The Ubiquitous Memristive Response in Solids

Basic ingredients universally available in the carrier transport of conductive solids are proved to be sufficient (not necessary) conditions for the formation of memory while symmetry, or the lack of it, plays a decisive role in the nature of this response. It suffices that the input driving frequency is of the order of the inverse relaxation time and that the nonequilibrium carrier densities are in the order of the quasi-equilibrium ones. Thus, memristive response with ON and OFF states at zero voltage, Type I, and vanishing ON– OFF ratio, Type II, arise naturally according to simple symmetry constraints and are contrasted here in a fully analytical picture. Figures of merit for the conductance and the robustness of the memory response are presented in the form of concise correlations between general intrinsic microscopic parameters such as relaxation times, activation energies, and efficiencies with external drives: voltage pulses, temperature, and illumination. Explicit analytical expressions unveil the mimicry of inductive- and capacitive-like leaning impedances without the need of relaxing the interpretation of flux that has been used for more stringent definitions of memristors.