Interlayer Potential Research Articles

Kekulé spirals and charge transfer cascades in twisted symmetric trilayer graphene

We study the phase diagram of magic-angle twisted symmetric trilayer graphene in the presence of uniaxial heterostrain and interlayer displacement field. For experimentally reasonable strain, our mean-field analysis finds robust Kekulé spiral order whose doping-dependent ordering vector is incommensurate with the moiré superlattice, consistent with recent scanning tunneling microscopy experiments, and paralleling the behavior of closely related twisted bilayer graphene (TBG) systems. Strikingly, we identify a possibility absent in TBG: the existence of Kekulé spiral order even at zero strain for experimentally realistic values of the interlayer potential in a trilayer. Our studies also reveal a complex pattern of charge transfer between weakly and strongly dispersive bands in strained trilayer samples as the density is tuned by electrostatic gating, that can be understood intuitively in terms of the “cascades” in the compressibility of magic-angle TBG. Published by the American Physical Society 2024

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides.

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

Flat bands and high Chern numbers in twisted multilayer graphene

Motivated by recent Physical Review Letters of Wang and Liu [Phys. Rev. Lett. 128(17), 176403 (2022)] and Ledwith, Vishwanath, and Khalaf [Phys. Rev. Lett. 128(17), 176404 (2022)], we study [G. Tarnopolsky, A. Kruchkov, and A. Vishwanath, Phys. Rev. Lett. 122(10), 106405 (2019)] chiral model of two sheets of n-layer Bernal stacked graphene twisted by a small angle using the framework developed by Becker et al. [Probab. Math. Phys. 3(1), 69 (2022)]. We show that magic angles of this model are exactly the same as magic angles of chiral twisted bilayer graphene with multiplicity. For small inter-layer tunneling potentials, we compute the band separation at Dirac points as we turning on the tunneling parameter. Flat band eigenfunctions are also constructed using a new theta function argument and this yields a complex line bundle with the Chern number −n.

Tuning of Redox Energy of Transition-Metal Ions through the Utilization of Interlayer Potentials in Layered Perovskites: Development of a Titanium-Based Superior HER Catalyst in an Acidic Medium

Tuning of Redox Energy of Transition-Metal Ions through the Utilization of Interlayer Potentials in Layered Perovskites: Development of a Titanium-Based Superior HER Catalyst in an Acidic Medium

Registry-Dependent Potential for Interfaces of Water with Graphene

An anisotropic interlayer potential that can accurately describe the van der Waals interaction of the water–graphene interface is presented. The force field is benchmarked against the many-body dispersion-corrected density functional theory. The parametrization of the interlayer potential demonstrates a satisfactory agreement with the reference data set of binding energy curves and sliding potential energy surfaces for various configurations of a water molecule deposited on monolayer graphene, indicating that the developed force field significantly enhances the accuracy in the empirical description of water–graphene interfacial interactions. The water contact angles of monolayer and multilayer graphene extracted from molecular dynamics simulations based on this force field are close to the experimental measurements and predict the hydrophilic nature of graphene. The theoretical approach proposed in this work can be easily adapted to heterointerfaces formed with water and other two-dimensional materials, providing a reliable and versatile platform for studying the wetting properties of these materials.

2D/2D g-C3N4/ZnxCd1-xS Van der Waals heterojunctions modulation: Interfacial chemical bond accelerating charge separation for enhanced photocatalytic CO2 reduction

