Abstract
Ultrathin sheets of transition metal dichalcogenides (MX2) with charge density waves (CDWs) is increasingly gaining interest as a promising candidate for graphene-like devices. Although experimental data including stripe/quasi-stripe structure and hidden states have been reported, the ground state of ultrathin MX2 compounds and, in particular, the origin of anisotropic (stripe and quasi-stripe) CDW phases is a long-standing problem. Anisotropic CDW phases have been explained by Coulomb interaction between domain walls and inter-layer interaction. However, these models assume that anisotropic domain walls can exist in the first place. Here, we report that anisotropic CDW domain walls can appear naturally without assuming anisotropic interactions: We explain the origin of these phases by topological defect theory (line defects in a two-dimensional plane) and interference between harmonics of macroscopic CDW wave functions. We revisit the McMillan-Nakanishi-Shiba model for monolayer 1T-TaS2 and 2H-TaSe2 and show that CDWs with wave vectors that are separated by 120° (i.e. the three-fold rotation symmetry of the underlying lattice) contain a free-energy landscape with many local minima. Then, we remove this 120° constraint and show that free energy local minima corresponding to the stripe and quasi-stripe phases appear. Our results imply that Coulomb interaction between domain walls and inter-layer interaction may be secondary factors for the appearance of stripe and quasi-stripe CDW phases. Furthermore, this model explains our recent experimental result (appearance of the quasi-stripe structure in monolayer 1T-TaS2) and can predict new CDW phases, hence it may become the basis to study CDW further. We anticipate our results to be a starting point for further study in two-dimensional physics, such as explanation of “Hidden CDW states”, study the interplay between supersolid symmetry and lattice symmetry, and application to other van der Waals structures.
Highlights
Anisotropic structures such as stripe phases can be explained by anisotropic interaction between the constituent atoms, electrons, or liquid crystal polymers[1]
In this article we report that stripe and quasi-stripe charge density waves (CDWs) domain walls can appear without anisotropic interactions and explain the origin of these phases by topological defect theory and interference between harmonics of macroscopic CDW wave functions
These materials exhibit various CDW phases which are characterized by domain walls
Summary
Anisotropic structures such as stripe phases can be explained by anisotropic interaction between the constituent atoms, electrons, or liquid crystal polymers[1]. The appearance of stripe domain walls and quasi-stripe (triclinic) domain walls[8,11,12] has been explained by Coulomb interaction between domain walls[13] and three-dimensional stacking[14]. In this article we report that stripe and quasi-stripe CDW domain walls can appear without anisotropic interactions and explain the origin of these phases by topological defect theory (line defects in a two-dimensional plane) and interference between harmonics of macroscopic CDW wave functions. Our method is to use a Ginzburg-Landau model for a CDW with general wave vectors Q(i) (i = 1, 2, 3) satisfying the triple-Q condition Q(1) + Q(2) + Q(3) = 0 (see Methods for detail) This model was first introduced by McMillan[9,31,32] to explain the IC-C phase transition. It is noteworthy that the free energy only involves the terms compatible with the crystal symmetry and the only input from experimental data is the incommensurate wave vectors
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