Interlayer Coupling Strength Research Articles

Emergent Dynamics and Spatio Temporal Patterns on Multiplex Neuronal Networks.

We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the dynamics of single neurons, we analyze the possible patterns of dynamics in each layer separately and report emergent patterns of activity like in-phase synchronized oscillations and amplitude death (AD) for excitatory coupling and anti-phase mixed-mode oscillations (MMO) in multi-clusters with phase regularities when the connections are inhibitory. When they are multiplexed, with neurons of one layer coupled with excitatory synaptic coupling and neurons of the other layer coupled with inhibitory synaptic coupling, we observe the transfer or selection of interesting patterns of collective behavior between the layers. While the revival of oscillations occurs in the layer with excitatory coupling, the transition from anti-phase to in-phase and vice versa is observed in the other layer with inhibitory synaptic coupling. We also discuss how the selection of these spatio temporal patterns can be controlled by tuning the intralayer or interlayer coupling strengths or increasing the range of non-local coupling. With one layer having electrical coupling while the other synaptic coupling of excitatory(inhibitory)type, we find in-phase(anti-phase) synchronized patterns of activity among neurons in both layers.

Synchronizability of Multi-Layer-Coupled Star-Composed Networks

In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the synchronizability of these kinds of networks are derived in the case of bounded and unbounded synchronized regions. The relationships among the synchronizability, the number of layers, the length of the paths, the branchings, and the interlayer and intralayer coupling strengths in the two cases are studied. At the same time, the simulation experiments are carried out with the MATLAB software, and the simulated images of the two symmetrical structure networks’ synchronizability are compared. Finally, the factors affecting the synchronizability of multi-layer-coupled star-composed networks are found. On this basis, optimization schemes are given to improve the synchronizability of multi-layer-coupled star-composed networks and the influences of the number of central nodes on the networks’ synchronizability are further studied.

Analysis of the synchronizability of two-layer chain networks with two inter-layer edges

The structure and dynamics of multi-layer networks are the frontiers in the current network science research. The inter-layer connections in a multi-layer network directly affect the dynamics, propagation, diffusion, and synchronization of the entire multi-layer network. However, there is rarely systematic theory or method for the general structure of multi-layer networks. People can only start with a simple structure to explore how the inter-layer connections affect the overall dynamic behaviors of multiple layers. The work of this paper aims at the two-layer networks where each layer is a chain network. Through graph theory and numerical calculation, this problem is explored to find the optimization method of the inter-layer connections. First of all, according to the master stability function method, this paper proves that when the synchronous region is unbounded, a multi-layer network with the same network structure at each layer has a certain inter-layer coupling strength threshold, so that the entire network reaches the maximum synchronizability, which is the synchronizability of its single-layer network. Secondly, the simulations show that when there are only two edges between layers, the optimal positions are respectively located at $1/4$ and $3/4$ of each chain, while the worst positions are the end node of the chain and its neighbor node. Furthermore, we discuss in detail about the optimal connection modes of two-layer chain networks when the number of single-layer nodes is $4N+x~(x=0,~1,~2,~3)$ using the master stability function method and “network shortest distance” structure index. In the case that the single-layer nodes number is $4N$, there are $4$ optimal connection modes; in the other three cases, there is only one optimal connection mode respectively. Finally, we propose the expression of the optimal inter-layer coupling strength, and then verify the correctness of the expression by calculating the optimal inter-layer coupling strength values of the two-layer chain network with different sizes.

