Graphene Superlattices Research Articles

Functional nanoporous graphene superlattice

Two-dimensional (2D) superlattices, formed by stacking sublattices of 2D materials, have emerged as a powerful platform for tailoring and enhancing material properties beyond their intrinsic characteristics. However, conventional synthesis methods are limited to pristine 2D material sublattices, posing a significant practical challenge when it comes to stacking chemically modified sublattices. Here we report a chemical synthesis method that overcomes this challenge by creating a unique 2D graphene superlattice, stacking graphene sublattices with monodisperse, nanometer-sized, square-shaped pores and strategically doped elements at the pore edges. The resulting graphene superlattice exhibits remarkable correlations between quantum phases at both the electron and phonon levels, leading to diverse functionalities, such as electromagnetic shielding, energy harvesting, optoelectronics, and thermoelectrics. Overall, our findings not only provide chemical design principles for synthesizing and understanding functional 2D superlattices but also expand their enhanced functionality and extensive application potential compared to their pristine counterparts.

Transport Anisotropy in One-Dimensional Graphene Superlattice in the High Kronig-Penney Potential Limit.

One-dimensional graphene superlattice subjected to strong Kronig-Penney (KP) potential is promising for achieving the electron-lensing effect, while previous studies utilizing the modulated dielectric gates can only yield a moderate, spatially dispersed potential profile. Here, we realize high KP potential modulation of graphene via nanoscale ferroelectric domain gating. Graphene transistors are fabricated on PbZr_{0.2}Ti_{0.8}O_{3} back gates patterned with periodic, 100-200nm wide stripe domains. Because of band reconstruction, the h-BN top gating induces satellite Dirac points in samples with current along the superlattice vector s[over ^], a feature absent in samples with current perpendicular to s[over ^]. The satellite Dirac point position scales with the superlattice period (L) as ∝L^{β}, with β=-1.18±0.06. These results can be well explained by the high KP potential scenario, with the Fermi velocity perpendicular to s[over ^] quenched to about 1% of that for pristine graphene. Our study presents a promising material platform for realizing electron supercollimation and investigating flat band phenomena.

Kagome Quantum Oscillations in Graphene Superlattices.

Electronic spectra of solids subjected to a magnetic field are often discussed in terms of Landau levels and Hofstadter-butterfly-style Brown-Zak minibands manifested by magneto-oscillations in two-dimensional electron systems. Here, we present the semiclassical precursors of these quantum magneto-oscillations which appear in graphene superlattices at low magnetic field near the Lifshitz transitions and persist at elevated temperatures. These oscillations originate from Aharonov-Bohm interference of electron waves following open trajectories that belong to a kagome-shaped network of paths characteristic for Lifshitz transitions in the moire superlattice minibands of twistronic graphenes.

Computational Study of the Enhancement of Graphene Electrodes for Use in Li-Ion Batteries via Forming Superlattices with Transition Metal Dichalcogenides.

In our study, we examined nine transition metal dichalcogenide (TMDC)-graphene superlattices as potential Li-ion intercalation electrodes. We determined their voltages, with ScS2-graphene in T- and R-phases showing the highest at around 3 V, while the others ranged from 0 to 1.5 V. Most superlattices exhibited minimal volumetric expansion (5 to 10%), similar to NMC (8%), except for SnS2-T and NiS2-T, which expanded up to nearly 20%. We evaluated their capacities using a stability metric, EIS, and found that ScS2-T, ScS2-R, and TiS2-T could be intercalated up to two Li ions per MX2 unit without decomposing to Li2S, yielding capacities of 306.77 mA h/g for both ScS2 phases and 310.84 mA h/g for TiS2-T, roughly equivalent to LiC2. MoS2-T could accept Li up to a limit of a = 15/16 in LiaMoS2Cb, corresponding to a capacity of 121.29 mA h/g (equivalent to LiC4). Examining the influence of graphene layers on MoS2-T, we observed a voltage decrease and an initial EIS decrease before effectively flat lining, which is due to charge donation to the middle graphene layer, reducing the electron concentration near the TMDC layer. As graphene layers increased, overall volume expansion decreased with Li intercalation, which is attributed to the in-plane expansion changing. Our results underscore the potential of TMDC-graphene superlattices as Li-ion intercalation electrodes, offering low volumetric expansions, high capacities, and a wide voltage range. These superlattices all show an increase in the capacity of the graphene.

Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice.

Electron superlattices allow the engineering of correlated and topological quantum phenomena. The recent emergence of moiré superlattices in two-dimensional heterostructures has led to exciting discoveries related to quantum phenomena. However, the requirement for the moiré pattern poses stringent limitations, and its potential cannot be switched on and off. Here, we demonstrate remote engineering and on/off switching of correlated states in bilayer graphene. Employing a remote Coulomb superlattice realized by localized electrons in twisted bilayer WS2, we impose a Coulomb superlattice in the bilayer graphene with period and strength determined by the twisted bilayer WS2. When the remote superlattice is turned off, the two-dimensional electron gas in the bilayer graphene is described by a Fermi liquid. When it is turned on, correlated insulating states at both integer and fractional filling factors emerge. This approach enables in situ control of correlated quantum phenomena in two-dimensional materials hosting a two-dimensional electron gas.

Emergence of symmetric and asymmetric Dirac points under periodic electric and vector potentials in ABA-trilayer graphene superlattice.

We have theoretically investigated the impact of both periodic electric and vector potentials on the low energy spectrum of ABA-trilayer graphene superlattice. Finite energy Dirac points appear in the energy spectrum due to the application of the vector potential. These extra Dirac points are symmetric about k y = 0 plane for equal barrier and well widths. For different barriers and well widths, one Dirac point shifts away and the second Dirac point shifts towards the k y = 0 plane. The extra Dirac points are not only generated from the original Dirac point but also emerge from the valleys developed in the energy spectrum. The application of both electric and vector potentials with identical barrier and well widths breaks the symmetry of the spectrum about the Fermi level. When the electric and vector potentials are asymmetric with all three layers having the same electric potentials, the energy spectrum becomes asymmetric about the Fermi level, and this asymmetric behavior of both potentials annihilates the original Dirac point from the spectrum. When all the layers have different electric potentials and both electric and vector potentials are asymmetric, the spectrum becomes asymmetric again, but this time the asymmetry of the spectrum occurs across the k y = 0 plane.

Trans-dimensionality of electron/hole channels in multilayer in-plane heterostructures comprising graphene and hBN superlattice

Abstract Using density functional theory, we investigated trilayer in-plane heterostructures consisting of graphene and hBN strips in terms of their interlayer stacking arrangements. The trilayer hBN/graphene superlattices possess flat dispersion bands at their band edges, the wave function distribution of which strongly depends on the interlayer stacking arrangement. The wave functions of the valence and conduction band edges of the trilayer heterostructure with AA’ stacking are distributed throughout the layers implying a two-dimensional carrier distribution. In contrast, we found one-dimensional carrier channels along the border between graphene and hBN for electrons and holes in the trilayer heterosheet with rhombohedral interlayer stacking. These unique carrier distributions are ascribed to the interlayer dipole moment arising from asymmetric arrangements of B and N atoms across the layers. Therefore, the trilayer in-plane heterostructures of graphene and hBN superlattice possess trans-dimensional carriers in terms of their interlayer stacking arrangement.

