Stacking boundaries and transport in bilayer graphene

Metal-Semiconductor Behavior along the Line of Stacking Order Change in Gated Multilayer Graphene

We investigated gated multilayer graphene with stacking order changes along the armchair direction. We consider that some layers cracked to release shear strain at the stacking domain wall. The energy cones of graphene overlap along the corresponding direction in the k-space, so the topological gapless states from different valleys also overlap. However, these states strongly interact and split due to atomic-scale defects caused by the broken layers, yielding an effective energy gap. We find that for some gate voltages, the gap states cross and the metallic behavior along the stacking domain wall can be restored. In particular cases, a flat band appears at the Fermi energy. We show that for small variations in the gate voltage, the charge occupying this band oscillates between the outer layers.

Emerging Characteristics and Properties of Moiré Materials

In recent years, scientists have conducted extensive research on Moiré materials and have discovered some compelling properties. The Moiré superlattice allows superconductivity through flat-band and strong correlation effects. The presence of flat bands causes the Moiré material to exhibit topological properties as well. Modulating electronic interactions with magnetic fields in Moiré materials enables the fractional quantum Hall effect. In addition, Moiré materials have ferromagnetic and antiferromagnetic properties. By tuning the interlayer coupling and spin interactions of the Moiré superlattice, different magnetic properties can be achieved. Finally, this review also discusses the applications of Moiré materials in the fields of photocurrent, superconductivity, and thermoelectricity. Overall, Moiré superlattices provide a new dimension in the development of two-dimensional materials.

Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.

Impact of Electric Field Disorder on Broken-Symmetry States in Ultraclean Bilayer Graphene

Bilayer graphene (BLG) has multiple internal degrees of freedom and a constant density of states down to the charge neutrality point when trigonal warping is ignored. Consequently, it is susceptible to various competing ground states. However, a coherent experimental determination of the ground state has been challenging due to the interaction-disorder interplay. Here we present an extensive transport study in a series of dually gated freestanding BLG devices and identify the layer-antiferromagnet as the ground state with a continuous strength across all devices. This strength correlates with the width of the state in the electric field. We systematically identify electric-field disorder─spatial variations in the interlayer potential difference─as the main source responsible for the observations. Our results pinpoint for the first time the importance of electric-field disorder on spontaneous symmetry breaking in BLG and solve a long-standing debate on its ground state. The electric-field disorder should be universal to all 2D materials.

Moiré patterns of twisted bilayer antimonene and their structural and electronic transition

Interlayer twisting in two-dimensional (2D) van der Waals (vdW) heterostructures often leads to a periodic moiré pattern which is a superlattice structure on top of the original atomic lattice of the 2D layers. The formation of a moiré superlattice can be accompanied by a significant structural reconstruction and ultra-flat electronic bands. The moiré superlattice is typically built with a tunable scale by controlling the rotation angle θ between the individual 2D layers. In this paper, we report the structural reconstruction and electronic transition in moiré patterns of twisted bilayer antimonene, based on Kohn-Sham density functional theory calculations. Starting from rigid moiré structures, the atomic relaxation leads to an array of high-symmetry stacking domains with soliton boundaries through a vortex-like reconstruction. For twist angle θ≤ 6.01°, the impact of the structural reconstruction on the electronic bands becomes very significant, in the appearance of flat bands at the valence band edge, and no magic angle is required for the flat bands to appear in the 2D Sb moiré patterns. Both inhomogeneous interlayer hybridization and local strain are found to be responsible for the formation of these flat electronic bands.

Tailoring spintronic and opto-electronic characteristics of bilayer AlN through MnO x clusters intercalation; an ab initio study

Adopting ab initio density functional theory (DFT) technique, the spintronic and opto-electronic characteristics of MnO x (i.e., Mn, MnO, MnO2, MnO3 and MnO4) clusters intercalated bilayer AlN (BL/AlN) systems are investigated in this paper. In terms of electron transfer, charge transfer occurs from BL/AlN to the MnO x clusters. MnO x clusters intercalation induces magnetic behavior in the non-magnetic AlN system. The splitting of electronic bands occurs, thus producing spintronic trends in the electronic structure of BL/AlN system. Further, MnO x intercalation converts insulating BL/AlN to a half metal/semiconductor material during spin up/down bands depending upon the type of impurity cluster present in its lattice. For instance, Mn, MnO and MnO2 intercalation in BL/AlN produces a half metallic BL/AlN system as surface states are available at the Fermi Energy (E F) level for spin up and down band channels, accordingly. Whereas, MnO3 and MnO4 intercalation produces a conducting BL/AlN system having a 0.5 eV and 0.6 eV band gap during the spin down band channel, respectively. During spin up band channels these systems behave as semiconductors with band gaps of 1.4 eV and 1.2 eV, respectively. In terms of optical characteristics (i.e., absorption coefficient, reflectivity and energy loss spectrum (ELS)), it was found that MnO x intercalation improves the absorption spectrum in the low electron energy range and absorption peaks are observed in the 0-3 eV energy range, which are not present in the absorption spectrum of pure BL/AlN. The static reflectivity parameter of BL/AlN is increased after MnO x intercalation and the ELS parameter obtains significant peak intensities in the 0-2 eV energy range, whereas for pure BL/AlN, ELS contains negligible value in this energy range. Outcomes of this study indicate that, MnO x clusters intercalation in BL/AlN is a suitable technique to tailor its spintronic and opto-electronic trends. Thus, experimental investigation can be carried out on the systems discussed in this work, so as to fabricate practical layered AlN systems that are functional in the field of nano-technology.