The fabrication of Van der Waals (VDW) heterojunctions between two-dimensional materials has recently sparked the curiosity of researchers due to their compact interfaces, low energy barriers and efficient interfacial electron mobility efficiency. However, the relatively weak VDW interactions and VDW gap inhibits the migration of carriers across layers. Herein, we developed a novel 2D/2D ZnxCd1-xS/g-C3N4 catalysts for regulating VDW heterojunctions by the interface engineering. ZnxCd1-xS nanosheets are strongly coordinated with g-C3N4, and the compact VDW heterojunctions and Zn/Cd molar ratios modulation induces Cd-N bonds to modulate the electronic structure at the interface. Evidenced by the experimental and theoretical calculation analysis, the constructed interfacial Cd-N bonds could function as a novel electron transport bridge between Zn0.8Cd0.2S and g-C3N4, enabling the photogenerated electron-hole pairs to be efficiently migrated directionally across the interlayer potential barrier. Therefore, Zn0.8Cd0.2S/g-C3N4 exhibits the enhanced CO2 reduction performance that is 3.2 times better than that of pure g-C3N4 without the usage of co-catalysts or sacrificial agents. This work introduces an avenue to regulate Van der Waals heterojunctions and provides an efficient photocatalyst for green energy conversion.

Staggered pseudo magnetic field in twisted transition metal dichalcogenides: Physical origin and experimental consequences

In systems comprised of two layers of certain semiconductors stacked with a certain twist angle, the quantum mechanics of electron transfer between layers is believed to give rise to a ``staggered flux'' physics in which electrons move as though exposed to an extremely strong, but rapidly spatially varying, magnetic field. This staggered flux, heretofore thought of as a theoretical construct, is shown to give rise to dramatic, observable behavior, including ``Hofstadter butterfly'' structures in the electron spectrum, sign reversals in the Hall effect, and edge currents in systems with junctions or spatially varying interlayer potentials.

Polarizability characteristics of twisted bilayer graphene quantum dots in the absence of periodic moiré potential.

Recent studies have documented a rich phenomenology in twisted bilayer graphene (TBG), which is significantly relevant to interlayer electronic coupling, in particular to the cases under an applied electric field. While polarizability measures the response of electrons against applied fields, this work adopts a unique strategy of decomposing global polarizability into distributional contributions to access the interlayer polarization in TBG, as a function of varying twisting angles (θ). Through the construction of a model of twisted graphene quantum dots, we assess distributional polarizability at the first-principles level. Our findings demonstrate that the polarizability perpendicular to the graphene plates can be decomposed into intralayer dipoles and interlayer charge-transfer (CT) components, the latter of which provides an explicit measurement of the interlayer coupling strength and charge transfer potential. Our analysis further reveals that interlayer polarizability dominates the polarizability variation during twisting. Intriguingly, the largest interlayer polarizability and CT driven by an external field occur in the misaligned structures with a size-dependent small angle corresponding to the first appearance of AB stacking, rather than the well-recognized Bernal structures. A derived equation is then employed to address the size dependence on the angle corresponding to the largest values in interlayer polarizability and CT. Our investigation not only characterizes the CT features in the interlayer polarizability of TBG quantum dots, but also sheds light on the existence of the strongest interlayer coupling and charge transfer at small twist angles in the presence of an external electric field, thereby providing a comprehensive understanding of the novel properties of graphene-based nanomaterials.

Phonon physics in twisted two-dimensional materials

As one of the most effective manipulation means to control the physical properties of two-dimensional van der Waals stacking materials, the twisted angle periodically regulates the interlayer interaction potential by generating moiré patterns. The decrease in Brillouin zone size and the change of high symmetry direction caused by the interlayer twisted angle lead to the emergence of the hybrid folded phonons—moiré phonons, which have noticeable impacts on phonon properties. This paper reviews the recent developments and discoveries on phonon properties in twisted two-dimensional stacking homogeneous and heterogeneous systems and focuses on the impacts of the interlayer twisted angle on phonon dispersion, such as interlayer coupling phonon modes and moiré phonons. Meanwhile, we introduced the recent research on the influence of the interlayer twisted angle on phonon transport behavior along the in-plane and out-of-plane directions. In addition, the theoretical and experimental open questions and challenges faced in the phonon characteristics of twisted two-dimensional materials are discussed, and some possible solutions are put forward.

