferroelectric properties, both spontaneous polarization and Curie temperature under negative pressure had been predicted in the past from first principles and recently confirmed experimentally. In contrast, piezoelectric properties are expected to increase by positive pressure, through polarization rotation. Here we investigate the piezoelectric response of the classical PbTiO3, Pb(Zr,Ti)O3 and BaTiO3 perovskite ferroelectrics under negative pressure from first principles and find significant enhancement. Piezoelectric response is then tested experimentally on free-standing PbTiO3 and Pb(Zr,Ti)O3 nanowires under self-sustained negative pressure, confirming the theoretical prediction. Numerical simulations verify that negative pressure in nanowires is the origin of the enhanced electromechanical properties. The results may be useful in the development of highly performing piezoelectrics, including lead-free ones.