Probabilistic model of resistance jumps in memristive devices.

Resistance switching memory cells such as electrochemical metallization cells and valence change mechanism cells have the potential to revolutionize information processing and storage. However, the creation of deterministic resistance switching devices is a challenging problem that is still open. At present, the modeling of resistance switching cells is dominantly based on deterministic models that fail to capture the cycle-to-cycle variability intrinsic to these devices. Herewith we introduce a state probability distribution function and associated integrodifferential equation to describe the switching process consisting of a set of stochastic jumps. Numerical and analytical solutions of the equation have been found in two model cases. This work expands the toolbox of models available for resistance switching cells and related devices and enables a rigorous description of intrinsic physical behavior not available in other models.

Memristive Ising circuits.

The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically driven circuits of stochastic binary resistors with memory. A key feature of our realization is the simultaneous coexistence of ferromagnetic and antiferromagnetic interactions between two neighboring spins-an extraordinary property not available in nature. We demonstrate that the statistics of circuit states may perfectly match the ones found in the Ising model with ferromagnetic or antiferromagnetic interactions, and, importantly, the corresponding Ising model parameters can be extracted from the probabilities of circuit states. Using this finding, the Ising Hamiltonian is reconstructed in several model cases, and it is shown that different types of interaction can be realized in circuits of stochastic memristors.

Custodial Chiral Symmetry in a Su-Schrieffer-Heeger Electrical Circuit with Memory.

Custodial symmetries are common in the standard model of particle physics. They arise when quantum corrections to a parameter are proportional to the parameter itself. Here, we show that a custodial symmetry of the chiral type is also present in a classical Su-Schrieffer-Heeger (SSH) electrical circuit with memory. In the absence of memory, the SSH circuit supports a symmetry-protected topological edge state. Memory induces nonlinearities that break chiral symmetry explicitly and spread the state across the circuit. However, the resulting state is still protected against perturbations by the ensuing custodial chiral symmetry. These predictions can be verified experimentally and demonstrate the interplay between symmetry and memory.

On the validity of memristor modeling in the neural network literature.

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks.

Snap-through transition of buckled graphene membranes for memcapacitor applications.

Using computational and theoretical approaches, we investigate the snap-through transition of buckled graphene membranes. Our main interest is related to the possibility of using the buckled membrane as a plate of capacitor with memory (memcapacitor). For this purpose, we performed molecular-dynamics (MD) simulations and elasticity theory calculations of the up-to-down and down-to-up snap-through transitions for membranes of several sizes. We have obtained expressions for the threshold switching forces for both up-to-down and down-to-up transitions. Moreover, the up-to-down threshold switching force was calculated using the density functional theory (DFT). Our DFT results are in general agreement with MD and analytical theory findings. Our systematic approach can be used for the description of other structures, including nanomechanical and biological ones, experiencing the snap-through transition.

Surface effects on ionic Coulomb blockade in nanometer-size pores.

Ionic Coulomb blockade in nanopores is a phenomenon that shares some similarities but also differences with its electronic counterpart. Here, we investigate this phenomenon extensively using all-atom molecular dynamics of ionic transport through nanopores of about one nanometer in diameter and up to several nanometers in length. Our goal is to better understand the role of atomic roughness and structure of the pore walls in the ionic Coulomb blockade. Our numerical results reveal the following general trends. First, the nanopore selectivity changes with its diameter, and the nanopore position in the membrane influences the current strength. Second, the ionic transport through the nanopore takes place in a hopping-like fashion over a set of discretized states caused by local electric fields due to membrane atoms. In some cases, this creates a slow-varying 'crystal-like' structure of ions inside the nanopore. Third, while at a given voltage, the resistance of the nanopore depends on its length, the slope of this dependence appears to be independent of the molarity of ions. An effective kinetic model that captures the ionic Coulomb blockade behavior observed in MD simulations is formulated.

Metastable memristive lines for signal transmission and information processing applications.