Gaussian and Gaussian-pulsed-like Fermi velocity graphene structures

Gaussian and Gaussian-related structures are quite attractive due to its versatility to modulate the electronic transport, including its possibility as electron filters. Here, we show that these non-conventional profiles are not the exception when dealing with Fermi velocity barriers in monolayer graphene. In particular, we show that Gaussian Fermi velocity graphene barriers (G-FVGBs) and Gaussian-pulsed-like Fermi velocity graphene superlattices (GPL-FVGSLs) can serve as electron band-pass filters and oscillating conductance structures. We reach this conclusion by theoretically studying the transmission and transport properties of the mentioned structures. The study is based on the continuum model, the transfer matrix method and the Landauer–Büttiker formalism. We find nearly flat transmission bands or pass bands for G-FVGBs modulable through the system parameters. The pass bands improve as the maximum ratio of Fermi velocities () increases, however its omnidirectional range is reduced. These characteristics result in a decaying conductance (integrated transmission) with . The integrated transmission remains practically unaltered with the size of the system due to the saturation of the electron pass band filtering. In the case of GPL-FVGSLs the GPL profile results in regions of high transmission probability that can merge as flat transmission minibands if the pulse fraction and the superlattice parameters are appropriately tuned. The GPL profile also results in conductance (integrated transmission) oscillations that can be multiplied or reduced in number by adjusting the pulse fraction as well as the superlattice parameters.

Nodal band-off-diagonal superconductivity in twisted graphene superlattices

The superconducting state and mechanism are among the least understood phenomena in twisted graphene systems. Recent tunneling experiments indicate a transition between nodal and gapped pairing with electron filling, which is not naturally understood within current theory. We demonstrate that the coexistence of superconductivity and flavor polarization leads to pairing channels that are guaranteed by symmetry to be entirely band-off-diagonal, with a variety of consequences: most notably, the pairing invariant under all symmetries can have Bogoliubov Fermi surfaces in the superconducting state with protected nodal lines, or may be fully gapped, depending on parameters, and the band-off-diagonal chiral p-wave state exhibits transitions between gapped and nodal regions upon varying the doping. We demonstrate that band-off-diagonal pairing can be the leading state when only phonons are considered, and is also uniquely favored by fluctuations of a time-reversal-symmetric intervalley coherent order motivated by recent experiments. Consequently, band-off-diagonal superconductivity allows for the reconciliation of several key experimental observations in graphene moiré systems.

Moiré Superlattice Structure of Pleated Trilayer Graphene Imaged by 4D Scanning Transmission Electron Microscopy.

Moiré superlattices in graphene arise from rotational twists in stacked 2D layers, leading to specific band structures, charge density and interlayer electron and excitonic interactions. The periodicities in bilayer graphene moiré lattices are given by a simple moiré basis vector that describes periodic oscillations in atomic density. The addition of a third layer to form trilayer graphene generates a moiré lattice comprised of multiple harmonics that do not occur in bilayer systems, leading to nontrivial crystal symmetries. Here, we use atomic resolution 4D-scanning transmission electron microscopy to study atomic structure in bilayer and trilayer graphene moiré superlattices and use 4D-STEM to map the electric fields to show subtle variations in the long-range moiré patterns. We show that monolayer graphene folded into an S-bend graphene pleat produces trilayer moiré superlattices with both small (<2°) and larger twist angles (7-30°). Annular in-plane electric field concentrations are detected in high angle bilayers due to overlapping rotated graphene hexagons in each layer. The presence of a third low angle twisted layer in S-bend trilayer graphene, introduces a long-range modulation of the atomic structure so that no real space unit cell is detected. By directly imaging trilayer moiré harmonics that span from picoscale to nanoscale using 4D-STEM, we gain insights into the complex spatial distributions of atomic density and electric fields in trilayer twisted layered materials.

Design of quasiperiodic magnetic superlattices and domain walls supporting bound states

We study the simplest Lamé magnetic superlattice in graphene, finding its allowed and forbidden energy bands and band-edge states explicitly. Then, we design quasiperiodic magnetic superlattices supporting bound states using Darboux transformations. This technique enables us to add any finite number of bound states, which we exemplify with the most straightforward cases of one and two bound states in the designed spectrum. The topics of magnetic superlattices and domain walls in gapped graphene turn out to be connected by a unitary transformation in the limit of significantly large oscillation periods. We show that the generated quasiperiodic magnetic superlattices are also linked to domain walls, with the bound states keeping their nature in such a limit.