Intralayer synchronization in a duplex network with noise

This paper concerns the impact of environmental noise on the intralayer synchronization of the duplex networks. A duplex network contains two layers. Different from the previous works (Tang et al., 2018; Shen & Tang, 2018), environmental noise is introduced into the dynamical system of the duplex network. We incorporate both the interlayer delay and the intralayer delay into the dynamical system. Both of the delays are time‐varying. However, Tang et al. (2018) only considered the intralayer delays, and they were assumed as constants, while Shen and Tang (2018) did not consider the interlayer delay or intralayer delay. When the system does not achieve automatic intralayer synchronization, we introduce two controllers: one is the state‐feedback controller and the other is the adaptive state‐feedback controller. Interestingly, we find that the intralayer synchronization will be achieved automatically if the interlayer coupling strength is large enough and the intralayer coupling strength is small enough under the situation that the time‐varying interlayer delays are absent. Finally, some interesting simulation results are obtained for the Chua–Chua chaotic system withapplication of our theoretic results, which show the feasibility and effectiveness of our control schemes.

Interlayer polarizability in twisted bilayer graphene quantum dots

Many of the intriguing properties of bilayer graphene (BLG) are related to interlayer electronic coupling. Since this coupling is sensitive to an applied electric field perpendicular to the layers, we develop a strategy for determining interlayer coupling by decomposing the total electric dipole polarizability, which measures the response of electrons to applied fields, into site-specific contributions and consequently the intralayer and interlayer components. The interlayer polarizability is evaluated from field-induced electron density variations computed with a first-principles approach for twisted BLG quantum dots (QDs). Changes in interlayer polarizability dominate the polarizability variation with twist angle. In addition to the well-recognized strong coupling in the Bernal stackings, enhanced coupling is revealed for the structures at small and size-dependent twist angles when AB stacking first appears in the outermost shell of the QD. The values of these magic angles depend on the QD size. This paper not only provides an approach for measuring interlayer coupling strength but also indicates the existence of strong interlayer coupling even at small twist angles, which could be important for understanding the properties of twisted BLG.

Identifying important nodes for temporal networks based on the ASAM model

The identification of important nodes in a temporal network is of great significance for the analysis and control of the information dissemination process. In this work, the multi-layer coupled network analysis method is employed to identify important nodes in a temporal network. First, to overcome the problem of a fixed constant being unable to reflect differences in the inter-layer coupling relationship, and by combining a node’s own neighbors and common neighbors of nodes in two-time layers, a new Enhanced Similarity Index (ESI) is proposed to measure the inter-layer coupling relationship. Secondly, the attenuation factor is introduced to more accurately describe the inter-layer coupling relationship. Finally, an Attenuation-Based Supra-Adjacency Matrix (ASAM) temporal network modeling method based on the attenuation of the inter-layer coupling strength is proposed. The importance of nodes in the temporal network is evaluated by calculating the eigenvector centrality of the nodes in each time layer in the temporal network. It is found that after deleting a certain percentage of the important nodes identified by the ASAM method, the temporal Largest Connected Component (LCC) of the network becomes smaller, and the network performance is improved as compared with the SAM and SSAM methods. The results indicate that the important nodes identified by the ASAM are at the core of the network and have a greater impact on the network structure and functions. This demonstrates that the proposed ASAM model can more effectively identify important nodes in the temporal network, and has significant application value in this research field.

Topological Weyl magnons and thermal Hall effect in layered honeycomb ferromagnets

In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of $\mathrm{Cr}{\mathrm{I}}_{3}$. We show that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling ${J}_{c}$, which moreover has a qualitatively different effect in the ABC stacking compared to the AA stacking adopted by other authors. The nontrivial Chern number of the lowest magnon band is stabilized by the next-nearest-neighbor Dzyaloshinskii-Moriya interaction in each honeycomb layer, resulting in the hopping term similar to that in the electronic Haldane model for graphene. However, we also find several gapless Weyl points, separating the nonequivalent Chern insulating phases, tuned by the ratio of the interlayer coupling ${J}_{c}$ and the third-neighbor Heisenberg interaction ${J}_{3}$. We further show that the topological character of magnon bands results in nonzero thermal Hall conductivity, whose sign and magnitude depend on ${J}_{c}$ and the intralayer couplings. Since the interlayer coupling strength ${J}_{c}$ can be easily tuned by applying pressure to the quasi-2D material such as $\mathrm{Cr}{\mathrm{I}}_{3}$, this provides a potential route to tuning the magnon thermal Hall effect in an experiment.

