Ferroelectric switchable valleytricity in 2D multiferroic semiconductors

Efficient control of the valley index is of great importance for both fundamental research and device applications, yet it remains a challenging problem. Here, through symmetry analysis and an effective k·p model, we propose a novel mechanism for coupling valley index with ferroelectricity in a two-dimensional (2D) multiferroic lattice. The physics behind this is that inequivalent potential arising from ferroelectricity can reverse and annihilate nonsymmetric trigons. Owing to the intimate connection between nonsymmetric trigons and valley physics, the valley index is locked to ferroelectric polarization. This enables the efficient electrical reversal of valley index for carriers and the electrical creation/annihilation of valley polarization. Moreover, based on first-principles calculations, we validate this mechanism in the 2D multiferroic semiconductor TiCr₂O₄, which favors the paraelectric state as a metastable state. Our work establishes a new paradigm for the design and optimization of valleytronic devices.