Relaxation effects in twisted bilayer graphene: A multiscale approach

We present a multiscale density functional theory (DFT) informed molecular dynamics and tight-binding approach to capture the interdependent atomic and electronic structures of twisted bilayer graphene. We calibrate the flat band magic angle to be at ${\ensuremath{\theta}}_{\mathrm{M}}=1.{08}^{\ensuremath{\circ}}$ by rescaling the interlayer tunneling for different atomic structure relaxation models as a way to resolve the indeterminacy of existing atomic and electronic structure models whose predicted magic angles vary widely between $0.{9}^{\ensuremath{\circ}}$ and $1.{3}^{\ensuremath{\circ}}$. The interatomic force fields are built using input from various stacking and interlayer distance-dependent DFT total energies including the exact exchange and random phase approximation ($\mathrm{EXX}+\mathrm{RPA}$). We use a Fermi velocity of ${\ensuremath{\upsilon}}_{\mathrm{F}}\ensuremath{\simeq}{10}^{6}$ m/s for graphene that is enhanced by $\ensuremath{\sim}15%$ over the local density approximation (LDA) values. Based on this atomic and electronic structure model we obtain high-resolution spectral functions comparable with experimental angle-resolved photoemission spectroscopy. Our analysis of the interdependence between the atomic and electronic structures indicates that the intralayer elastic parameters compatible with the DFT-LDA, which are stiffer by $\ensuremath{\sim}30%$ than widely used reactive empirical bond order force fields, can combine with $\mathrm{EXX}+\mathrm{RPA}$ interlayer potentials to yield the magic angle at $\ensuremath{\sim}1.{08}^{\ensuremath{\circ}}$ without further rescaling of the interlayer tunneling.

Dynamical Mean-Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality

We present a comprehensive dynamical mean field study of the triangular moir\'e Hubbard model, which is believed to represent the physics of moir\'e bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, strange metal and quantum critical behaviors in distinct regions of the phase diagram. We show how magnetic order affects the resistivity. Our results elucidate the physics of the correlated states and the metal-insulator continuous transition recently observed in twisted homobilayer WSe$_2$ and heterobilayer MoTe$_2$/WSe$_2$ experiments.

Excitonic condensation and metal-semiconductor transition in AA bilayer graphene in an external magnetic field

In this paper, the effects of the external transverse magnetic field $B$ (perpendicular to the surface of the layers) on the electronic and excitonic properties are studied in the AA-stacked bilayer graphene (BLG). The effects of the Coulomb interactions and excitonic pairing have been taken into account and analyzed in detail within the bilayer Hubbard model. Both half-filling and partial filling regimes have been taken into account and the magnetic field dependence of a series of physical parameters was found. It is shown that the difference between the average electron concentrations in the layers vanishes at some critical value of magnetic field $B_{c}$ and the chemical potential is calculated numerically above and below that value. The role of the Coulomb interactions on the average carrier concentrations in the layers has been analyzed, and the excitonic order parameters have been calculated for different spin orientations. We found a possibility for the particle population inversion between the layers when varying the external magnetic field. The calculated electronic band structure in the AA-BLG shows the presence of metal-semiconductor transition, governed by the strength of the applied magnetic field or the interlayer interaction potential. We show that for high magnetic fields the band-gap is approaching the typical values of the gaps in the usual semiconductors. It is demonstrated that, at some parameter regimes, the AA-BLG behaves like a spin-valve device, by permitting the electron transport with only one spin direction. All calculations have been performed at the zero-temperature limit.

