Emergence of Improper Electronic Ferroelectricity and Flat Band in Twisted Bilayer Tl₂S

Two-dimensional (2D) ferroelectrics possessing out-of-plane (OP) polarization are highly desirable for applications and fundamental physics. Here, by first-principles calculations, we reveal that large-angle interlayer twisting can efficiently stabilize an unexpected ordering of sizable electric dipoles, producing OP polarization out of the centrosymmetric ground-state structure of Tl₂S, in great contrast to the recently proposed interlayer-sliding ferroelectricity. The ferroelectricity originates from a nonlinear coupling between a polar order dominantly contributed by electrons and an unstable phonon mode associated with a commensurate k point (1/3, 1/3, 0) in the two constituent monolayers, therefore indicating an improper and electronic ferroelectric nature. More interestingly, a flat band and a van Hove singularity occur in its electronic structures just below the Fermi level in the large-angle twisted bilayer Tl₂S. The unusual coexistence of improper electronic ferroelectricity, a flat band, and a van Hove singularity in one 2D material offers exceptional opportunities for exploring novel physics and applications.