Surface structure and stacking of the commensurate (13×13)R13.9∘ charge density wave phase of

Abstract

By quantitative low-energy electron diffraction (LEED) we investigate the extensively studied commensurate charge density wave (CDW) phase of trigonal tantalum disulphide (1T-TaS2), which develops at low temperatures with a (√ 13× √ 13)R13.9 • periodicity. A full-dynamical analysis of the energy dependence of diffraction spot intensities reveals the entire crystallographic surface structure, i.e. the detailed atomic positions within the outermost two trilayers consisting of 78 atoms as well as the CDW stacking. The analysis is based on an unusually large data set consisting of spectra for 128 inequivalent beams taken in the energy range 20-250 eV and an excellent fit quality expressed by a bestfit Pendry R-factor of R = 0.110. The LEED intensity analysis reveals that the well-accepted model of star-of-David-shaped clusters of Ta atoms for the bulk structure also holds for the outermost two TaS2 trilayers. Specifically, in both layers the clusters of Ta atoms contract laterally by up to 0.25Å and also slightly rotate within the superstructure cell, causing respective distortions as well as heavy bucklings (up to 0.23Å) in the adjacent sulphur layers. Most importantly, our analysis finds that the CDWs of the 1 st and 2 nd trilayer are vertically aligned, while there is a lateral shift of two units of the basic hexagonal lattice (6.71Å) between the 2 nd and 3 rd trilayer. The results may contribute to a better understanding of the intricate electronic structure of the reference compound 1T-TaS2 and guide the way to the analysis of complex structures in similar quantum materials.

Distinguishing a Mott Insulator from a Trivial Insulator with Atomic Adsorbates

“…The experiments seem to favor a bilayer stacking order, the layers within the bilayer stacked without a lateral translation [31][32][33][34][35] [a T A stacking, Fig. 1(a)] and each bilayer unit stacked with a translation of a half unit cell [32,34] [a T C stacking, Fig. 1(b)], where halffilled Ta 5d z 2 electrons within bilayers form a spin-singlet state to lead to a trivial bonding-antibonding energy gap against the Mott insulator model.…”

“…Very importantly, the above model ignores the interlayer hopping of electrons, which can crucially affect the bandwidth. The experiments seem to favor a bilayer stacking order, the layers within the bilayer stacked without a lateral translation [31][32][33][34][35] [a T A stacking, Fig. 1(a)] and each bilayer unit stacked with a translation of a half unit cell [32,34] [a T C stacking, Fig.…”

“…1(c) and 1(d)] and assign accurately the centers of DS clusters through the numerical processing of the STM images and compared them quantitatively between the neighboring layer. The top layer corresponds to the T C termination, which inevitably requests the bottom one as T A based on the alternative T A -T C stacking order at low temperature [32,34]. They both exhibit insulating tunneling spectra [the normalized differential tunneling conductance (dI/dV )] but with different band gaps of 250 and 400 meV as shown in Fig.…”

Doublon-like excitations and their phononic coupling in a Mott charge-density-wave system

“…The observation of two surfaces is relevant as follows: The status of 1T -TaS 2 as a Mott insulator was recently challenged [14,15] with the suggestion that staggered inter-layer stacking [16][17][18] could result in a simple band insulator through Peierls-like inter-layer dimerization. There is now mounting evidence from state-of-the-art X-ray diffraction [19], high-and low-energy electron diffraction [20,21] and STM experiments [22] that such an alternating stacking pattern is indeed realized in the lowtemperature phase, and the band insulating picture has attracted some support [23]. Nevertheless, we recognize that Peierls-like dimerization and an electron-correlation driven insulating state are not mutually exclusive [24], and behaviors consistent with a correlation-driven insulator continue to be reported [9,22,25].…”

Ultrafast Probing and Coherent Vibrational Control of a Surface Structural Phase Transition

“…Second, the complexity of dynamic structure factor calculations poses a significant challenge for the interpretation of results and thus ideally requires expertise in this field. In this regard, in a recent cooperation with Lutz Hammer and Tilman Kisslinger from the University of Erlangen-Nürnberg, such calculations have successfully been performed for the commensurate CDW phase of 1T -TaS 2 by a Master's student from our group, namely Gevin von Witte [319] (the associated experimental data shown in Fig. 7.4b was recorded together with Tilman Kisslinger over the course of this thesis).…”