Percolating networks of nanoparticles (PNNs) exhibit a range of brain-like properties and are well modeled by continuum percolation with tunneling. All of the PNNs studied to date for their potential use in neuromorphic computing have been two-dimensional (2D), formed by depositing particles onto flat insulating substrates. Since the brain itself is three-dimensional (3D), it is natural to ask whether improvements in the brain-like characteristics of the networks and in their usefulness for neuromorphic computing could be achieved by building 3D percolating-tunneling systems. Using realistic simulations, we investigated whether the properties would be significantly different if PNNs were fabricated in 3D, such that the network is no longer able to be represented as a planar graph. We found that the properties of 3D PNNs, including degree distributions and small-world characteristics, are surprisingly similar to those of 2D PNNs. We outline a possible method for fabrication of a 3D PNN and discuss the practical difficulties of achieving a truly percolating network. A straightforward analysis of power dissipation shows that 3D PNNs are likely to be considerably more difficult to cool than 2D PNNs. These results suggest that moving to 3D neuromorphic systems may not bring an improvement in computational performance.

Percolating networks of nanoparticles (PNNs) are promising systems for neuromorphic computing due to their brain-like network structure and dynamics. In particular, electrical spiking in PNNs meets criteria for criticality, which is thought to be the operating point for biological brains and associated with optimal computation. Previous work showed through simulations that spiking PNNs can be used as the core stochastic component in a probabilistic computing scheme. Here, we demonstrate a route to experimental implementation of an integer factorization algorithm. We outline an important modification to the algorithm previously used and demonstrate factorization of up to six-digit integers. Finally, we explore the effect of criticality in the context of the integer factorization task by comparing critical and non-critical systems. We show significant differences in the probability distribution of states generated by the critical and non-critical systems, though for the task considered, critical systems provide no advantage.

The biological brain is comprised of a complex, interconnected, self-assembled network of neurons and synapses. This network enables efficient and accurate information processing, unsurpassed by any other known computational system. Percolating networks of nanoparticles (PNNs) are complex, interconnected, self-assembled systems that exhibit many emergent brain-like characteristics. Notably, neuron-like spiking patterns from PNNs have been shown to be critical, similar to signals from the cortex. PNNs are therefore an appealing candidate for neuromorphic computational systems. Here, the inherent complexity of the patterns of switching events generated by PNNs is explored using several different measures. We begin by defining qualitative measures of spatial, temporal, and spatio-temporal complexity, and then investigate a quantitative measure of complexity that was developed for analysis of patterns of spikes from neurons in the cortex. We discuss adaptations of the method that are required for data from the electronic devices of interest and the impact of various pre-processing procedures on the analysis. Through these measures, it is shown that the neuron-like spiking patterns from PNNs are indeed complex and are clearly distinct from random and ordered data.

Percolating networks of nanoparticles (PNNs) are self-assembled nanoscale systems that possess brain-like characteristics that are useful for information processing, particularly within a reservoir computing (RC) framework. Previous work has successfully demonstrated one-dimensional RC tasks, such as chaotic time-series prediction and nonlinear transformation. We focus here on the challenge of two-dimensional (2D) tasks and introduce novel ‘follow the leader’ and ‘swarming’ tasks. In the first task a ‘follower’ is required to accurately track a ‘leader’ in two dimensions. The task is performed successfully for a range of trajectories and parameters, for both position-based tracking and velocity-based tracking incorporating inertia. In both cases, the task is successful even for trajectories unseen in training. We then successfully demonstrate a 2D implementation of swarming behavior. Each agent is represented by a PNN which is trained to react to the behavior of the other members of the swarm, such that the future trajectory of all agents is generated autonomously. As well as demonstrating that the computational capabilities of PNNs can be extended into two dimensions, this work presents a first step in the emulation of complex emergent biological behaviors such as swarming, and opens a new route to the solution of complex optimization problems.

The complex self-assembled network of neurons and synapses that comprises the biological brain enables natural information processing with remarkable efficiency. Percolating networks of nanoparticles (PNNs) are complex self-assembled nanoscale systems that have been shown to possess many promising brain-like attributes and which are therefore appealing systems for neuromorphic computation. Here experiments are performed that show that PNNs can be utilized as physical reservoirs within a nanoelectronic reservoir computing framework and demonstrate successful computation for several benchmark tasks (chaotic time series prediction, nonlinear transformation, and memory capacity). For each task, relevant literature results are compiled and it is shown that the performance of the PNNs compares favorably to that previously reported from nanoelectronic reservoirs. It is then demonstrated experimentally that PNNs can be used for spoken digit recognition with state-of-the-art accuracy. Finally, a parallel reservoir architecture is emulated, which increases the dimensionality and richness of the reservoir outputs and results in further improvements in performance across all tasks.

