Combining intrinsic and sliding-induced polarizations for multistates in two-dimensional ferroelectrics

Going beyond the bistability paradigm of the charge polarization in ferroelectrics is highly desired for ferroelectric (FE) memory devices toward ultrahigh-density information storage. Here, we propose to build multistates by combining the intrinsic and sliding-induced polarizations. The physics is that there is at least one order of magnitude difference in the energy barriers between these two types of polarizations, which leads to a significant difference in the electric fields for reversing the polarization. This difference, along with the symmetry breaking, allows for a unique flipping mechanism involving layer-by-layer sliding followed by layer-by-layer flipping during the transformation of the multistates. As a result, six and ten switchable states can be achieved for the $1{T}^{\ensuremath{''}}$ bilayers and trilayers, respectively. We further illustrate the concept in $H$-stacking bilayers and trilayers of $1{T}^{\ensuremath{''}}$ transition-metal dichalcogenides by first-principles calculations. Our study provides a route to design polarization multistates for developing next-generation memory devices.