Integrating negative capacitance (NC) into the field-effect transistors promises to break fundamental limits of power dissipation known as Boltzmann tyranny. However, realization of the stable static negative capacitance in the nontransient regime without hysteresis remains a daunting task. Here we show that the failure to implement the NC stems from the lack of understanding that its origin is fundamentally related with the inevitable emergence of the domain state. We put forth an ingenious design for the ferroelectric domain-based field-effect transistor with the stable reversible static negative capacitance. Using dielectric coating of the ferroelectric capacitor enables the tunability of the negative capacitance improving tremendously the performance of the field-effect transistors.

Discovery of topological polarization textures has put ferroelectrics at the frontier of topological matter science. Highsymmetry ferroelectric oxide materials allowing for freedom of the polarization vector rotation offer a fertile ground for emergent topological polar formations, like vortices, skyrmions, merons, and Hopfions. It has been commonly accepted that uniaxial ferroelectrics do not belong in the topological universe because strong anisotropy imposes insurmountable energy barriers for topological excitations. Here we show that uniaxial ferroelectrics provide unique opportunity for the formation of topological polarization networks comprising branching intertwined domains with opposite counterflowing polarization. We report that they host the topological state of matter: a crisscrossing structure of topologically protected colliding head-to-head and tail-to-tail polarization domains, which for decades has been considered impossible from the electrostatic viewpoint. The domain wall interfacing the counterflowing domains is a multiconnected surface, propagating through the whole volume of the ferroelectric.