Single layer TlX (X = Cl/Br/I) with a ferroelectric-valley coupling potential for an electrically tunable polarizer

Ferrovalley materials are generally hexagonal lattice systems with a ferromagnetism-valley coupling, in which the intrinsic ferromagnetism can induce valley polarization. However, as of now the number of ferrovalleys found is still limited. In this article, TlX (X = Cl/Br/I) single-layers (SLs) are proposed with a tetragonal lattice structure as well as ferroelectricity-valley coupling. Furthermore, they possess good mechanical and dynamic stability, and are expected to be synthesized in experiments. When applying an in-plane electric field or uniaxial strain, the SL-TlX (X = Cl/Br/I) show a robust valley polarization. Because the direction of polarization of SL-TlX (X = Cl/Br/I) can be controlled with a rapid reversal of the electric field direction, SL-TlX (X = Cl/Br/I) are potential valleytronic materials with an electrically controllable valley polarization. The SL-TlX (X = Cl/Br/I) have linear optical selection rules, different from those of traditional hexagonal lattice systems, giving them potential for manufacturing electrically controllable optical filters.