Probing miniband structure and Hofstadter butterfly in gated graphene superlattices via magnetotransport

The presence of periodic modulation in graphene leads to a reconstruction of the band structure and formation of minibands. In an external uniform magnetic field, a fractal energy spectrum called Hofstadter butterfly is formed. Particularly interesting in this regard are superlattices with tunable modulation strength, such as electrostatically induced ones in graphene. We perform quantum transport modeling in gate-induced square two-dimensional superlattice in graphene and investigate the relation to the details of the band structure. At low magnetic field the dynamics of carriers reflects the semi-classical orbits which depend on the mini band structure. We theoretically model transverse magnetic focusing, a ballistic transport technique by means of which we investigate the minibands, their extent and carrier type. We find a good agreement between the focusing spectra and the mini band structures obtained from the continuum model, proving usefulness of this technique. At high magnetic field the calculated four-probe resistance fit the Hofstadter butterfly spectrum obtained for our superlattice. Our quantum transport modeling provides an insight into the mini band structures, and can be applied to other superlattice geometries.

Stacking transfer of wafer-scale graphene-based van der Waals superlattices

High-quality graphene-based van der Waals superlattices are crucial for investigating physical properties and developing functional devices. However, achieving homogeneous wafer-scale graphene-based superlattices with controlled twist angles is challenging. Here, we present a flat-to-flat transfer method for fabricating wafer-scale graphene and graphene-based superlattices. The aqueous solution between graphene and substrate is removed by a two-step spinning-assisted dehydration procedure with the optimal wetting angle. Proton-assisted treatment is further used to clean graphene surfaces and interfaces, which also decouples graphene and neutralizes the doping levels. Twist angles between different layers are accurately controlled by adjusting the macroscopic stacking angle through their wafer flats. Transferred films exhibit minimal defects, homogeneous morphology, and uniform electrical properties over wafer scale. Even at room temperature, robust quantum Hall effects are observed in graphene films with centimetre-scale linewidth. Our stacking transfer method can facilitate the fabrication of graphene-based van der Waals superlattices and accelerate functional device applications.

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 two-dimensional layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it wasfound that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. Twist is now used routinely to adjust the properties of two-dimensional materials. Here, weinvestigate 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 Waalsmultilayers. This article is protected by copyright. All rights reserved.

Valley conductance and reflection probabilities in substrate-induced graphene superlattice

We study the transport properties of mass-less and spin-less Dirac fermions in a substrate-induced graphene super-lattice. The tight binding model for the super-lattice gives the energy band structure and we classify the topological regions (trivial and non-trivial) depending on the topological order parameter. The transfer matrix approach is used to compute the probabilities of the reflection and transmission in terms of structural parameters and we investigate the valley-switching phenomenon for all values of incident electron energies (E). We observe that the Dirac fermions with valley degree of freedom sometimes completely and other times partially reflect and transmit to the other valley under some specific values of structure parameters suggesting that we have a finite value of switching probability (≤100%) for all values of E. Moreover, the conductance exhibits striking behaviour, showing a peak at each Dirac point, which merges and subsequently vanishes depending on the structure parameters.

Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene.

Though the observation of the quantum anomalous Hall effect and nonlocal transport response reveals nontrivial band topology governed by the Berry curvature in twisted bilayer graphene, some recent works reported nonlinear Hall signals in graphene superlattices that are caused by the extrinsic disorder scattering rather than the intrinsic Berry curvature dipole moment. In this Letter, we report a Berry curvature dipole induced intrinsic nonlinear Hall effect in high-quality twisted bilayer graphene devices. We also find that the application of the displacement field substantially changes the direction and amplitude of the nonlinear Hall voltages, as a result of a field-induced sliding of the Berry curvature hotspots. Our Letter not only proves that the Berry curvature dipole could play a dominant role in generating the intrinsic nonlinear Hall signal in graphene superlattices with low disorder densities, but also demonstrates twisted bilayer graphene to be a sensitive and fine-tunable platform for second harmonic generation and rectification.

Thermodynamic properties of substrate-induced graphene superlattice in homogeneous magnetic field

In this article we study the thermodynamic properties of a substrate-induced graphene superlattice in the presence of uniform magnetic field B. We derive an expression for the partition function of the system with uniform magnetic field B using the zeta function approach and find all related thermodynamic functions such as Helmholtz free energy, total energy, specific heat capacity and entropy for three cases related to the sublattice potential. We also show that the Dulong-Petit law is verified for all cases in the high-temperature limit. These results may shed light on the study of graphene superlattices in the developement of thermo-electric devices.