Bandgap engineering of stacked two-dimensional polyaniline by twist angle

Stacking two-dimensional materials vertically by van der Waals interaction is a promising approach to realize band structure engineering. Recently, layered two-dimensional materials with adjusted twist angle provide a platform for various novel phenomena. By means of density functional theory and tight-binding modeling, we investigate the bilayer polyaniline (PANI) as a prototype to explore the bandgap tuning mechanism by interlayer twist. A wider and continuous bandgap tuning is found in twisted bilayer PANI compared with the tuning by interlayer translation. The unique bandgap tuning by twist angle can be understood by fast exponential decaying of interlayer coupling strength, twist angle dependent interlayer coupling patterns, and charge transfer effect. These findings might provide an efficient bandgap tuning method by twist angle in 2D layered materials, which is the key to applications in electronic and optical devices.

Mott insulating state and d+id superconductivity in an ABC graphene trilayer

Motivated by the recently experimental reported signatures of the tunable Mott insulating state and superconductivity in an ABC graphene trilayer superlattice, we investigate the charge compressibility, the spin correlation, and the superconducting instability within the Hubbard model on a three-layer honeycomb lattice. It is found that an antiferromagnetically ordered Mott insulator emerges beyond a critical $U_c$ at half-filling, and the electronic correlation drives a $d+id$ superconducting pairing to be dominant over other pairing patterns in a wide doped region. The effective pairing interaction with $d+id$ pairing symmetry is strongly enhanced with the increasing of on-site interaction, and suppressed as the interlayer coupling strength increases. Our intensive numerical results demonstrate that the insulating state and superconductivity in an ABC graphene trilayer are driven by strong electric correlation, and it may offer an attractive systems to explore rich correlated behaviors.

Synchronization scenarios in three-layer networks with a hub.

We study various relay synchronization scenarios in a three-layer network, where the middle (relay) layer is a single node, i.e., a hub. The two remote layers consist of non-locally coupled rings of FitzHugh-Nagumo oscillators modeling neuronal dynamics. All nodes of the remote layers are connected to the hub. The role of the hub and its importance for the existence of chimera states are investigated in dependence on the inter-layer coupling strength and inter-layer time delay. Tongue-like regions in the parameter plane exhibiting double chimeras, i.e., chimera states in the remote layers whose coherent cores are synchronized with each other, and salt-and-pepper states are found. At very low intra-layer coupling strength, when chimera states do not exist in single layers, these may be induced by the hub. Also, the influence of the dilution of links between the remote layers and the hub upon the dynamics is investigated. The greatest effect of dilution is observed when links to the coherent domain of the chimeras are removed.

Resonance-Enhanced Excitation of Interlayer Vibrations in Atomically Thin Black Phosphorus.

The strength of interlayer coupling critically affects the physical properties of 2D materials such as black phosphorus (BP), where the electronic structure depends sensitively on layer thickness. Rigid-layer vibrations reflect directly the interlayer coupling strength in 2D van der Waals solids, but measurement of these characteristic frequencies is made difficult by sample instability and small Raman scattering cross sections in atomically thin elemental crystals. Here, we overcome these challenges in BP by performing resonance-enhanced low-frequency Raman scattering under an argon-protective environment. Interlayer breathing modes for atomically thin BP were previously unobservable under conventional (nonresonant) excitation but became strongly enhanced when the excitation energy matched the sub-band electronic transitions of few-layer BP, down to bilayer thicknesses. The measured out-of-plane interlayer force constant was found to be 10.1 × 1019 N/m3 in BP, which is comparable to graphene. Accurate characterization of the interlayer coupling strength lays the foundation for future exploration of BP twisted structures and heterostructures.