Modulation of Magnetoresistance Polarity in BLG/SL-MoSe2 Heterostacks

Two-dimensional (2D) layered materials have an atomically thin and flat nature which makes it an ultimate candidate for spintronic devices. The spin-valve junctions (SVJs), composed of 2D materials, have been recognized as unique features of spin transport polarization. However, the magnetotransport properties of SVJs are highly influenced by the type of intervening layer (spacer) inserted between the ferromagnetic materials (FMs). In this situation, the spin filtering effect at the interfaces plays a critical role in the observation of the magnetoresistance (MR) of such magnetic structures, which can be improved by using promising hybrid structure. Here, we report MR of bilayer graphene (BLG), single-layer MoSe₂ (SL-MoSe₂), and BLG/SL-MoSe₂ heterostack SVJs. However, before annealing, BLG and SL-MoSe₂ SVJs demonstrate positive MR, but after annealing, BLG reverses its polarity while the SL-MoSe₂ maintains its polarity and demonstrated stable positive spin polarizations at both interfaces due to meager doping effect of ferromagnetic (FM) contacts. Further, Co/BLG/SL-MoSe₂/NiFe determines positive MR, i.e., ~ 1.71% and ~ 1.86% at T = 4 K before and after annealing, respectively. On the contrary, NiFe/BLG/SL-MoSe₂/Co SVJs showed positive MR before annealing and subsequently reversed its MR sign after annealing due to the proximity-induced effect of metals doping with graphene. The obtained results can be useful to comprehend the origin of polarity and the selection of non-magnetic material (spacer) for magnetotransport properties. Thus, this study established a new paragon for novel spintronic applications.

Two Phases with Different Domain Wall Networks and a Reentrant Phase Transition in Bilayer Graphene under Strain

The analytical two-chain Frenkel-Kontorova model is used to describe domain wall networks in bilayer graphene upon biaxial stretching of one of the layers. We show that the commensurate-incommensurate phase transition leading to formation of a regular triangular domain wall network at the relative biaxial elongation of 3.0×10^{-3} is followed by the transition to another incommensurate phase with a striped network at the elongation of 3.7×10^{-3}. The reentrant transition to the phase with a triangular domain wall network is predicted for the elongation ∼10^{-2}.

One-dimensional hexagonal boron nitride conducting channel

Hexagonal boron nitride (hBN) is an insulating two-dimensional (2D) material with a large bandgap. Although known for its interfacing with other 2D materials and structural similarities to graphene, the potential use of hBN in 2D electronics is limited by its insulating nature. Here, we report atomically sharp twin boundaries at AA'/AB stacking boundaries in chemical vapor deposition-synthesized few-layer hBN. We find that the twin boundary is composed of a 6'6' configuration, showing conducting feature with a zero bandgap. Furthermore, the formation mechanism of the atomically sharp twin boundaries is suggested by an analogy with stacking combinations of AA'/AB based on the observations of extended Klein edges at the layer boundaries of AB-stacked hBN. The atomically sharp AA'/AB stacking boundary is promising as an ultimate 1D electron channel embedded in insulating pristine hBN. This study will provide insights into the fabrication of single-hBN electronic devices.

Spin-layer locked gapless states in gated bilayer graphene

Gated bilayer graphene exhibits spin-degenerate gapless states with a topological character localized at stacking domain walls. These states allow for one-dimensional currents along the domain walls. We herein demonstrate that these topologically protected currents are spin-polarized and locked in a single layer when bilayer graphene contains stacking domain walls decorated with magnetic defects. The magnetic defects, which we model as π-vacancies, perturb the topological states but also lift their spin degeneracy. One gapless state survives the perturbation of these defects, and its spin polarization is largely localized in one layer. The spin-polarized current in the topological state flows in a single layer, and this finding suggests the possibility of effectively exploiting these states in spintronic applications.