Micro Eddy Current Facilitated by Screwed MoS2 Structure for Enhanced Hydrogen Evolution Reaction

AbstractEddy current is a magnetic field effect generated in alternating magnetic field (AMF), which could trigger continuous local heating, reducing the energy consumption without impairing the life of the catalyst or reactor. Unfortunately, the investigation of eddy current effect on transition metal disulfides (TMDs) electrocatalysis is still in its infancy, and its actual electrocatalytic applications has been impeded by the multilayered structure of traditional layered TMDs. Typically, the step pyramid MoS2, with a layer‐by‐layer stacking structure just like the silicon steel plate in the transformer, showing an inevitable interlayer potential barrier will suppress the generation of eddy current and cause low efficiency of magnetic heating. In this work, the designed screw pyramid MoS2 can facilitate the formation of micro eddy current and maximize utilization of magnetic heating to boost electrocatalytic activity, benefiting from its eliminated interlayer potential barrier. This work provides a new thinking for the design of field‐assisted electrocatalytic reactions and development of the advanced catalyst technology.

Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides.

van der Waals materials have greatly expanded our design space of heterostructures by allowing individual layers to be stacked at non-equilibrium configurations, for example via control of the twist angle. Such heterostructures not only combine characteristics of the individual building blocks, but can also exhibit physical properties absent in the parent compounds through interlayer interactions1. Here we report on a new family of nanometre-thick, two-dimensional (2D) ferroelectric semiconductors, where the individual constituents are well-studied non-ferroelectric monolayer transition metal dichalcogenides (TMDs), namely WSe2, MoSe2, WS2 and MoS2. By stacking two identical monolayer TMDs in parallel, we obtain electrically switchable rhombohedral-stacking configurations, with out-of-plane polarization that is flipped by in-plane sliding motion. Fabricating nearly parallel-stacked bilayers enables the visualization of moiré ferroelectric domains as well as electric field-induced domain wall motion with piezoelectric force microscopy. Furthermore, by using a nearby graphene electronic sensor in a ferroelectric field transistor geometry, we quantify the ferroelectric built-in interlayer potential, in good agreement with first-principles calculations. The new semiconducting ferroelectric properties of these four new TMDs opens up the possibility of studying the interplay between ferroelectricity and their rich electric and optical properties2-5.

Orbital Gating Driven by Giant Stark Effect in Tunneling Phototransistors.

Conventional gating in transistors uses electric fields through external dielectrics that require complex fabrication processes. Various optoelectronic devices deploy photogating by electric fields from trapped charges in neighbor nanoparticles or dielectrics under light illumination. Orbital gating driven by giant Stark effect is demonstrated in tunneling phototransistors based on 2H-MoTe2 without using external gating bias or slow charge trapping dynamics in photogating. The original self-gating by light illumination modulates the interlayer potential gradient by switching on and off the giant Stark effect where the dz 2-orbitals of molybdenum atoms play the dominant role. The orbital gating shifts the electronic bands of the top atomic layer of the MoTe2 by up to 100 meV, which is equivalent to modulation of a carrier density of 7.3 × 1011 cm-2 by electrical gating. Suppressing conventional photoconductivity, the orbital gating in tunneling phototransistors achieves low dark current, practical photoresponsivity (3357 AW-1 ), and fast switching time (0.5ms) simultaneously.

Tailoring the Band Structure of Twisted Double Bilayer Graphene with Pressure.

Twisted two-dimensional structures open new possibilities in band structure engineering. At magic twist angles, flat bands emerge, which gave a new drive to the field of strongly correlated physics. In twisted double bilayer graphene dual gating allows changing of the Fermi level and hence the electron density and also allows tuning of the interlayer potential, giving further control over band gaps. Here, we demonstrate that by application of hydrostatic pressure, an additional control of the band structure becomes possible due to the change of tunnel couplings between the layers. We find that the flat bands and the gaps separating them can be drastically changed by pressures up to 2 GPa, in good agreement with our theoretical simulations. Furthermore, our measurements suggest that in finite magnetic field due to pressure a topologically nontrivial band gap opens at the charge neutrality point at zero displacement field.