Synchronization in multiplex networks of chaotic oscillators with frequency mismatch

We explore numerically inter-layer synchronization of spatiotemporal patterns in a heterogeneous bilayer network of nonlocally coupled Rössler oscillators. Both layers exhibit phase chimera regimes with similar cluster structures, but there is a mean frequency mismatch between the layers. We show that an entrainment of the mean frequency in the interacting layers is observed already for sufficiently weak inter-layer coupling even when the frequency mismatch is large. At the same time, frequency synchronization does not mean structure synchronization. Our numerical study indicates that inter-layer synchronization takes place within noticeably shorter ranges of the frequency mismatch and the inter-layer coupling strength than the frequency synchronization regime. Besides, we show that the weakest chaotic behavior is observed when both frequency and structure synchronizations occur, while the most developed chaotic oscillations are typical when the spatiotemporal structures in the layers are desynchronized.

Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks.

Different methods have been proposed in the past few years to incite explosive synchronization (ES) in Kuramoto phase oscillators. In this work, we show that the introduction of a phase shift α in interlayer coupling terms of a two-layer multiplex network of Kuramoto oscillators can also instigate ES in the layers. As α→π/2, ES emerges along with hysteresis. The width of hysteresis depends on the phase shift α, interlayer coupling strength, and natural frequency mismatch between mirror nodes. A mean-field analysis is performed to justify the numerical results. Similar to earlier works, the suppression of synchronization is accountable for the occurrence of ES. The robustness of ES against changes in network topology and natural frequency distribution is tested. Finally, taking a suggestion from the synchronized state of the multiplex networks, we extend the results to classical single networks where some specific links are assigned phase-shifted interactions.

High-Throughput Computations of Cross-Plane Thermal Conductivity in Multilayer Stanene

Computational materials science based on data-driven approach has gained increasing interest in recent years. The capability of trained machine learning (ML) models, such as an artificial neural network (ANN), to predict the material properties without repetitive calculations is an appealing idea to save computational time. Thermal conductivity in single or multilayer structure is a quintessential property that plays a pivotal role in electronic applications. In this work, we exemplified a data-driven approach based on ML and high-throughput computation (HTC) to investigate the cross-plane thermal transport in multilayer stanene. Stanene has attracted considerable attention due to its novel electronic properties such as topological insulating features with a wide bandgap, making it an appealing candidate to ferry current in electronic devices. Classical molecular dynamics simulations are performed to extract the lattice thermal conductivities (κL). The calculated cross-plane κL is orders of magnitude lower than its lateral counterparts. Impact factors such as layer number, system temperature, interlayer coupling strength, and compressive/tensile strains are explored. It is found that κL of multilayer stanene in the cross-plane direction can be diminished by 86.7% with weakened coupling strength, or 66.6% with tensile strains. A total of 2700 κL data are generated using HTC, which are fed into 9 different ANN models for training and testing. The best prediction performance is given by the 2-layer ANN with 30 neurons in each layer.

Solitary states in multiplex neural networks: Onset and vulnerability

We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More specifically, we show that these patterns can be introduced via weak multiplexing into a network that is fully synchronized in isolation. We show that this result is robust under variations of the inter-layer coupling strength and largely independent of the choice of initial conditions. Moreover, we study the vulnerability of solitary states with respect to changes in the inter-layer topology. In more detail, we remove links that connect two solitary nodes of each layer and evaluate the resulting pattern. We find a highly non-trivial dependence of the survivability of the solitary states on topological (position in the network) and dynamical (phase of the oscillation) characteristics.

K-core percolation on interdependent and interconnected multiplex networks

Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k -core percolation, where a node fails when it connects to less than k neighbors. By deriving the self-consistent equations, we solve the key quantities of interests such as the critical threshold and size of the giant component and validate the theoretical predictions by numerical simulations. We find a rich phase transition phenomenon as we tune the inter-layer coupling strength. Specifically speaking, in the ER-ER multiplex networks, with the increase of coupling strength, the size of the giant component in each layer first undergoes a first-order transition and then a second-order transition and finally a first-order transition. This is due to the nature of inter-layer links with both connectivity and dependency. The system is more robust if the dependency on the initially robust network is strong and more vulnerable if the dependency on the initial attacked network is strong. These effects are even amplified in the cascading process. When applying our model to the SF-SF multiplex networks, the type of transition changes. The system undergoes a first-order phase transition first only when the two layers' mutually coupling is very strong and a second-order transition in all other conditions.