Spin-degenerate gapless states with a topological character are spin-polarized and locked in a single layer when bilayer graphene contains stacking domain walls decorated with magnetic defects.

Interface-Driven Partial Dislocation Formation in 2D Heterostructures

Van der Waals (vdW) epitaxy allows the fabrication of various heterostructures with dramatically released lattice matching conditions. This study demonstrates interface-driven stacking boundaries in WS₂ using epitaxially grown tungsten disulfide (WS₂ ) on wrinkled graphene. Graphene wrinkles function as highly reactive nucleation sites on WS₂ epilayers; however, they impede lateral growth and induce additional stress in the epilayer due to anisotropic friction. Moreover, partial dislocation-driven in-plane strain facilitates out-of-plane buckling with a height of 1 nm to release in-plane strain. Remarkably, in-plane strain relaxation at partial dislocations restores the bandgap to that of monolayer WS₂ due to reduced interlayer interaction. These findings clarify significant substrate morphology effects even in vdW epitaxy and are potentially useful for various applications involving modifying optical and electronic properties by manipulating extended 1D defects via substrate morphology control.

Ultraflatbands and Shear Solitons in Moiré Patterns of Twisted Bilayer Transition Metal Dichalcogenides

Ultraflatbands in twisted bilayers of two-dimensional materials have the potential to host strong correlations, including the Mott-insulating phase at half-filling of the band. Using first-principles density functional theory calculations, we show the emergence of ultraflatbands at the valence band edge in twisted bilayer MoS_{2}, a prototypical transition metal dichalcogenide. The computed band widths, 5 and 23 meV for 56.5° and 3.5° twist angles, respectively, are comparable to that of twisted bilayer graphene near "magic" angles. Large structural transformations in the moiré patterns lead to formation of shear solitons at stacking boundaries and strongly influence the electronic structure. We extend our analysis for twisted bilayer MoS_{2} to show that flatbands can occur at the valence band edge of twisted bilayer WS_{2}, MoSe_{2}, and WSe_{2} as well.

A family of finite-temperature electronic phase transitions in graphene multilayers

Suspended Bernal-stacked graphene multilayers up to an unexpectedly large thickness exhibit a broken-symmetry ground state whose origin remains to be understood. We show that a finite-temperature second-order phase transition occurs in multilayers whose critical temperature (T _c) increases from 12 kelvins (K) in bilayers to 100 K in heptalayers. A comparison of the data with a phenomenological model inspired by a mean-field approach suggests that the transition is associated with the appearance of a self-consistent valley- and spin-dependent staggered potential that changes sign from one layer to the next, appearing at T _c and increasing upon cooling. The systematic evolution with thickness of several measured quantities imposes constraints on any microscopic theory aiming to analyze the nature of electronic correlations in this system.

In situ manipulation and switching of dislocations in bilayer graphene

Topological defects in crystalline solids are of fundamental interest in physics and materials science because they can radically alter the properties of virtually any material. Of particular importance are line defects, known as dislocations, which are the main carriers of plasticity and have a tremendous effect on electronic and optical properties. Understanding and controlling the occurrence and behavior of those defects have been of major and ongoing interest since their discovery in the 1930s. This interest was renewed with the advent of two-dimensional materials in which a single topological defect can alter the functionality of the whole system and even create new physical phenomena. We present an experimental approach to directly manipulate dislocations in situ on the nanometer scale by using a dedicated scanning electron microscope setup. With this approach, key fundamental characteristics such as line tension, defect interaction, and node formation have been studied. A novel switching reaction, based on the recombination of dislocation lines, was found, which paves the way for the concept of switches made of a bimodal topological defect configuration.

Controlling the layer localization of gapless states in bilayer graphene with a gate voltage

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their origin. We find that the gate potential controls the layer localization of the two states, which switches non-trivially between layers depending on the applied gate voltage magnitude. We also show how these bilayer gapless states arise from bands of single-layer graphene by analyzing the formation of carbon bonds between layers. Based on this analysis we provide a model Hamiltonian with analytical solutions, which explains the layer localization as a function of the ratio between the applied potential and interlayer hopping. Our results open a route for the manipulation of gapless states in electronic devices, analogous to the proposed writing and reading memories in topological insulators.

Plasmon Reflections by Topological Electronic Boundaries in Bilayer Graphene

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contains additional confined bands which produce a structure-specific contrast of the local conductivity, in agreement with the experiment. The coupling between the confined modes and the surface plasmon scattering unveiled in this work is expected to be common to other topological electronic boundaries found in van der Waals materials. This coupling provides a qualitatively new pathway toward controlling plasmons in nanostructures.

