*In Nature **; h5-index 368.0 *

^{1-4}. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)

^{5}, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element

^{6-8}. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.

*Kumar Suhas, Williams R Stanley, Wang Ziwen*

*2020-Sep*