Incommensurate heterostructures of two-dimensional (2D) materials, despite their attractive electronic behaviour, are challenging to simulate because of the absence of translation symmetry. Experimental investigations of these structures often employ scanning tunneling microscopy (STM), however there is to date no comprehensive theory to simulate and predict a STM image in such systems. In this paper, we present a new approach to simulate STM images in arbitrary van der Waals (vdW) heterostructures, using a moir\'e plane wave expansion model (MPWEM). Contrary to computationally demanding conventional methods such as density functional theory that in practice require periodic boundaries, our method only relies on the description of the noninteracting STM images of the separate materials, and on a narrow set of intuitive semi-empirical parameters, successfully simulating experimental STM images down to angstrom-scale details. We illustrate and benchmark the model using selected vdW 2D systems composed of structurally and electronically distinct crystals. The MPWEM, generating reliable STM images within seconds, can serve as an initial prediction tool, which can prove to be useful in the investigation of vdW heterostructures, offers an avenue towards fast and reliable prediction methods in the growing field of twistronics.

Abstract Major efforts to reproduce functionalities and energy efficiency of the brain have been focused on the development of artificial neuromorphic systems based on crossbar arrays of memristive devices fabricated by top-down lithographic technologies. Although very powerful, this approach does not emulate the topology and the emergent behavior of biological neuronal circuits, where the principle of self-organization regulates both structure and function. In materia computing has been proposed as an alternative exploiting the complexity and collective phenomena originating from various classes of physical substrates composed of a large number of non-linear nanoscale junctions. Systems obtained by the self-assembling of nano-objects like nanoparticles and nanowires show spatio-temporal correlations in their electrical activity and functional synaptic connectivity with nonlinear dynamics. The development of design-less networks offers powerful brain-inspired computing capabilities and the possibility of investigating critical dynamics in complex adaptive systems. Here we review and discuss the relevant aspects concerning the fabrication, characterization, modeling, and implementation of networks of nanostructures for data processing and computing applications. Different nanoscale electrical conduction mechanisms and their influence on the meso- and macroscopic functional properties of the systems are considered. Criticality, avalanche effects, edge-of-chaos, emergent behavior, synaptic functionalities are discussed in detail together with applications for unconventional computing. Finally, we discuss the challenges related to the integration of nanostructured networks and with standard microelectronics architectures.

As growth in global demand for computing power continues to outpace ongoing improvements in transistor-based hardware, novel computing solutions are required. One promising approach employs stochastic nanoscale devices to accelerate probabilistic computing algorithms. Percolating Networks of Nanoparticles (PNNs) exhibit stochastic spiking, which is of particular interest as it meets criteria for criticality which is associated with a range of computational advantages. Here, we show several ways in which spiking PNNs can be used as the core stochastic components of coupled networks that allow successful factorization of integers up to 945. We demonstrate asynchronous operation and show that a single device is sufficient to solve all factorization tasks and to generate multiple solutions simultaneously.

Structural superlubricity is a special frictionless contact in which two crystals are in incommensurate arrangement such that relative in-plane translation is associated with vanishing energy barrier crossing. So far, it has been realized in multilayer graphene and other van der Waals (2D crystals with hexagonal or triangular crystalline symmetries, leading to isotropic frictionless contacts. Directional structural superlubricity, to date unrealized in 2D systems, is possible when the reciprocal lattices of the two crystals coincide in one direction only. Here, directional structural superlubricity a α-bismuthene/graphite van der Waals system is evidenced, manifested by spontaneous hopping of the islands over hundreds of nanometers at room temperature, resolved by low-energy electron microscopy and supported by registry simulations. Statistical analysis of individual and collective α-bismuthene islands populations reveal a heavy-tailed distribution of the hopping lengths and sticking times indicative of Lévy flight dynamics, largely unobserved in condensed-matter systems.