Valley current generation using biased bilayer graphene dots

Intrinsic and extrinsic valley Hall effects are predicted to emerge in graphene systems with uniform or spatially-varying mass terms. Extrinsic mechanisms, mediated by the valley-dependent scattering of electrons at the Fermi surface, can be directly linked to quantum transport simulations. This is a promising route towards more complete experimental investigation of valleytronic phenomena in graphene, but a major obstacle is the difficulty in applying the sublattice-dependent potentials required. Here we show that strongly valley-dependent scattering also emerges from bilayer graphene quantum dots, where the gap size can be easily modulated using the interlayer potentials in dual-gated devices. Robust valley-dependent scattering and concomitant valley currents are observed for a range of systems, and we investigate the role of dot size, mass strength and additional potential terms. Finally, we note that a strong valley splitting of electronic current also emerges when a biased bilayer dot is embedded in a single layer of graphene, but that the effect is less robust than for a bilayer host. Our findings suggest that bilayer graphene devices with custom mass profiles provide an excellent platform for future valleytronic exploration of two-dimensional materials.

Phase diagram and orbital Chern insulator in twisted double bilayer graphene

Compared with twisted bilayer graphene, twisted double bilayer graphene (TDBG) provides another important platform to realize the moir\'e flat bands. In this paper, we first calculate the valley Chern number phase diagram of TDBG in the parameter space spanned by the twist angle and the interlayer electric potential. To include the effects of interactions, we then phenomenologically introduce the spin-splitting and valley-splitting. We find that when the valley splitting is larger than the bandwidth of the first conduction band so that a gap is opened and the spin splitting is relatively weak, the orbital Chern insulator emerges at half-filling, associated with a large orbital magnetization (OM). Further calculations suggest that there is no sign reversal of the OM when the Fermi energy goes from the bottom to the top of the half-filling gap, as the OM remains negative in both AB-AB stacking and AB-BA stacking. The implications of our results for the ongoing experiments are also discussed.

Misalignment instability in magic-angle twisted bilayer graphene on hexagonal boron nitride

We study the stability and electronic structure of magic-angle twisted bilayer graphene on the hexagonal boron nitride (TBG/BN). Structural relaxation has been performed for commensurate supercells of the heterostructures with different twist angles () and stackings between TBG and BN. We find that the slightly misaligned configuration with and the AA/AA stacking has the globally lowest total energy due to the constructive interference of the moiré interlayer potentials and thus the greatly enhanced relaxation in its 1 × 1 commensurate supercell. Gaps are opened at the Fermi level (E F ) for small supercells with the stackings that enable strong breaking of the C 2 symmetry in the atomic structure of TBG. For large supercells with close to those of the 1 × 1 supercells, the broadened flat bands can still be resolved from the spectral functions. The is also identified as a critical angle for the evolution of the electronic structure with , at which the energy range of the mini-bands around E F begins to become narrower with increasing and their gaps from the dispersive bands become wider. The discovered stablest TBG/BN with a finite of about 0.54∘ and its gapped flat bands agree with recent experimental observations.

Comparative studies of thermal conductivity for bilayer graphene with different potential functions in molecular dynamic simulations

Potential functions play an essential role in the heat transport of the nano-scale materials when they are investigated by molecular dynamics simulations. In this paper, the thermal conductivity of bilayer graphene (BLG) is calculated by the non-equilibrium molecular dynamics using different in-layer and interlayer potentials. It is found that the Kolmogorov-Crespi (K-C) potential gives a lower thermal conductivity than Lennard-Jones (L-J) potential when they are used to describe the interlayer interaction of C–C atoms. The calculation results using K-C potential show that compared to L-J potential, there is about 10% reduction in thermal conductivity of BLG. For the in-layer interaction potentials, the TERSOFF potential provides much higher thermal conductivity than it from REBO and AIREBO potentials. In addition, the thermtal conductivity of BLG shows notably different temperature-dependence and same size effect calculated with various potentials. Based on the phonon density of states and phonon dispersion calculations, we find the simulation results calculated by K-C + REBO potential are in excellent agreement with the experimental values.