Electronic state modulation of the Star of David lattice by stacking of $\sqrt{13}\times \sqrt{13}$ domains in $1T-{\mathrm{TaSe}}_2$

In layered van der Waals materials, the stacking of layers plays a crucial role in their electronic states. To investigate the effect of stacking of layers on the electronic states, we utilized the stacking of two kinds of $\sqrt{13}\times \sqrt{13}$ domains, which are rotated $27.8{}^{\circ }$ relative to each other, in Nb-substituted $1T\text{−}\mathrm{Ta}{\mathrm{Se}}_2$. We found the appearance of a two-dimensional superstructure of the Star of David (SoD) lattice. The SoDs in the superstructure show three different electronic states due to the different stackings of the SoDs between the top surface and the layer below. This stacking of $\sqrt{13}\times \sqrt{13}$ domains provides insights into the effects of stacking on electronic structure and has the potential to produce unique electronic states.

Figure 1

(a) The crystal structure of $1T\text{−}\mathrm{M}{\mathrm{X}}_2$ (M, transition metal; X, chalcogen) in the normal state, drawn by vesta [2]. (b) Schematic picture of the “Star of David” (SoD) and two kinds of $\sqrt{13}\times \sqrt{13}$ domains. (c) The stacking pattern of two kinds of $\sqrt{13}\times \sqrt{13}$ domains. SoDs in the upper (lower) layer are illustrated with blue (gray) stars. The superstructure of the SoD lattice appears. The unit cell of the superstructure is indicated by black stars. See also the Supplemental Material. (d) The three types of SoD stacking. Each stacking is referred to as type 1, 2, or 3 and is shown in red, blue, or green, respectively, in (c). Each stacking vector is represented as d = c (type 1), d = c $\pm$ 2a (type 2), or d = c $\pm$ a (type 3), with a and c being the lattice unit vectors. The unit cell of the superstructure is formed with type 1 stars as the center, type 2 as the first-nearest neighbor, and type 3 as the second-nearest neighbor.

Figure 2

(a) STM image of Nb-substituted $1T\text{−}\mathrm{Ta}{\mathrm{Se}}_2$ on a $100\times 100{\mathrm{nm}}^2$ field of view. The set point of the STM image is ($-200$ mV, 100 pA). The triangle lattice seen in the figure is the SoD lattice. The inset is the magnified STM image around the domain wall with phase slip of the SoD lattice shown by the yellow square in Fig. 2. In the inset image, the domain wall is shown by the orange dashed line. The set point of the STM image in the inset is ($+600$ mV, 100 pA). (b) FFT image of (a). The FFT image shows two sets of sixfold FFT spots rotated about ${28}^{\circ }$ relative to each other (indicated by red and blue circles). (c) Inverse FFT images of each spot in (b), superimposed on the STM image shown in (a). The colors of the regions correspond to those of the circles in (b). The regions shown by the dashed lines represent the inverse FFT image of spots marked by the white circles in (b). (d) Three types of tunneling spectra observed at the locations marked as “A,” “B,” and “C” in (a). The set point of each tunneling spectrum is ($+600$ mV, 100 pA).

Figure 3

The periodic spatial modulation of the electronic states near the boundary between $\sqrt{13}\times \sqrt{13}$ domains. (a) Magnified STM image of the area inside the black dashed square in Fig. 2. The set point is ($+600$ mV, 100 pA). (b) Schematic illustration of the configuration of the three kinds of SoD (SoD#1, #2, and #3), superimposed on (a). The unit cell of the superstructure is formed with SoD#1 as the center, SoD#2 as the first-nearest neighbor, and SoD#3 as the second-nearest neighbor. The orange dashed lines show the boundaries of $\sqrt{13}\times \sqrt{13}$ domains. The set point is ($+600$ mV, 100 pA). (c)–(e) $dI/dV$ maps at 0 mV (c), $+100$ mV (d), and $+200$ mV (e) at the same field of view as (a). The set point is ($+600$ mV, 100 pA).

Figure 4

Three kinds of electronic states in SoDs with different stacking appeared in the unit cell of the superstructure. The set point of the tunneling spectra is ($+600$ mV, 100 pA).