Strain-induced polar discontinuities in two-dimensional materials from combined first-principles and Schr\"odinger-Poisson simulations

The local application of mechanical stress in piezoelectric materials gives rise to boundaries across which the electric polarization changes. Polarization charges appear along such polar discontinuities and the ensuing electric fields drive a charge reconstruction with the accumulation of free carriers at the boundaries. This is particularly relevant for two-dimensional materials that can sustain very large strains and display record piezoelectric responses. Here we show by first-principles simulations the emergence of one-dimensional wires of free electrons and holes along strain interfaces, taking SnSe as a paradigmatic material. We complement this by developing a Schr\"odinger-Poisson approach specifically designed for two-dimensional materials that it is able to reproduce the ab-initio results and also to extend them to regimes of parameters and system sizes that would be unaffordable in first principles calculations. This model allows us to assess the degree of tunability for the free charge in the wires coming from strain values and profiles, and to obtain the critical size at which the interfaces start to be metallic.