Complex Strain Scapes in Reconstructed Transition-Metal Dichalcogenide Moiré Superlattices

Abstract

We investigate the intrinsic strain associated with the coupling of twisted MoS2/MoSe2 heterobilayers by combining experiments and molecular dynamics simulations. Our study reveals that small twist angles (between 0 and 2°) give rise to considerable atomic reconstructions, large moiré periodicities, and high levels of local strain (with an average value of ∼1%). Moreover, the formation of moiré superlattices is assisted by specific reconstructions of stacking domains. This process leads to a complex strain distribution characterized by a combined deformation state of uniaxial, biaxial, and shear components. Lattice reconstruction is hindered with larger twist angles (>10°) that produce moiré patterns of small periodicity and negligible strains. Polarization-dependent Raman experiments also evidence the presence of an intricate strain distribution in heterobilayers with near-0° twist angles through the splitting of the E2g 1 mode of the top (MoS2) layer due to atomic reconstruction. Detailed analyses of moiré patterns measured by AFM unveil varying degrees of anisotropy in the moiré superlattices due to the heterostrain induced during the stacking of monolayers.

Nonlinear Hall effects in two-dimensional moiré superlattices

“…The white hexagon indicates the moiré Brillouin zone [30] ; (d) the Berry curvature distribution after introducing a strain strength of 0.6% along zigzag direction [30] , the unbalanced distribution results in finite Berry curvature dipole; (e) the band energy E of magic angle twisted bilayer graphene calculated using an ab initio tight-binding method, the bands shown in blue are ultra-flat [36] ; (f) comparison between the bandwidth W (thick blue line) and the on-site Coulomb interaction energy U (thin coloured lines for different values of κ) for different twist angles θ [36] ; (g) a summary of tunable electronic properties in twisted transition metal dichalcogenides verified by different temperature dependences, blue showed Fermi liquid (T 2 ) behaviour, red showed strange metal (T-linear) behaviour, grey showed insulating behaviour [39] . [95] 、转角石墨烯 [96] 、转 角过渡金属硫族化合物 [97][98][99][100] 中都已被观察到. 在 这些材料中, 由于不同区域具有不同堆叠方式和不 同的堆叠能量, 在原子重构作用下, 堆叠能量低…”

“…察到原子重构现象 [97][98][99][100] . 原子重构会在超晶格中 产生复杂的应力场(图2(b)) [94,101] , 此外, 在样品制 备过程中也会引入一些微小应力, 这一应力足以打 破材料对称性.…”

Mesoscopic Stacking Reconfigurations in Stacked van der Waals Film

“…Several reports studied the Raman signatures in stacked-bilayer systems which are summarized in Table S1 (Supporting Information). [18][19][20][21][22][23] Twist-angle-dependent Raman studies have provided information on angle-dependent interlayer interactions, the superlattice effect of the moiré structures, and delicate changes in the strain field due to atomic rearrangements. This rich information from a single measurement tool opens the possibility of using Raman spectroscopy as a versatile characterization tool for stacked vdW materials.…”

Quantifying Strain in Moiré Superlattice

“…Raman spectroscopy is an effective technique for probing symmetries and strain in 2D materials, particularly through the 2-fold degenerate E 2g mode. ,, In the presence of a 2D strain tensor ε ij , the 2D secular equation for Raman spectra takes the form | lefttrue p ε x x + q ε y y − λ 2 r ε x y 2 r ε x y p ε y y + q ε x x − λ | = 0 where ( p , q , r ) are three components of the phonon deformation potential, λ = ω 2 – ω 0 2 ≈ 2ω 0 Δω, ω 0 is the frequency of the optical phonons in the absence of strain, and Δω is the frequency shift . Solving eq , we obtain two eigenvalues and the corresponding frequency shifts: normalΔ ω 1,2 = λ 1,2 2 ω 0 = 1 2 ω 0 [ p + q 2 false( ε x x + ε y y false) ± ( p − q 2 ) 2 ...…”

“…Raman spectroscopy is an effective technique for probing symmetries and strain in 2D materials, particularly through the 2-fold degenerate E 2g mode. 4,7,31 In the presence of a 2D strain tensor ε ij , the 2D secular equation for Raman spectra takes the form…”