Structural Phase Transition and Interlayer Coupling in Few-Layer 1T' and Td MoTe2.

We performed polarized Raman spectroscopy on mechanically exfoliated few-layer MoTe2 samples and observed both 1T' and Td phases at room temperature. Few-layer 1T' and Td MoTe2 exhibited a significant difference especially in interlayer vibration modes, from which the interlayer coupling strengths were extracted using the linear chain model: strong in-plane anisotropy was observed in both phases. Furthermore, temperature-dependent Raman measurements revealed a peculiar phase transition behavior in few-layer 1T' MoTe2. In contrast to bulk 1T' MoTe2 crystals, where the phase transition to the Td phase occurs at ∼250 K, the temperature-driven phase transition to the Td phase is increasingly suppressed as the thickness is reduced, and the transition and the critical temperature varied dramatically from sample to sample even for the same thickness. Raman spectra of intermediate phases that correspond to neither 1T' nor Td phase with different interlayer vibration modes were observed, which suggests that several metastable phases exist with similar total energies.

Unique superdiffusion induced by directionality in multiplex networks

The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a framework to analyze dynamical processes on interconnected complex systems with directionality.

Extension of synchronizability analysis based on vital factors: Extending validity to multilayer fully coupled networks

Abstract In this paper, we study the synchronizability of multilayer fully coupled networks and their simplest equivalent networks and then discuss the vital factors affecting the synchronizability. First, we use the master stability method to theoretically deduce the synchronizability of a multilayer fully coupled network and its simplest equivalent network. It is proven that a multilayer fully coupled network has the same synchronizability as its corresponding simplest equivalent network. Second, we conduct experiments to verify the derivation and observe the process of synchronization. Finally, we analyze the factors affecting the synchronizability of multilayer fully coupled networks. The five influencing factors are identified as the intralayer coupling strength, the interlayer coupling strength, the number of nodes in each network layer, the number of vital nodes and the number of layers in the network. The current findings allow us to gain a deeper understanding of the synchronization behavior and properties of real-world networks.

Quantum anomalous Hall phase in synthetic bilayers via twistronics without a twist

We recently proposed quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions [Phys. Rev. Lett. 125, 030504 (2020)]. Conceptually, the scheme is based on the idea that aphysical monolayer optical lattice of desired geometry is upgraded to a synthetic bilayer system by identifyingthe internal states of the trapped atoms with synthetic spatial dimensions. The couplings between the internalstates, i.e. between sites on the two layers, can be exquisitely controlled by laser induced Raman transitions.By spatially modulating the interlayer coupling, Moir\'e-like patterns can be directly imprinted on the latticewithout the need of a physical twist of the layers. This scheme leads practically to a uniform pattern across thelattice with the added advantage of widely tunable interlayer coupling strengths. The latter feature facilitates theengineering of flat bands at larger "magic" angles, or more directly, for smaller unit cells than in conventionaltwisted materials. In this paper we extend these ideas and demonstrate that our system exhibits topologicalband structures under appropriate conditions. To achieve non-trivial band topology we consider imanaginarynext-to-nearest neighbor tunnelings that drive the system into a quantum anomalous Hall phase. In particular,we focus on three groups of bands, whose their Chern numbers triplet can be associated to a trivial insulator(0,0,0), a standard non-trivial (-1,0,1) and a non-standard non-trivial (-1,1,0). We identify regimes of parameterswhere these three situations occur. We show the presence of an anomalous Hall phase and the appearance oftopological edge states. Our works open the path for experiments on topological effects in twistronics without atwist