ARPES Signatures of Few-Layer Twistronic Graphenes.

Diverse emergent correlated electron phenomena have been observed in twisted-graphene layers. Many electronic structure predictions have been reported exploring this new field, but with few momentum-resolved electronic structure measurements to test them. We use angle-resolved photoemission spectroscopy to study the twist-dependent (1° < θ < 8°) band structure of twisted-bilayer, monolayer-on-bilayer, and double-bilayer graphene (tDBG). Direct comparison is made between experiment and theory, using a hybrid k·p model for interlayer coupling. Quantitative agreement is found across twist angles, stacking geometries, and back-gate voltages, validating the models and revealing field-induced gaps in twisted graphenes. However, for tDBG at θ = 1.5 ± 0.2°, close to the magic angle θ = 1.3°, a flat band is found near the Fermi level with measured bandwidth Ew = 31 ± 5 meV. An analysis of the gap between the flat band and the next valence band shows deviations between experiment (Δh = 46 ± 5 meV) and theory (Δh = 5 meV), indicative of lattice relaxation in this regime.

Enhanced excitonic features in an anisotropic ReS2/WSe2 heterostructure.

Two-dimensional (2D) semiconductors have opened new horizons for future optoelectronic applications through efficient light-matter and many-body interactions at quantum level. Anisotropic 2D materials like rhenium disulphide (ReS2) present a new class of materials with polarized excitonic resonances. Here, we demonstrate a WSe2/ReS2 heterostructure which exhibits a significant photoluminescence quenching at room temperature as well as at low temperatures. This indicates an efficient charge transfer due to the electron-hole exchange interaction. The band alignment of two materials suggests that electrons optically injected into WSe2 are transferred to ReS2. Polarization resolved luminescence measurements reveal two additional polarization-sensitive exciton peaks in ReS2 in addition to the two conventional exciton resonances X1 and X2. Furthermore, for ReS2 we observe two charged excitons (trions) with binding energies of 18 meV and 15 meV, respectively. The bi-excitons of WSe2 become polarization sensitive and inherit polarizing properties from the underlying ReS2 layers, which act as patterned substrates for top layer. Overall, our findings provide a better understanding of optical signatures in 2D anisotropic materials.

Moiré Superlattice Effects and Band Structure Evolution in Near-30-Degree Twisted Bilayer Graphene.

In stacks of two-dimensional crystals, mismatch of their lattice constants and misalignment of crystallographic axes lead to formation of moiré patterns. We show that moiré superlattice effects persist in twisted bilayer graphene (tBLG) with large twists and short moiré periods. Using angle-resolved photoemission, we observe dramatic changes in valence band topology across large regions of the Brillouin zone, including the vicinity of the saddle point at M and across 3 eV from the Dirac points. In this energy range, we resolve several moiré minibands and detect signatures of secondary Dirac points in the reconstructed dispersions. For twists θ > 21.8°, the low-energy minigaps are not due to cone anticrossing as is the case at smaller twist angles but rather due to moiré scattering of electrons in one graphene layer on the potential of the other which generates intervalley coupling. Our work demonstrates the robustness of the mechanisms which enable engineering of electronic dispersions of stacks of two-dimensional crystals by tuning the interface twist angles. It also shows that large-angle tBLG hosts electronic minigaps and van Hove singularities of different origin which, given recent progress in extreme doping of graphene, could be explored experimentally.

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns.

We construct a two-tailed peaks-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.

Visualizing Orbital Content of Electronic Bands in Anisotropic 2D Semiconducting ReSe2.

Many properties of layered materials change as they are thinned from their bulk forms down to single layers, with examples including indirect-to-direct band gap transition in 2H semiconducting transition metal dichalcogenides as well as thickness-dependent changes in the valence band structure in post-transition-metal monochalcogenides and black phosphorus. Here, we use angle-resolved photoemission spectroscopy to study the electronic band structure of monolayer ReSe2, a semiconductor with a distorted 1T structure and in-plane anisotropy. By changing the polarization of incoming photons, we demonstrate that for ReSe2, in contrast to the 2H materials, the out-of-plane transition metal dz2 and chalcogen pz orbitals do not contribute significantly to the top of the valence band, which explains the reported weak changes in the electronic structure of this compound as a function of layer number. We estimate a band gap of 1.7 eV in pristine ReSe2 using scanning tunneling spectroscopy and explore the implications on the gap following surface doping with potassium. A lower bound of 1.4 eV is estimated for the gap in the fully doped case, suggesting that doping-dependent many-body effects significantly affect the electronic properties of ReSe2. Our results, supported by density functional theory calculations, provide insight into the mechanisms behind polarization-dependent optical properties of rhenium dichalcogenides and highlight their place among two-dimensional crystals.

Spectroscopic Signatures of Electronic Excitations in Raman Scattering in Thin Films of Rhombohedral Graphite.

Rhombohedral graphite features peculiar electronic properties, including persistence of low-energy surface bands of a topological nature. Here, we study the contribution of electron-hole excitations toward inelastic light scattering in thin films of rhombohedral graphite. We show that, in contrast to the featureless electron-hole contribution toward Raman spectrum of graphitic films with Bernal stacking, the inelastic light scattering accompanied by electron-hole excitations in crystals with rhombohedral stacking produces distinct features in the Raman signal which can be used both to identify the stacking and to determine the number of layers in the film.

