Memristors

A memristor is a passive two-terminal electronic device whose resistance depends on the history of current that has flowed through it. In the memristor model, V = M(q) I, where M is memristance that depends on the total electric charge q that has passed, equivalently the derivative of magnetic flux with respect to charge (dφ/dq). The device “remembers” past activity in its resistance, even when power is removed.

The concept was proposed by Leon O. Chua in 1971 as the fourth fundamental circuit element, completing the relationship between charge and flux. A practical memristor was first demonstrated in 2008 by researchers at HP Labs, who used a thin film of titanium dioxide and observed a resistance that changed with the history of current flow. Since then, various material systems have been explored, including other metal-oxide films and doped polymers.

Key properties include a pinched hysteresis loop in the current–voltage plane and non-volatile resistance state, allowing storage of information without power. The internal state is often modeled by a state variable representing dopant distribution or similar, which evolves with applied current or voltage. Memristors are studied for non-volatile memory (RRAM) and for neuromorphic computing, where they can emulate synaptic weight changes. They are often implemented in dense crossbar arrays to enable scalable memory and processing-in-memory architectures.

Terminology and scope: some devices exhibiting history-dependent resistance are described as memristive systems rather than ideal memristors; real devices may not satisfy the exact mathematical memristor model and show variability, endurance, and retention challenges. The concept remains a framework for understanding resistive switching phenomena and analog memory and computation.