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It is well known that one needs an external source of energy to provide voltage amplification. Because of this, conventional circuit elements such as resistors, inductors or capacitors cannot provide amplification all by themselves. Here, we demonstrate that a ferroelectric can cause a differential amplification without needing such an external energy source. As the ferroelectric switches from one polarization state to the other, a transfer of energy takes place from the ferroelectric to the dielectric, determined by the ratio of their capacitances, which, in turn, leads to the differential amplification. {This amplification is very different in nature from conventional inductor-capacitor based circuits where an oscillatory amplification can be observed. The demonstration of differential voltage amplification from completely passive capacitor elements only, has fundamental ramifications for next generation electronics.

We demonstrate an electrically induced, non-volatile, metal-insulator phase transition in a MoS$_2$ transistor. A single crystalline, epitaxially grown, PbZr$_{0.2}$Ti$_{0.8}$O$_3$ (PZT) was placed in the gate of a field effect transistor made of thin film MoS$_2$. When a gate voltage is applied to this ferroelectric gated transistor, a clear transition from insulator to metal and vice versa is observed. Importantly, when the gate voltage is turned off, the remnant polarization in the ferroelectric can keep the MoS$_2$ in its original phase, thereby providing a non-volatile state. Thus a metallic or insulating phase can be written, erased or retained simply by applying a gate voltage to the transistor.