Piezoelectric networks and ferroelectric domains in twistronic superlattices in WS<sub>2</sub>/MoS<sub>2</sub> and WSe<sub>2</sub>/MoSe<sub>2</sub> bilayers
V V Enaldiev, F Ferreira, S J Magorrian, Vladimir I Fal’ko
Abstract
Abstract Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials, in particular, due to the formation of moiré superlattice structures. In twisted bilayers of transition metal dichalcogenides moiré superlattice effects are additionally enriched by the lack of inversion symmetry in each monolayer unit cell. Here, we use multiscale modelling to establish a rich variety of confinement conditions for electrons, holes and layer-indirect excitons in twistronic WX 2 /MoX 2 bilayers (X = S,Se). Such trapping of charge carriers and excitons is caused by ferroelectric (interlayer) polarisation and piezoelectric effects generated by the reconstruction of twistronic bilayers into preferential stacking domains separated by domain wall networks. For almost aligned bilayers with anti-parallel (AP) orientation of WX 2 and MoX 2 unit cells, we find that upon lattice relaxation piezoelectric potential modulation traps holes and electrons in the opposite corners—WMo and XX (tungsten over molybdenum versus overlaying chalcogens)—of hexagonal-shaped 2H (simultaneously WX and XMo) stacking domains, swapping their positions at a twist angle <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≳</mml:mo> </mml:math> 0.2 ∘ . This crossover happens at such small angles (set by a very small lattice mismatch between WX 2 and MoX 2 ) that would impose an alignment accuracy and homogeneity better than 0.1 ∘ for achieving reproducibility of electronic characteristics of such heterostructures. At the same time, for all angles, XX corners provide 30 meV deep traps for the interlayer excitons. In bilayers with parallel (P) orientation of WX 2 and MoX 2 unit cells, band edges for both electrons and holes appear in triangular domains, where WX 2 chalcogens set over MoX 2 molybdenums. We find that, due to a weak ferroelectric polarisation, these triangular domains act as 130 meV deep quantum boxes for interlayer excitons for twist angles <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>≲</mml:mo> <mml:msup> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>∘</mml:mo> </mml:mrow> </mml:msup> </mml:math> , shifting towards XX stacking sites of the domain wall network at larger twist angles.