Lanthanide nitride species have recently been shown to be easily formed at ambient temperatures and low pressures via the reaction of clean lanthanide surfaces with molecular nitrogen. However, understanding and predicting the nature and efficiency of this process is still in its infancy. In this work we report on the nitridation of the surface of two lanthanide metals, gadolinium (Gd) and samarium (Sm). To that end, epitaxial gadolinium and samarium thin layers are grown on AlN(0001) by molecular beam epitaxy and exposed to molecular nitrogen in high vacuum conditions and ambient temperature. In situ reflection high-energy electron diffraction is used to monitor the growth of Gd in real time, as well as the subsequent exposure to nitrogen, showing a clear transition from a pure Gd surface to a gadolinium nitride (GdN) surface layer. The formation of a nitride layer is further reinforced by magnetic measurements showing clear contributions from the Gd metal and GdN surface layers. Formation of SmN is investigated using synchrotron X-ray photoelectron spectroscopy to probe the surface of Sm pre- and post-nitrogen exposure, showing a change in the surface valence from divalent to trivalent samarium, and confirming the nitridation of the pure Sm surface layer.

The biological brain is a highly efficient computational system in which information processing is performed via electrical spikes. Neuromorphic computing systems that work on similar principles could support the development of the next generation of artificial intelligence and, in particular, enable low-power edge computing. Percolating networks of nanoparticles (PNNs) have previously been shown to exhibit critical spiking behavior, with promise for highly efficient natural computation. Here we employ a rate coding scheme to show that PNNs can perform Boolean operations and image classification. Near perfect accuracy is achieved in both tasks by manipulating the spiking activity using certain control voltages. We demonstrate that the key to successful computation is that nanoscale tunnel gaps within the percolating networks transform input data through a powerful modulus-like nonlinearity. These results provide a basis for implementation of further computational schemes that exploit the brain-like criticality of these networks.

The connectivity of self-assembled networks of nanowires and nanoparticles is believed to strongly influence their performance in brainlike (neuromorphic) computing applications. Here we present a new perspective on the connectivity of these networks in which their neuronlike active elements are viewed in the same way as the nodes in artificial and biological neuronal networks. We consider two-dimensional and quasi-three-dimensional networks of nanowires and percolating networks of nanoparticles and show that, from this new perspective, they all have similar small-world characteristics. Other characteristics which may impact the computational performance of the networks are also investigated, including their assortativity and the scalefree nature of the nanoparticle networks. Taken together, these results allow comparison of key network characteristics for a variety of self-assembled nanoscale networks, and provide a basis for detailed investigations of computational performance.

Using a simple sequential deposition method, we grow black-phosphorus-like antimonene (alpha-antimonene) on top of alpha-bismuthene nanoislands. Due to the lattice mismatch between the a-antimonene overlayer and the bismuthene bases, the heterostructure exhibits a moire pattern whose periodicitiy (similar to 8 +/- 1 nm) is amongst the largest periodicities ever observed in 2D systems. We use scanning tunnelling microscopy and spectroscopy to show that this moir ' e pattern modulates both the electronic states in the bulk and the edge states of the a-antimonene, and therefore leads to local modulations of the topological phase. We present calculations which elucidate the effects of strain on the bandstructure of a-Sb and discuss detailed spectroscopy results for the edge states, as well as the effect of interlayer interactions between the a-Sb and a-Bi structures.

Percolating Networks of Nanoparticles (PNNs) are under investigation as candidates for physical implementations of reservoir computing (RC). Several promising features have been identified in PNNs, such as brain-like critical dynamics, long-range spatiotemporal correlations and nonlinear I-V characteristics. However, the information processing capability of PNNs remains to be demonstrated. Here we present detailed modelling of PNNs operating in the tunneling regime as delayed-dynamical reservoirs (DDRs). The computational capacity of these reservoirs is successfully demonstrated by their performance in two benchmark tasks: waveform discrimination and tenth-order nonlinear auto-regressive moving average (NARMA10) time series prediction. Furthermore, the interplay between the PNN response time and the delayed feedback is elucidated, providing valuable insight for future DDR design.

Reservoir computing (RC) has attracted significant interest as a framework for the implementation of novel neuromorphic computing architectures. Previously attention has been focussed on software-based reservoirs, where it has been demonstrated that reservoir topology plays a role in task performance, and functional advantage has been attributed to small-world and scale-free connectivity. However in hardware systems, such as electronic memristor networks, the mechanisms responsible for the reservoir dynamics are very different and the role of reservoir topology is largely unknown. Here we compare the performance of a range of memristive reservoirs in several RC tasks that are chosen to highlight different system requirements. We focus on percolating networks of nanoparticles (PNNs) which are novel self-assembled nanoscale systems that exhibit scale-free and small-world properties. We find that the performance of regular arrays of uniform memristive elements is limited by their symmetry but that this symmetry can be broken either by a heterogeneous distribution of memristor properties or a scale-free topology. The best perfomance across all tasks is observed for a scale-free network with uniform memistor properties. These results provide insight into the role of topology in neuromorphic reservoirs as well as an overview of the computational performance of scale-free networks of memristors in a range of benchmark tasks.

