  Two-dimensional (2D) materials are suitable hosts for the intercalation of
extrinsic guest ions such as Li+, Na+ and K+ as the interlayer coupling is
weak. This allows ion intercalation engineering of 2D materials, which may be a
key to advancing technological applications in energy storage, neuromorphic
electronics, and bioelectronics. However, ions that are extrinsic to the host
materials possess challenges in fabrication of devices as there are extra steps
of ion intercalation. This results in degradation of the long-term stability of
the intercalated atomically thin structures. Here, we introduce large-area
single-crystal ultra-thin layered MnO$_2$ via chemical vapor deposition,
spontaneously intercalated by potassium ions during the synthesis. We studied
the ultra-thin 2D K-MnO$_2$ in detail and showed that charge transport in these
crystals is dominated by motion of hydrated potassium ions in the interlayer
space. Moreover, K-MnO$_2$ crystals exhibit reversible layered-to-spinel phase
transition accompanied by an optical contrast change based on the electrical
and optical modulation of the potassium and the interlayer water concentration.
We used the electric field driven ionic motion in K-MnO$_2$ based devices to
demonstrate the memristive properties of two terminal devices. As a possible
application we showed that K-MnO$_2$ memristors display synapse-like behavior
such as short and long-term potentiation and depression as well as ionic
coupling effects.
