Relaxation effects in twisted bilayer molybdenum disulfide: structure, stability, and electronic properties
Florian M. Arnold, Alireza Ghasemifard, Agnieszka Kuc, Jens Kunstmann, Thomas Heine
Abstract
Abstract Manipulating the interlayer twist angle is a powerful tool to tailor the properties of layered two-dimensional crystals. The twist angle has a determinant impact on these systems’ atomistic structure and electronic properties. This includes the corrugation of individual layers, formation of stacking domains and other structural elements, and electronic structure changes due to the atomic reconstruction and superlattice effects. However, how these properties change with the twist angle, θ , is not yet well understood. Here, we monitor the change of twisted bilayer (tBL) MoS 2 characteristics as a function of θ . We identify distinct structural regimes, each with particular structural and electronic properties. We employ a hierarchical approach ranging from a reactive force field through the density-functional-based tight-binding approach and density-functional theory. To obtain a comprehensive overview, we analyzed a large number of tBLs with twist angles in the range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>0.2</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>…</mml:mo> <mml:msup> <mml:mn>59.6</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> . Some systems include up to half a million atoms, making structure optimization and electronic property calculation challenging. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>13</mml:mn> </mml:mrow> <mml:mo>°</mml:mo> </mml:msup> <mml:mo>≲</mml:mo> <mml:mi>θ</mml:mi> <mml:mo>≲</mml:mo> <mml:msup> <mml:mrow> <mml:mn>47</mml:mn> </mml:mrow> <mml:mo>°</mml:mo> </mml:msup> </mml:mrow> </mml:math> , the structure is well-described by a moiré regime composed of two rigidly twisted monolayers. At small twist angles ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>⩽</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mn>57</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo>⩽</mml:mo> <mml:mi>θ</mml:mi> </mml:math> ), a domain-soliton regime evolves, where the structure contains large triangular stacking domains, separated by a network of strain solitons and short-ranged high-energy nodes. The corrugation of the layers and the emerging superlattice of solitons and stacking domains affects the electronic structure. Emerging predominant characteristic features are Dirac cones at K and kagome bands. These features flatten for θ approaching 0 ∘ and 60 ∘ . Our results show at which range of θ the characteristic features of the reconstruction, namely extended stacking domains, the soliton network, and superlattice, emerge and give rise to exciting electronics. We expect our findings also to be relevant for other tBL systems.