Imaging Mobility of Charge Order Topology via Charge Density Wave Interferometery

Charge density waves (CDWs) are emergent correlated electron behavior that span crystals with strong electron-lattice coupling and are associated with exciting phenomena such as metal–insulator transitions and superconductivity. Often described as a superlattice crystal of electrons, CDWs can also accommodate defects such as dislocations and elastic deformations. CDW defects are of a particular interest as they are believed to dominate conductance [1] and mediate phase transitions of the charge lattice itself [2–4]. Topological defects in a CDW are even expected to locally host superconductivity [5]. Therefore, understanding the formation, destruction, and mechanics of CDW defects is paramount to harnessing the full potential of charge ordered materials.<br/><br/>TaS₂ is prototypical layered CDW system that hosts multiple CDW phases tuned by temperature, thickness and polytype [6–8]. Octahedrally coordinated 1T-TaS₂ at room temperature hosts a nearly-commensurate (NC-) CDW lacking long-range order, and a long-range ordered commensurate (C-) CDW below 200 K. While the nature of order in NC-CDW phase remains unclear, it is generally accepted that NC-CDW incorporates discommensurations (i.e., slips in the CDW phase) [3, 4]. Real space measurement of the nanoscale structure of the NC-CDW is complicated by out-of-plane incoherence of the CDW; features are washed out in atomic resolution measurements. Here we use CDW moiré engineering to magnify and image the structure of CDW dislocations in the NC-CDW phase of TaS₂.<br/><br/>We generate a CDW moiré by synthesizing an endotaxial polytype heterostructure [9] that stabilizes both NC- and C-CDW phase layers embedded in a metallic prismatic matrix. Here the long-range ordered C-CDW serves as a grating with which the NC-CDW interferes. The resulting moiré interference pattern resolves a topological defect present in the NC-CDW. This pattern effectively encodes and magnifies the phase information in the NC- and C-CDW phases, taking advantage of the fact that NC- and C-CDWs diffract electrons with only slightly different momentum. By collecting scanned nanobeam diffraction patterns (i.e., 4D scanning transmission electron microscopy (STEM)) with the convergence angle and camera length tuned such that both C and NC reflections are incident on a single pixel of an electron microscope pixel array detector (EMPAD), moiré interference patterns are speedily acquired in parallel at every point in reciprocal space that the superlattice peaks nearly coincide.<br/><br/>In summary, we image CDW defects by employing 4D-STEM on polytype heterostructures of TaS₂. The interference from C and NC-CDW forms a moiré pattern that encodes the phase disorder of the NC phase, allowing defects to be imaged despite the out of plane incoherence inherent to the system. This work suggests a new experimental framework that can shed light on difficult-to-study CDW mechanics.<br/> <br/>[1] AW Tsen et al., <i>Proc. Natl. Acad. Sci.</i> <b>112</b> (2015) p.15054.<br/>[2] WL McMillan, <i>Phys. Rev. B</i> <b>12</b> (1975) p. 1187.<br/>[3] WL McMillan, <i>Phys. Rev. B </i><b>14</b> (1976) p. 1496.<br/>[4] K Nakanish and H. Shiba, <i>J. Phys. Soc. Jpn.</i> <b>43</b> (1977) p.1839.<br/>[5] B Leridon et al., <i>New J. Phys.</i> <b>22</b> (2020) 073075.<br/>[6] JA Wilson, FJ Di Salvo, S Mahajan <i>Adv. Phys.</i> <b>24</b> (1975) p.117.<br/>[7] Y Yu et al., <i>Nat. Nanotech. </i><b>10</b> (2015) 270.<br/>[8] E Martino et al., <i>npj 2D Mater. App.</i> <b>4</b> (2020) 7.<br/>[9] SH. Sung et al., <i>Nat. Commun.</i> <b>13</b> (2022) p.413.