  Using molecular dynamics simulations, we show that, when subject to a
periodic external electric field, a nanopore in ionic solution acts as a
capacitor with memory (memcapacitor) at various frequencies and strengths of
the electric field. Most importantly, the hysteresis loop of this memcapacitor
shows both negative and diverging capacitance as a function of the voltage. The
origin of this effect stems from the slow polarizability of the ionic solution
due to the finite mobility of ions in water. We develop a microscopic
quantitative model which captures the main features we observe in the
simulations and suggest experimental tests of our predictions. We also suggest
a possible memory mechanism due to the transport of ions through the nanopore
itself, which may be observed at small frequencies. These effects may be
important in both DNA sequencing proposals using nanopores and possibly in the
dynamics of action potentials in neurons.
