Electric currents in networks of interconnected memristors

Chua [IEEE Trans. Circuit Theory 1, 507 (1971).] argued that, in addition to the standard resistors, capacitors, and inductors, there must be a fourth fundamental element in electrical circuits, which he called a memory resistor or memristor. Strukov et al. [Nature (London) 453, 80 (2008)] showed how memristive behavior arises in some thin semiconducting films. Unlike other passive elements, however, a memristor with large sizes cannot be fabricated, because scale up of a memristor to dimensions of the order of microns causes loss of the memristive effect by decreasing the width of the doped region relative to the overall size of the memristor. A microscale memristor is, however, essential to most of the potential applications. One way of fabricating such a microscale memristor without losing the memristive effect is to make a network of very small interconnected memristors. We report the results of numerical simulations of electrical currents in such networks of interconnected memristors, as well as memristors and Ohmic conductors. The memristor networks exhibit a rich variety of interesting properties, including weakly and strongly memristive regimes, a possible first-order transition at the connectivity threshold, generation of second harmonics in the strongly memristive regime, and the universal dependence of the network's strength on the frequency. Moreover, we show that the polarity of the memristors can play an important role in the overall properties of the memristor network, in particular its speed of switching, which may have a potentially important application to faster computers. None of these properties are exhibited by linear resistor networks, or even by nonlinear resistor networks without a memory effect.