skip to main content

This content will become publicly available on December 1, 2023

Title: Torsional periodic lattice distortions and diffraction of twisted 2D materials
Abstract Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 .
; ; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
1749774 2039380
Publication Date:
Journal Name:
Nature Communications
Sponsoring Org:
National Science Foundation
More Like this
  1. Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN; rotations between the two lattices, as is the case for twisted bilayer graphene; and strains between two identical layers in a bilayer. Moiré patterns are responsible for a number of new electronic phenomena observed in recent years in van der Waals heterostructures, including the observation of superlattice Dirac points for graphene on BN, collective electronic phases in twisted bilayers and twisted double bilayers, and trapping of excitons in the moiré potential. An open question is whether we can use moiré potentials to achieve strong trapping potentials for electrons. Here, we report a technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals materials. We use strain engineering to create on-demand soliton networks in transition metal dichalcogenides. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of this network occur in bound pairs with different interlayer stacking arrangements.more »One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Soliton networks thus provide a path to engineer deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.« less
  2. Abstract

    Recent discoveries of exotic physical phenomena, such as unconventional superconductivity in magic‐angle twisted bilayer graphene, dissipationless Dirac fermions in topological insulators, and quantum spin liquids, have triggered tremendous interest in quantum materials. The macroscopic revelation of quantum mechanical effects in quantum materials is associated with strong electron–electron correlations in the lattice, particularly where materials have reduced dimensionality. Owing to the strong correlations and confined geometry, altering atomic spacing and crystal symmetry via strain has emerged as an effective and versatile pathway for perturbing the subtle equilibrium of quantum states. This review highlights recent advances in strain‐tunable quantum phenomena and functionalities, with particular focus on low‐dimensional quantum materials. Experimental strategies for strain engineering are first discussed in terms of heterogeneity and elastic reconfigurability of strain distribution. The nontrivial quantum properties of several strain‐quantum coupled platforms, including 2D van der Waals materials and heterostructures, topological insulators, superconducting oxides, and metal halide perovskites, are next outlined, with current challenges and future opportunities in quantum straintronics followed. Overall, strain engineering of quantum phenomena and functionalities is a rich field for fundamental research of many‐body interactions and holds substantial promise for next‐generation electronics capable of ultrafast, dissipationless, and secure information processing and communications.

  3. We performed high-pressure x-ray diffraction (XRD), Raman, and transport measurements combined with first-principles calculations to investigate the behavior of tin diselenide (SnSe2) under compression. The obtained single-crystal XRD data indicate the formation of a (1/3,1/3,0)-type superlattice above 17 GPa. According to our density functional theory results, the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a momentum wave vector q=(1/3,1/3,0). In contrast, similar PLD transitions associated with charge density wave (CDW) orderings in transition metal dichalcogenides (TMDs) do not involve significant Fermi surface nesting. The discovered pressure-induced PLD is quite remarkable, as pressure usually suppresses CDW phases in related materials. Our findings, therefore, provide new playgrounds to study the intricate mechanisms governing the emergence of PLD in TMD-related materials.
  4. The tin-selenide and tin-sulfide classes of materials undergo multiple structural transitions under high pressure leading to periodic lattice distortions, superconductivity, and topologically non-trivial phases, yet a number of controversies exist regarding the structural transformations in these systems. We perform first-principles calculations within the framework of density functional theory and a careful comparison of our results with available experiments on SnSe 2 reveals that the apparent contradictions among high-pressure results can be attributed to differences in experimental conditions. We further demonstrate that under hydrostatic pressure a superstructure can be stabilized above 20 GPa in SnS 2 via a periodic lattice distortion as found recently in the case of SnSe 2 , and that this pressure-induced phase transition is due to the combined effect of Fermi surface nesting and electron–phonon coupling at a momentum wave vector q = (1/3, 1/3, 0). In addition, we investigate the contribution of nonadiabatic corrections on the calculated phonon frequencies, and show that the quantitative agreement between theory and experiment for the high-energy A 1g phonon mode is improved when these effects are taken into account. Finally, we examine the nature of the superconducting state recently observed in SnSe 2 under nonhydrostatic pressure and predict the emergencemore »of superconductivity with a comparable critical temperature in SnS 2 under similar experimental conditions. Interestingly, in the periodic lattice distorted phases, the critical temperature is found to be reduced by an order of magnitude due to the restructuring of the Fermi surface.« less
  5. Controlling the growth of complex relaxor ferroelectric thin films and understanding the relationship between biaxial strain–structural domain characteristics are desirable for designing materials with a high electromechanical response. For this purpose, epitaxial thin films free of extended defects and secondary phases are urgently needed. Here, we used optimized growth parameters and target compositions to obtain epitaxial (40–45 nm) 0.67Pb(Mg 1/3 Nb 2/3 )O 3 –0.33PbTiO 3 /(20 nm) SrRuO 3 (PMN–33PT/SRO) heterostructures using pulsed-laser deposition (PLD) on singly terminated SrTiO 3 (STO) and ReScO 3 (RSO) substrates with Re = Dy, Tb, Gd, Sm, and Nd. In situ reflection high-energy electron diffraction (RHEED) and high-resolution X-ray diffraction (HR-XRD) analysis confirmed high-quality and single-phase thin films with smooth 2D surfaces. High-resolution scanning transmission electron microscopy (HR-STEM) revealed sharp interfaces and homogeneous strain further confirming the epitaxial cube-on-cube growth mode of the PMN–33PT/SRO heterostructures. The combined XRD reciprocal space maps (RSMs) and piezoresponse force microscopy (PFM) analysis revealed that the domain structure of the PMN–33PT heterostructures is sensitive to the applied compressive strain. From the RSM patterns, an evolution from a butterfly-shaped diffraction pattern for mildly strained PMN–33PT layers, which is evidence of stabilization of relaxor domains, to disc-shaped diffraction patterns formore »high compressive strains with a highly distorted tetragonal structure, is observed. The PFM amplitude and phase of the PMN–33PT thin films confirmed the relaxor-like for a strain state below ∼1.13%, while for higher compressive strain (∼1.9%) the irregularly shaped and poled ferroelectric domains were observed. Interestingly, the PFM phase hysteresis loops of the PMN–33PT heterostructures grown on the SSO substrates (strain state of ∼0.8%) exhibited an enhanced coercive field which is about two times larger than that of the thin films grown on GSO and NSO substrates. The obtained results show that epitaxial strain engineering could serve as an effective approach for tailoring and enhancing the functional properties in relaxor ferroelectrics.« less