Yuriy V. Pershin

Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors

We extend the notion of memristive systems to capacitive and inductive elements, namely, capacitors and inductors whose properties depend on the state and history of the system. All these elements typically show pinched hysteretic loops in the two constitutive variables that define them: current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the meminductor. We argue that these devices are common at the nanoscale, where the dynamical properties of electrons and ions are likely to depend on the history of the system, at least within certain time scales. These elements and their combination in circuits open up new functionalities in electronics and are likely to find applications in neuromorphic devices to simulate learning, adaptive, and spontaneous behavior.

Memory effects in complex materials and nanoscale systems

Memory effects are ubiquitous in nature and are particularly relevant at the nanoscale where the dynamical properties of electrons and ions strongly depend on the history of the system, at least within certain time scales. We review here the memory properties of various materials and systems which appear most strikingly in their non-trivial, time-dependent resistive, capacitative and inductive characteristics. We describe these characteristics within the framework of memristors, memcapacitors and meminductors, namely memory-circuit elements with properties that depend on the history and state of the system. We examine basic issues related to such systems and critically report on both theoretical and experimental progress in understanding their functionalities. We also discuss possible applications of memory effects in various areas of science and technology ranging from digital to analog electronics, biologically inspired circuits and learning. We finally discuss future research opportunities in the field.

Practical Approach to Programmable Analog Circuits With Memristors

We suggest an approach to use memristors (resistors with memory) in programmable analog circuits. Our idea consists in a circuit design in which low voltages are applied to memristors during their operation as analog circuit elements and high voltages are used to program the memristors states. This way, as it was demonstrated in recent experiments, the state of memristors does not essentially change during analog mode operation. As an example of our approach, we have built several programmable analog circuits demonstrating memristor-based programming of threshold, gain and frequency. In these circuits the role of memristor is played by a memristor emulator developed by us.

Memristive model of amoeba learning

Recently, it was shown that the amoebalike cell Physarum polycephalum when exposed to a pattern of periodic environmental changes learns and adapts its behavior in anticipation of the next stimulus to come. Here we show that such behavior can be mapped into the response of a simple electronic circuit consisting of a LC contour and a memory-resistor (a memristor) to a train of voltage pulses that mimic environment changes. We also identify a possible biological origin of the memristive behavior in the cell. These biological memory features are likely to occur in other unicellular as well as multicellular organisms, albeit in different forms. Therefore, the above memristive circuit model, which has learning properties, is useful to better understand the origins of primitive intelligence.

Neuromorphic, Digital, and Quantum Computation With Memory Circuit Elements

Memory effects are ubiquitous in nature and the class of memory circuit elements - which includes memristive, memcapacitive, and meminductive systems - shows great potential to understand and simulate the associated physical processes. Here, we show that such elements can also be used in electronic schemes mimicking biologically inspired computer architectures, performing digital logic and arithmetic operations, and can expand the capabilities of certain quantum computation schemes. In particular, we will discuss some examples where the concept of memory elements is relevant to the realization of associative memory in neuronal circuits, spike-timing-dependent plasticity (STDP) of synapses, and digital and field-programmable quantum computing.

The parallel approach

Memcomputing is an emergent computing paradigm that employs two-terminal electronic devices with memory, namely, memristive, memcapacitive or meminductive systems, to store and process information at the same physical location. Complex networks of such devices can be considered as massively-parallel processors performing computation in an unconventional way. In this contribution, we discuss essential memcomputing criteria as well as several possible practical realizations of memcomputing based on nanoscale electronic devices with memory.

Memristive circuits simulate memcapacitors and meminductors

Electronic circuits with memristors (resistors with memory) that operate as memcapacitors (capacitors with memory) and meminductors (inductors with memory) are proposed. Using a memristor emulator, the suggested circuits have been built and their operation has been demonstrated, showing a useful and interesting connection between the three memory elements.

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.

Effect of spin-orbit interaction and in-plane magnetic field on the conductance of a quasi-one-dimensional system

We study the effect of spin-orbit interaction and in-plane effective magnetic field on the conductance of a quasi-one-dimensional ballistic electron system. The effective magnetic field includes the externally applied field, as well as the field due to polarized nuclear spins. The interplay of the spin-orbit interaction with effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps, introducing the dependence of the subband energies on the field direction. We generalize the Landauer formula at finite temperatures to incorporate these special features of the dispersion relation. The obtained formula describes the conductance of a ballistic conductor with an arbitrary dispersion relation.

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.