Current-controlled memristors: Resistive switching systems with negative capacitance and inverted hysteresis

Resistive switching in memristors is being amply investigated for different applications in nonvolatile memory, neuromorphic computing, and programmable logic devices. Memristors are conducting devices in which the conductance depends on one or more slow internal state variables, and they exhibit strongly nonlinear properties and intense memory effects. Here, we address the characterization of current-controlled memristors by small-perturbation frequency-resolved impedance techniques. We show that the equivalent circuit obtained at different stationary points provides essential information about the dynamic behavior in voltage cycling and transient response to a square perturbation. The general method enables the analysis of stability and hysteresis in current-voltage curves. The current-controlled memristor very naturally produces a negative capacitance effect, and we review several devices reported in the literature, including discharge tubes and metal-oxide memristors, to expose the deep connections between the sign of the capacitance and the type of hysteresis.