Spontaneous isospin polarization and quantum Hall ferromagnetism in a rhombohedral trilayer graphene superlattice

Moiré superlattices in van der Waals heterostructures have recently attracted enormous interests, due to the highly controllable electronic correlation that gives rise to superconductivity, ferromagnetism, and nontrivial topological properties. To gain a deep understanding of such exotic properties, it is essential to clarify the broken symmetry between spin and valley flavors which universally exists in these ground states. Here in a rhombohedral trilayer graphene crystallographically aligned with a hexagonal boron nitride, we report various kinds of symmetry-breaking transition tuned by displacement fields (D) and magnetic fields: (i) While it is well known that a finite D can enhance correlation to result in correlated insulators at fractional fillings of a flat band, we find the correlation gap emerges before the flavor is fully filled at a positive D, but the sequence is reversed at a negative D. (ii) Around zero D, electronic correlation can be invoked by narrow Landau levels, leading to quantum Hall ferromagnetism that lifts all the degeneracies including not only spin and valley but also orbital degrees of freedom. Our result unveils the complication of transitions between symmetry-breaking phases, shedding light on the mechanisms of various exotic phenomena in strongly correlated systems.

Dynamical properties of quasiparticles in a tunable Kekulé graphene superlattice

We investigate the dynamical properties of quasiparticles in graphene superlattices with three typical Kekulé distortions (i.e., Kekulé-O, Kekulé-Y and Kekulé-M). On the one hand, we numerically show the visualized evolution process of Kekulé quasiparticles; while on the other hand, we analytically obtain the centroid trajectory of the quasiparticles, and both of them agree well with each other. The results reveal that the relativistic Zitterbewegung (ZB) phenomenon occurs in the Kekulé systems. Furthermore, through analyzing the frequency of ZB, we unveil the one-to-one relationship between ZB and Kekulé textures, i.e., the ZB frequencies of Kekulé-O, Kekulé-Y and Kekulé-M quasiparticles feature single, double and six frequencies, respectively. Finally, we propose a scheme to distinguish among different Kekulé textures from the dynamical perspective. The predictions in this paper are expected to be experimentally verified in the near future, so as to facilitate further research of Kekulé structures in solid materials or artificial systems.

Electron-phonon coupling superconductivity and tunable topological state in carbon-rich selenide monolayers

The coexistence of Dirac cones and Van Hove singularities (VHSs), as the notable feature on prominent electronic band structure in recently hot-topic Lieb lattice and twisted graphene superlattice materials, has recently drawn tremendous attention since it offers an ideal platform for realizing correlation-driven electronic states (e.g., superconductivity and topological state). Here, we have identified two two-dimensional (2D) crystals, namely ${\mathrm{C}}_{4}\mathrm{Se}$ and ${\mathrm{C}}_{5}\mathrm{Se}$, which exhibit the coexistence of Dirac cones and VHSs. Based on ab initio calculations and the Bardeen-Cooper-Schrieffer theory, we investigated the electron-phonon coupling and possible superconductivity in both structures. The results indicate that ${\mathrm{C}}_{4}\mathrm{Se}$ possesses intrinsic superconducting states, whereas ${\mathrm{C}}_{5}\mathrm{Se}$ exhibits tunable superconductivity when doped. Their superconducting critical temperature (${T}_{c}$) can reach up to 11.6 and 11.2 K, respectively, surpassing the majority of 2D superconductors. Besides, we uncovered an approximate Dirac cone in ${\mathrm{C}}_{6}\mathrm{Se}$ with a small band gap of 0.17 eV. Via the application of a biaxial compressive strain, remarkably, the ${\mathrm{C}}_{6}\mathrm{Se}$ can be transformed into a topological insulator. These findings highlight the potential of carbon-rich C-Se 2D crystals as a promising platform for investigating fascinating band structures and physical states, thus advancing our comprehension of 2D crystals.