Retraction Note: Large local lattice expansion in graphene adlayers grown on copper.

The authors unanimously wish to retract this Article due to their concerns about the interpretation of the low-energy electron microscopy (LEEM) and diffraction (LEED) patterns reported in the manuscript. In this study, the authors used spatial and angle-resolved photoemission spectroscopy (ARPES) to characterize graphene monolayers grown on copper foils, and observed regions of graphene adlayers with enhanced graphene/Cu interaction, higher Dirac cone doping level, moiré mini Dirac cones and large lattice expansion. All these properties have been clearly verified and reproduced by photoemission spectroscopy as well as explained by density functional theory. LEEM and LEED characterization were also carried out to confirm the existence of a moiré superlattice and lattice expansion, and the results were included in the main manuscript and Supplementary Information. On further analysis of the LEEM/LEED data, it seems that while the existence of a moiré superlattice can be corroborated, the conclusion of graphene lattice expansion (7%) based on spatially resolved ARPES determinations cannot be confirmed by the LEEM/LEED measurements. The authors realized that these measurements were collected from statistically non-representative areas of the sample. Moreover, the fact that the raw microLEED images bear an asymmetry factor of as much as 5% due to the instrumental aberration makes it impossible to estimate any compression or expansion of the same order. Consequently, their conclusion on the graphene lattice expansion can only be supported by the photoemission data. In view that more complete and reliable structural determinations should be conducted, all authors wish to retract this Article.

Large local lattice expansion in graphene adlayers grown on copper.

Variations of the lattice parameter can significantly change the properties of a material, and, in particular, its electronic behaviour. In the case of graphene, however, variations of the lattice constant with respect to graphite have been limited to less than 2.5% due to its well-established high in-plane stiffness. Here, through systematic electronic and lattice structure studies, we report regions where the lattice constant of graphene monolayers grown on copper by chemical vapour deposition increases up to ~7.5% of its relaxed value. Density functional theory calculations confirm that this expanded phase is energetically metastable and driven by the enhanced interaction between the substrate and the graphene adlayer. We also prove that this phase possesses distinctive chemical and electronic properties. The inherent phase complexity of graphene grown on copper foils revealed in this study may inspire the investigation of possible metastable phases in other seemingly simple heterostructure systems.

Emergence of Interfacial Polarons from Electron-Phonon Coupling in Graphene/h-BN van der Waals Heterostructures.

van der Waals heterostructures, vertical stacks of layered materials, offer new opportunities for novel quantum phenomena which are absent in their constituent components. Here we report the emergence of polaron quasiparticles at the interface of graphene/hexagonal boron nitride (h-BN) heterostructures. Using nanospot angle-resolved photoemission spectroscopy, we observe zone-corner replicas of h-BN valence band maxima, with energy spacing coincident with the highest phonon energy of the heterostructure, an indication of Fröhlich polaron formation due to forward-scattering electron-phonon coupling. Parabolic fitting of the h-BN bands yields an effective mass enhancement of ∼2.3, suggesting an intermediate coupling strength. Our theoretical simulations based on Migdal-Eliashberg theory corroborate the experimental results, allowing the extraction of microscopic physical parameters. Moreover, renormalization of graphene π-band is observed due to the hybridization with the h-BN band. Our work generalizes the polaron study from transition metal oxides to van der Waals heterostructures with higher material flexibility, highlighting interlayer coupling as an extra degree of freedom to explore emergent phenomena.

Electronic bandstructure and van der Waals coupling of ReSe2 revealed by high-resolution angle-resolved photoemission spectroscopy.

ReSe2 and ReS2 are unusual compounds amongst the layered transition metal dichalcogenides as a result of their low symmetry, with a characteristic in-plane anisotropy due to in-plane rhenium 'chains'. They preserve inversion symmetry independent of the number of layers and, in contrast to more well-known transition metal dichalcogenides, bulk and few-monolayer Re-TMD compounds have been proposed to behave as electronically and vibrational decoupled layers. Here, we probe for the first time the electronic band structure of bulk ReSe2 by direct nanoscale angle-resolved photoemission spectroscopy. We find a highly anisotropic in- and out-of-plane electronic structure, with the valence band maxima located away from any particular high-symmetry direction. The effective mass doubles its value perpendicular to the Re chains and the interlayer van der Waals coupling generates significant electronic dispersion normal to the layers. Our density functional theory calculations, including spin-orbit effects, are in excellent agreement with these experimental findings.

Anomalous sequence of quantum Hall liquids revealing a tunable Lifshitz transition in bilayer graphene.

Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse electric field. Here, we drive the Lifshitz transition in bilayer graphene to experimentally controllable carrier densities by applying a large transverse electric field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are observed, indicating that deeper in the valence band the constant energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calculated evolution of the Landau level spectrum. The observed evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.

Transport signatures of pseudomagnetic Landau levels in strained graphene ribbons.

In inhomogeneously strained graphene, low-energy electrons experience a valley-antisymmetric pseudomagnetic field which leads to the formation of localized states at the edge between the valence and conduction bands, understood in terms of peculiar n=0 pseudomagnetic Landau levels. Here we show that such states can manifest themselves as an isolated quadruplet of low-energy conductance resonances in a suspended stretched graphene ribbon, where clamping by the metallic contacts results in a strong inhomogeneity of strain near the ribbon ends.