Neuromorphic computers are defined as non-von Neumann computers whose structure and function are inspired by brains and that are composed of neurons and synapses (C. D. Schuman, Nature Computational Science, 21, 10 (2022). The next real game changer will be 'neuromorphic computing' with AI, and at the heart of neuromorphic computing is the electrical circuit element 'memristor'.

There are three basic two terminals passive elements in an electrical circuit: resistor, inductor, and capacitor. The existence of a fourth element 'memristor' was predicted in the early 1970s by L. Chua (IEEE Trans Circuit Theory 18 507 (1971)),  and then it was first realized physically in 2008 (D. Strukov et al. Nature 453 80 (2008)). Since then rapid progress has been made in this field, especially during the last five years.

The physics behind a class of this revolutionary element ‘memristor’ namely Mott-insulator based memristor is deceptively simple but at the same time very exotic and robust. In this class, an applied electric field can tilt the balance between the electron 'potential energy' and 'kinetic energy', and in turn make the electron change its character from 'more particle-like' (in the Mott insulator state) to 'more wave-like' (in the correlated electron metal state). This change in electronic state takes place in a very similar fashion water turns into ice in the ice trays of household refrigerators.

In scientific parlance, such a relatively abrupt change in the state of matter is known as first-order phase transition (FOPT). It is omnipresent, with the classic example being boiling and freezing of water. The existence of FOPT involving a change in the lattice and/or spin degree of freedom in solid materials is also fairly well known. During the last decade or so it has become apparent that the change in the magnetic and lattice structure associated with such FOPT in a material can give rise to various interesting functional properties of technological importance (S. B. Roy. J. Phys.: Condensed Matter 25 183201 (2013)). It is also realized that such functional materials are mostly multicomponent alloys and chemical compounds, where the actual composition varies around some average composition due to disorder that is frozen in as the solid crystallizes from the melt. Such static, quenched-in, purely statistical compositional disorder would introduce a landscape of transition temperatures in a system undergoing FOPT. In addition, the disorder will also cause a phase-coexistence of equilibrium and metastable phases associated with supercooling/superheating across a first-order phase transition. Such phase coexistence at a point, that is possible to tune by external parameters like temperature and magnetic field, can give rise to several functional properties of technological importance.

Here we have applied various ideas developed in connection with our earlier studies on functional magnetic materials, to the study of electric field-induced Mott-insulator to metal transition in archetypal Mott insulator V₂O₃. We have shown how the electro-thermal history effects and phase-coexistence observed across the first-order Mott transition can give rise to interesting memristive effects. We envisage that such studies would eventually lead to the discovery of robust memristor devices operating at room temperature.