We present a systematic investigation of the edge states (ESs) of two-dimensional alpha-bismuthene (alpha-Bi) structures self-assembled on highly oriented pyrolytic graphite substrates, using scanning tunnelling microscopy and scanning tunnelling spectroscopy. The measurements are carried out for 3ML, 5ML and 7ML thick Bi structures. Our spectroscopy studies reveal clear features at the edges of the 5ML and 7ML thick structures, and the positions of the ESs coincide with the topographical step edges. In contrast, in 3ML structures the ESs appear to be absent and instead new states are sometimes observed, far from the topographical edge. These states are associated with a moire pattern and result from strain-induced modulation of the topology. Our observations demonstrate the impact on the ESs of coupling to adjacent structures.

Physical systems that exhibit brain-like behaviour are currently under intense investigation as platforms for neuromorphic computing. We show that discontinuous metal films, comprising irregular flat islands on a substrate and formed using simple evaporation processes, exhibit correlated avalanches of electrical signals that mimic those observed in the cortex. We further demonstrate that these signals meet established criteria for criticality. We perform a detailed experimental investigation of the atomic-scale switching processes that are responsible for these signals, and show that they mimic the integrate-and-fire mechanism of biological neurons. Using numerical simulations and a simple circuit model, we show that the characteristic features of the switching events are dependent on the network state and the local position of the switch within the complex network. We conclude that discontinuous films provide an interesting potential platform for brain-inspired computing.

Random networks of nanoparticle-based memristive switches enable pathways for emulating highly complex and self-organized synaptic connectivity together with their emergent functional behavior known from biological neuronal networks. They therefore embody a distinct class of neuromorphic hardware architectures and provide an alternative to highly regular arrays of memristors. Especially, networks of memristive nanoparticles (NPs) poised at the percolation threshold are promising due to their capabilities of showing brain-like activity such as critical dynamics or long-range temporal correlation (LRTC), which are closely connected to the computational capabilities in biological neuronal networks. Here, we adapt this concept to networks of Ag-NPs poised at the electrical percolation threshold, where the memristive properties are governed by electro-chemical metallization. We show that critical dynamics and LRTC are preserved although the nature of individual memristive gaps throughout the network is fundamentally changed by filling the gaps with an insulating matrix. The results in this work generate important contributions towards the practical applicability of critical dynamics and LRTC in percolating NP networks by elucidating the consequences of NP network encapsulation, which is considered as an important step towards device integration.

The electrodes used for flexible photovoltaic cells require materials that are transparent, conductive and flexible. All these features seem to be met by graphene, on the basis of which we were able to construct the anode. Here we show that increase of the graphene work function is possible using an additional layer of molybdenum or rhenium oxides. Moreover, we show that a single crystalline layer of MoO3-x can increase the work function of the graphene. In consequence there is a real chance for practical applications of graphene in electronics.

Networks of nanowires are currently being explored for a range of applications in brain-like (or neuromorphic) computing, and especially in reservoir computing (RC). Fabrication of real-world computing devices requires that the nanowires are deposited sequentially, leading to stacking of the wires on top of each other. However, most simulations of computational tasks using these systems treat the nanowires as 1D objects lying in a perfectly 2D plane - the effect of stacking on RC performance has not yet been established. Here we use detailed simulations to compare the performance of perfectly 2D and quasi-3D (stacked) networks of nanowires in two tasks: memory capacity and nonlinear transformation. We also show that our model of the junctions between nanowires is general enough to describe a wide range of memristive networks, and consider the impact of physically realistic electrode configurations on performance. We show that the various networks and configurations have a strikingly similar performance in RC tasks, which is surprising given their radically different topologies. Our results show that networks with an experimentally achievable number of electrodes perform close to the upper bounds achievable when using the information from every wire. However, we also show important differences, in particular that the quasi-3D networks are more resilient to changes in the input parameters, generalizing better to noisy training data. Since previous literature suggests that topology plays an important role in computing performance, these results may have important implications for future applications of nanowire networks in neuromorphic computing.