Traditional studies of memristive devices have mainly focused on their applications in nonvolatile information storage and information processing. Here, we demonstrate that the third fundamental component of information technologies-the transfer of information-can also be employed with memristive devices. For this purpose, we introduce a metastable memristive circuit. Combining metastable memristive circuits into a line, one obtains an architecture capable of transferring a signal edge from one space location to another. We emphasize that the suggested metastable memristive lines employ only resistive circuit components. Moreover, their networks (for example, Y-connected lines) have an information processing capability.

Finding Stable Graphene Conformations from Pull and Release Experiments with Molecular Dynamics.

Here, we demonstrate that stable conformations of graphene nanoribbons can be identified using pull and release experiments, when the stretching force applied to a single-layer graphene nanoribbon is suddenly removed. As it is follows from our numerical experiments performed by means of molecular dynamics simulations, in such experiments, favorable conditions for the creation of folded structures exist. Importantly, at finite temperatures, the process of folding is probabilistic. We have calculated the transition probabilities to folded conformations for a graphene nanoribbon of a selected size. Moreover, the ground state conformation has been identified and it is shown that its type is dependent on the nanoribbon length. We anticipate that the suggested pull and release approach to graphene folding may find applications in the theoretical studies and fabrication of emergent materials and their structures.

The theory of spin noise spectroscopy: a review.

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.

Memristive Sisyphus circuit for clock signal generation.

Frequency generators are widely used in electronics. Here, we report the design and experimental realization of a memristive frequency generator employing a unique combination of only digital logic gates, a single-supply voltage and a realistic thresholdtype memristive device. In our circuit, the oscillator frequency and duty cycle are defined by the switching characteristics of the memristive device and external resistors. We demonstrate the circuit operation both experimentally, using a memristor emulator, and theoretically, using a model memristive device with threshold. Importantly, nanoscale realizations of memristive devices offer small-size alternatives to conventional quartz-based oscillators. In addition, the suggested approach can be used for mimicking some cyclic (Sisyphus) processes in nature, such as "dripping ants" or drops from leaky faucets.

Switching synchronization in one-dimensional memristive networks.

We report on a switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high- to low-resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with results of our numerical simulations.

Electric field cycling behavior of ferroelectric hafnium oxide.

HfO2 based ferroelectrics are lead-free, simple binary oxides with nonperovskite structure and low permittivity. They just recently started attracting attention of theoretical groups in the fields of ferroelectric memories and electrostatic supercapacitors. A modified approach of harmonic analysis is introduced for temperature-dependent studies of the field cycling behavior and the underlying defect mechanisms. Activation energies for wake-up and fatigue are extracted. Notably, all values are about 100 meV, which is 1 order of magnitude lower than for conventional ferroelectrics like lead zirconate titanate (PZT). This difference is mainly atttributed to the one to two orders of magnitude higher electric fields used for cycling and to the different surface to volume ratios between the 10 nm thin films in this study and the bulk samples of former measurements or simulations. Moreover, a new, analog-like split-up effect of switching peaks by field cycling is discovered and is explained by a network model based on memcapacitive behavior as a result of defect redistribution.

Giant up-conversion efficiency of InGaAs quantum dots in a planar microcavity.

Self-assembled InGaAs quantum dots (QDs) were fabricated inside a planar microcavity with two vertical cavity modes. This allowed us to excite the QDs coupled to one of the vertical cavity modes through two propagating cavity modes to study their down- and up-converted photoluminescence (PL). The up-converted PL increased continuously with the increasing temperature, reaching an intensity level comparable to that of the down-converted PL at ~120 K. This giant efficiency in the up-converted PL of InGaAs QDs was enhanced by about 2 orders of magnitude with respect to a similar structure without cavity. We tentatively explain the enhanced up-converted signal as a direct consequence of the modified spontaneous emission properties of the QDs in the microcavity, combined with the phonon absorption and emission effects.

Self-organization and solution of shortest-path optimization problems with memristive networks.

