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

Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors

https://physics.ucsd.edu/~diventra/synapselearningpub.pdf

Experimental demonstration of associative memory with memristive neural networks

We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux $\phi$ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just this year. We present the properties of a single memristor, memristors in series and parallel, as well as ideal memristor-capacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. We find that the memristor has hysteretic current-voltage characteristics. We show that the ideal MC (ML) circuit undergoes non-exponential charge (current) decay with two time-scales, and that by switching the polarity of the capacitor, an ideal MCL circuit can be tuned from overdamped to underdamped. We present simple models which show that these unusual properties are closely related to the memristor's internal dynamics. This tutorial complements the pedagogy of ideal circuit elements (R,C, and L) and the properties of their circuits.

The elusive memristor: properties of basic electrical circuits

Advances in the fabrication and characterization of nanoscale systems now allow for a better understanding of one of the most basic issues in science and technology: the flow of heat at the microscopic level. In this Colloquium recent advances are surveyed and an understanding of physical mechanisms of energy transport in nanostructures is presented, focusing mainly on molecular junctions and atomic wires. Basic issues are examined such as thermal conductivity, thermoelectricity, local temperature and heating, and the relation between heat current density and temperature gradient---known as Fourier's law. Both theoretical and experimental progress are critically reported in each of these issues and future research opportunities in the field are discussed.

Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions

We present an introduction to and a tutorial on the properties of the recently discovered ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux in a circuit and complements a resistor R, a capacitor C and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just last year. We present the properties of a single memristor, memristors in series and parallel, as well as ideal memristor–capacitor (MC), memristor–inductor (ML) and memristor–capacitor–inductor (MCL) circuits. We find that the memristor has hysteretic current–voltage characteristics. We show that the ideal MC (ML) circuit undergoes non-exponential charge (current) decay with two time scales and that by switching the polarity of the capacitor, an ideal MCL circuit can be tuned from overdamped to underdamped. We present simple models which show that these unusual properties are closely related to the memristor's internal dynamics. This tutorial complements the pedagogy of ideal circuit elements (R, C and L) and the properties of their circuits, and is aimed at undergraduate physics and electrical engineering students.

/pdf/the-elusive-memristor-properties-of-basic-electrical-234wworjcm.pdf

Recently, in addition to the well-known resistor, capacitor, and inductor, a fourth passive circuit element, named memristor, has been identified following theoretical predictions. The model example used in such case consisted in a nanoscale system with coupled ionic and electronic transport. Here, we discuss a system whose memristive behavior is based entirely on the electron-spin degree of freedom, which allows for a more convenient control than the ionic transport in nanostructures. An analysis of time-dependent spin transport at a semiconductor/ferromagnet junction provides a direct evidence of memristive behavior. Our scheme is fundamentally different from previously discussed schemes of memristive systems and broadens the possible range of applications of semiconductor spintronics.

/pdf/spin-memristive-systems-spin-memory-effects-in-semiconductor-4bi5c6ufkd.pdf

Spin Memristive Systems: Spin Memory Effects in Semiconductor Spintronics

Using the memristive properties of vanadium dioxide, we experimentally demonstrate an adaptive filter by placing a memristor into an LC contour. This circuit reacts to the application of select frequency signals by sharpening the quality factor of its resonant response, and thus “learns” according to the input waveform. The proposed circuit employs only analog passive elements, and may find applications in biologically inspired processing and information storage. We also extend the learning-circuit framework mathematically to include memory-reactive elements, such as memcapacitors and meminductors, and show how this expands the functionality of adaptive memory filters.

/pdf/memristive-adaptive-filters-3uexx7s9w0.pdf

Memristive Adaptive Filters

Suggested are circuit realisations of emulators transforming memristive devices into effective floating memcapacitive and meminductive systems. The emulator's circuits are based on second generation current conveyors and involve either four single-output or two dual-output current conveyors. The equations governing the resulting memcapactive and meminductive systems are presented.

Emulation of floating memcapacitors and meminductors using current conveyors

We suggest a possible realization of a solid-state memory capacitive (memcapacitive) system. Our approach relies on the slow polarization rate of a medium between plates of a regular capacitor. To achieve this goal, we consider a multilayer structure embedded in a capacitor. The multilayer structure is formed by metallic layers separated by an insulator so that nonlinear electronic transport (tunneling) between the layers can occur. The suggested memcapacitor shows hysteretic charge-voltage and capacitance-voltage curves, and both negative and diverging capacitance within certain ranges of the field. This proposal can be easily realized experimentally and indicates the possibility of information storage in memcapacitive systems.

/pdf/solid-state-memcapacitive-system-with-negative-and-diverging-3fgqpt2dfs.pdf

Solid-state memcapacitive system with negative and diverging capacitance

Quantum master equations are common tools to describe the dynamics of many-body systems open to an environment. Due to the interaction with the latter, even for the case of noninteracting electrons, the computational cost to solve these equations increases exponentially with the particle number. We propose a simple scheme, which allows to study the dynamics of $N$ noninteracting electrons taking into account both dissipation effects and Fermi statistics, with a computational cost that scales linearly with $N$. Our method is based on a mapping of the many-body system to a specific set of effective single-particle systems. We provide detailed numerical results showing excellent agreement between the effective single-particle scheme and the exact many-body one, as obtained from studying the dynamics of two different systems. In the first, we study optically-induced currents in quantum rings at zero temperature, and in the second we study a linear chain coupled at its ends to two thermal baths with different (finite) temperatures. In addition, we give an analytical justification for our method, based on an exact averaging over the many-body states of the original master equations.

/pdf/effective-single-particle-order-n-scheme-for-the-dynamics-of-2f13uar5cu.pdf

Yu. V. Pershin

Papers

Spin Memristive Systems: Spin Memory Effects in Semiconductor Spintronics

Memristive Adaptive Filters

Emulation of floating memcapacitors and meminductors using current conveyors

Solid-state memcapacitive system with negative and diverging capacitance

Effective single-particle order- N scheme for the dynamics of open noninteracting many-body systems