We develop a theory for long wavelength phonons originating at dislocations separating domains in small-angle twisted homobilayers of 2D materials such as graphene and MX$_2$ transition metal dichalcogenides (M=Mo,W; X=S,Se). We find that both partial and perfect dislocations, forming due to lattice relaxation in the twisted bilayers with parallel and anti-parallel alignment of unit cells of the constituent layers, respectively, support several one-dimensional subbands of the {\it interdomain} phonons. We show that spectrum of the lowest gapless subband is characterized by imaginary frequencies, for wave-numbers below a critical value, dependent on the dislocation orientation, which indicates an instability for long enough straight partial and perfect dislocations. We argue that pinning potential and/or small deformations of the dislocations could stabilize the gapless phonon spectra. The other subbands are gapped, with subband bottoms lying below the frequency of interlayer shear mode in domains, which facilitates their detection with the help of optical and magnetotransport techniques.
Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such dislocations by analogy with the Burgers vector of standard bulk dislocations. Analytical solutions for the structure and energy of edge stacking dislocations in bilayer graphene are obtained depending on the magnitude of elongation and angles between the edge Burgers vector, direction of elongation and edge. The barrier for penetration of stacking dislocation…
We investigate the electronic structure of realistic partial dislocation networks in bilayer graphene that feature annihilating, wandering, and intersecting partial lines. We find charge accumulation states at partials that are sensitive to Fermi energy and partial Burgers vector but not to the screw versus edge character of the partial. These states are shown to be current carrying, with the current density executing a spiral motion along the dislocation line with a strong interlayer component to the current. Close to the Dirac point localization on partials switches to localization on inters…
Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed dependin…
We apply a multiscale modeling approach to study lattice reconstruction in marginally twisted bilayers of transition metal dichalcogenides (TMD). For this, we develop DFT-parametrized interpolation formulae for interlayer adhesion energies of MoSe$_2$, WSe$_2$, MoS$_2$, and WS$_2$, combine those with elasticity theory, and analyze the bilayer lattice relaxation into mesoscale domain structures. Paying particular attention to the inversion asymmetry of TMD monolayers, we show that 3R and 2H stacking domains, separated by a network of dislocations develop for twist angles $θ^{\circ}<θ^{\circ}_P\…
Model description of patterns of atomic displacements in twisted bilayer systems has been proposed. The model is based on the consideration of several dislocation ensembles, employing a language that is widely used for grain boundaries and film/substrate systems. We show that three ensembles of parallel screw dislocations are sufficient both to describe the rotation of the layers as a whole, and for the vortex-like displacements resulting from elastic relaxation. The results give a clear explanation of the observed features of the structural state such as vortices, accompanied by alternating s…
Moiré structures in small-angle-twisted bilayers of two-dimensional semiconductors with a broken-symmetry interface form arrays of ferroelectric domains with periodically alternating out-of-plane polarization. Here, we propose a network theory for the tunability of such FE domain structure by applying an electric field perpendicular to the 2D crystal. Using multiscale analysis, we derive a fully parametrized string-theory-like description of the domain wall network and show that it undergoes a qualitative change, after the arcs of partial dislocation like domain walls merge (near the network n…
Quantifying superlubricity of bilayer graphene from the mobility of interface dislocations
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Material Research Laboratory, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校材料研究实验室）
We show that partial dislocations, defects that naturally arise in bilayer graphene, host an analogue of the mass inversion Volkov-Pankratov (VP) states, the spectrum of excited states at a topologically non-trivial interface. In contrast to the dislocation states arising from the change in valley Chern index, such states (i) exist both with and without an interlayer bias, i.e. for metallic as well as insulating bulk and (ii) have distinct electron and hole bound states, whose number is proportional to the dislocation width. Recently discovered at heterojunctions of 3d topological insulators, …
Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every angle is energetically favorable. Recent experiments on rotation-tunable electronics reveal the existence of a discrete set of angles at which the rotation-tunable electronics assume the most stable configurations. Nevertheless, a quantitative map for locating these intrinsically preferred twist angles in twisted bilayer system has not been available, posing challenges for the on-demand design of twisted electronics that are intrinsically stable at desired twist angles. Here …
Semiconducting ferroelectric materials with low energy polarisation switching offer a platform for next-generation electronics such as ferroelectric field-effect transistors. Ferroelectric domains at symmetry-broken interfaces of transition metal dichalcogenide films provide an opportunity to combine the potential of semiconducting ferroelectrics with the design flexibility of two-dimensional material devices. Here, local control of ferroelectric domains in a marginally twisted WS2 bilayer is demonstrated with a scanning tunneling microscope at room temperature, and their observed reversible e…
Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moiré superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such lo…
Van der Waals heterostructures form a massive interdisciplinary research field, fueled by the rich material science opportunities presented by layer assembly of artificial solids with controlled composition, order and relative rotation of adjacent atomic planes. Here we use atomic resolution transmission electron microscopy and multiscale modeling to show that the lattice of MoS$_2$ and WS$_2$ bilayers twisted to a small angle, $θ<3^{\circ}$, reconstructs into energetically favorable stacking domains separated by a network of stacking faults. For crystal alignments close to 3R stacking, a tess…
We provide a method for the generation of effective continuum Hamiltonians that goes beyond the well known k.p method in being equally effective in both high, and low (or no) symmetry situations. Our approach is based on a surprising exact map of the two-centre tight-binding method onto a compact continuum Hamiltonian, with a precise condition given for the hermiticity of the latter object. We apply this method to a broad range of low dimensional systems of both high and low symmetry: graphene, graphdiyne, γ-graphyne, 6,6,12-graphyne, twist bilayer graphene, and partial dislocation networks in…
In twisted bilayer graphene (TBG) a moiré pattern forms that introduces a new length scale to the material. At the 'magic' twist angle of 1.1°, this causes a flat band to form, yielding emergent properties such as correlated insulator behavior and superconductivity [1-4]. In general, the moiré structure in TBG varies spatially, influencing the local electronic properties [5-9] and hence the outcome of macroscopic charge transport experiments. In particular, to understand the wide variety observed in the phase diagrams and critical temperatures, a more detailed understanding of the local moiré …
The two-chain Frenkel-Kontorova model is applied for an analytical description of the energy and structure of the network of domain walls in bilayer graphene. Using this approach, the commensurate-incommensurate phase transition upon biaxial stretching of one of the graphene layers is considered. We demonstrate that formation of the equilateral triangular network of domain walls becomes energetically favourable above the critical relative biaxial elongation of the bottom layer of $3.0\cdot 10^{-3}$. It is shown that the optimal period of the triangular network of domain walls is inversely prop…
