In accordance with one component, a power field effect transistor is proposed, including a substrate, a channel, a gate electrode, and a gate insulator. The gate insulator is arranged at least partly between the gate electrode and the channel and includes a material having a hysteresis with respect to its polarization, such that a switching state of the transistor produced by a voltage applied to the gate electrode is maintained after the voltage has been switched off. Furthermore, a half-bridge circuit is proposed, including a high-side transistor in accordance with the construction according to the disclosure, and a low-side transistor, and also methods and circuits for driving.