Manipulating topological transformations of polar structures through real-time observation of the dynamic polarization evolution

Topological structures based on controllable ferroelectric or ferromagnetic domain configurations offer the opportunity to develop microelectronic devices such as high-density memories. Despite the increasing experimental and theoretical insights into various domain structures (such as polar spirals, polar wave, polar vortex) over the past decade, manipulating the topological transformations of polar structures and comprehensively understanding its underlying mechanism remains lacking. By conducting an in-situ non-contact bias technique, here we systematically investigate the real-time topological transformations of polar structures in PbTiO3/SrTiO3 multilayers at an atomic level. The procedure of vortex pair splitting and the transformation from polar vortex to polar wave and out-of-plane polarization are observed step by step. Furthermore, the redistribution of charge in various topological structures has been demonstrated under an external bias. This provides new insights for the symbiosis of polar and charge and offers an opportunity for a new generation of microelectronic devices.

Visualization of Schrodinger Equations Polar Wave Functions for Non-Central Coulombic Rosen Morse Potential in ExcitationState nr = 2 and l = 1

Research has been conducted which shows the quantization visualization of hydrogen atom orbitals angular space in Rosen Morse potential system interference when the electrons are excited in the state of nr= 2 and l = 1 through the polar function analysis of the Schrödinger Potential of Non-Central Coloumbic Rosen Morse. The polar Schrödinger equation is solved using the Romanovski polynomial method to obtain the polar wave function. To show the accuracy of the analysis, the polar wave function spectrum i s visualized with Matlab-based computer programming.