Anomalous Dirac point transport due to extended defects in bilayer graphene

Charge transport at the Dirac point in bilayer graphene exhibits two dramatically different transport states, insulating and metallic, that occur in apparently otherwise indistinguishable experimental samples. We demonstrate that the existence of these two transport states has its origin in an interplay between evanescent modes, that dominate charge transport near the Dirac point, and disordered configurations of extended defects in the form of partial dislocations. In a large ensemble of bilayer systems with randomly positioned partial dislocations, the distribution of conductivities is found to be strongly peaked at both the insulating and metallic limits. We argue that this distribution form, that occurs only at the Dirac point, lies at the heart of the observation of both metallic and insulating states in bilayer graphene.

In seemingly indistinguishable bilayer graphene samples, two distinct transport regimes, insulating and metallic, have been identified experimentally. Here, the authors demonstrate that these two states originate from the interplay between extended defects and evanescent modes at the Dirac point.

Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching

Recent experiments [L. Ju, et al., Nature, 2015, 520, 650] confirm the existence of gapless states at domain walls created in gated bilayer graphene, when the sublattice stacking is changed from AB to BA. These states are significant because they are topologically protected, valley-polarized and give rise to conductance along the domain wall. Current theoretical models predict the appearance of such states only at domain walls, which preserve the sublattice order. Here we show that the appearance of the topologically protected states in stacking domain walls can be much more common in bilayer graphene, since they can also emerge in unexpected geometries, e.g., at grain boundaries with atomic-scale topological defects. We focus on a bilayer system in which one of the layers contains a line of octagon-double pentagon defects that mix graphene sublattices. We demonstrate that gap states are preserved even with pentagonal defects. Remarkably, unlike previous predictions, the number of gap states changes by inverting the gate polarization, yielding an asymmetric conductance along the grain boundary under gate reversal. This effect, linked to defect states, should be detectable in transport measurements and could be exploited in electrical switches.

Interlayer interaction and related properties of bilayer hexagonal boron nitride: ab initio study

Properties of hexagonal boron nitride bilayer related to interlayer interaction (width and formation energy of dislocations, shear mode frequency, etc.) are estimated by approximation of potential energy surface by first Fourier harmonics.

Slippage in stacking of graphene nanofragments induced by spin polarization

Spin polarization and stacking are interesting effects in complex molecular systems and are both presented in graphene-based materials. Their possible combination may provide a new perspective in understanding the intermolecular force. The nanoscale graphene structures with zigzag edges could possess spin-polarized ground states. However, the mechanical effect of spin polarization in stacking of graphene nanofragments is not clear. Here we demonstrate the displacement between two stacked rhombic graphene nanofragments induced by spin polarization, using first-principles density-functional methods. We found that, in stacking of two rhombic graphene nanofragments, a spin-polarized stacked conformation with zero total spin is energetically more favorable than the closed-shell stacking. The spin-polarized conformation gives a further horizontal interlayer displacement within 1 angstrom compared with the closed-shell structure. This result highlights that, besides the well-known phenomenologically interpreted van der Waals forces, a specific mechanism dependent on the monomeric spin polarization may lead to obvious mechanical effects in some intermolecular interactions.

High-performance graphene-based hole conductor-free perovskite solar cells: Schottky junction enhanced hole extraction and electron blocking

Multilayered graphene and single-layered graphene are assembled onto perovskite films in the form of Schottky junctions and ohmic contacts, respectively, for the production of a graphene-based hole transporting material-free perovskite solar cell. Multilayered graphene extracts charge selectively and efficiently, delivering a higher efficiency of 11.5% than single-layered graphene (6.7%).

Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene

Close to charge neutrality, the electronic properties of graphene and its multilayers are sensitive to electron-electron interactions. In bilayers, for instance, interactions are predicted to open a gap between valence and conduction bands, turning the system into an insulator. In mono and (Bernal-stacked) trilayers, which remain conducting at low temperature, interactions do not have equally drastic consequences. It is expected that interaction effects become weaker for thicker multilayers, whose behaviour should converge to that of graphite. Here we show that this expectation does not correspond to reality by revealing the occurrence of an insulating state close to charge neutrality in Bernal-stacked tetralayer graphene. The phenomenology-incompatible with the behaviour expected from the single-particle band structure-resembles that observed in bilayers, but the insulating state in tetralayers is visible at higher temperature. We explain our findings, and the systematic even-odd effect of interactions in Bernal-stacked layers of different thickness that emerges from experiments, in terms of a generalization of the interaction-driven, symmetry-broken states proposed for bilayers.

Feature-rich magnetic quantization in sliding bilayer graphenes

The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.