We show that memristive networks, namely networks of resistors with memory, can efficiently solve shortest-path optimization problems. Indeed, the presence of memory (time nonlocality) promotes self organization of the network into the shortest possible path(s). We introduce a network entropy function to characterize the self-organized evolution, show the solution of the shortest-path problem and demonstrate the healing property of the solution path. Finally, we provide an algorithm to solve the traveling salesman problem. Similar considerations apply to networks of memcapacitors and meminductors, and networks with memory in various dimensions.

Nonequilibrium spin noise spectroscopy.

Spin noise spectroscopy is an experimental approach to obtain correlators of mesoscopic spin fluctuations in time by purely optical means. We explore the information that this technique can provide when it is applied to a weakly nonequilibrium regime when an electric current is driven through a sample by an electric field. We find that the noise power spectrum of conducting electrons experiences a shift, which is proportional to the strength of the spin-orbit coupling for electrons moving along the electric field direction. We propose applications of this effect to measurements of spin-orbit coupling anisotropy and separation of spin noise of conducting and localized electrons.

On the physical properties of memristive, memcapacitive and meminductive systems.

We discuss the physical properties of realistic memristive, memcapacitive and meminductive systems. In particular, by employing the well-known theory of response functions and microscopic derivations, we show that resistors, capacitors and inductors with memory emerge naturally in the response of systems-especially those of nanoscale dimensions-subjected to external perturbations. As a consequence, since memristances, memcapacitances and meminductances are simply response functions, they are not necessarily finite. This means that, unlike what has always been argued in some literature, diverging and non-crossing input-output curves of all these memory elements are physically possible in both quantum and classical regimes. For similar reasons, it is not surprising to find memcapacitances and meminductances that acquire negative values at certain times during dynamics, while the passivity criterion of memristive systems imposes always a non-negative value on the resistance at any given time. We finally show that ideal memristors, namely those whose state depends only on the charge that flows through them (or on the history of the voltage), are subject to very strict physical conditions and are unable to protect their memory state against the unavoidable fluctuations, and therefore are susceptible to a stochastic catastrophe. Similar considerations apply to ideal memcapacitors and meminductors.

Changing the state of a memristive system with white noise.

Can we change the average state of a resistor by simply applying white noise? We show that the answer to this question is positive if the resistor has memory of its past dynamics (a memristive system). We also prove that, if the memory arises only from the charge flowing through the resistor-an ideal memristor-then the current flowing through such memristor cannot charge a capacitor connected in series and, therefore, cannot produce useful work. However, the memristive system may skew the charge probability density on the capacitor, an effect that can be measured experimentally.

Complex dynamics and scale invariance of one-dimensional memristive networks.

Memristive systems, namely, resistive systems with memory, are currently attracting considerable attention. Here we show that even the simplest one-dimensional network formed by the most common memristive elements with voltage threshold bears nontrivial physical properties. In particular, by taking into account the single element variability we find (1) dynamical acceleration and slowing down of the total resistance in adiabatic processes, (2) dependence of the final state on the history of the input signal with same initial conditions, (3) existence of switching avalanches in memristive ladders, and (4) independence of the dynamics voltage threshold with respect to the number of memristive elements in the network (scale invariance). An important criterion for this scale invariance is the presence of memristive systems with very small threshold voltages in the ensemble. These results elucidate the role of memory in complex networks and are relevant to technological applications of these systems.

Memory models of adaptive behavior.

Adaptive response to varying environment is a common feature of biological organisms. Reproducing such features in electronic systems and circuits is of great importance for a variety of applications. We consider memory models inspired by an intriguing ability of slime molds to both memorize the period of temperature and humidity variations and anticipate the next variations to come, when appropriately trained. Effective circuit models of such behavior are designed using: 1) a set of LC contours with memristive damping and 2) a single memcapacitive system-based adaptive contour with memristive damping. We consider these two approaches in detail by comparing their results and predictions. Finally, possible biological experiments that would discriminate between the models are discussed. In this paper, we also introduce an effective description of certain memory circuit elements.