Local Real-Space View of the Achiral $1T\text{−}{\mathrm{TiSe}}_2$ $2\times 2\times 2$ Charge Density Wave

The transition metal dichalcogenide $1T\text{−}{\mathrm{TiSe}}_2$-two-dimensional layered material undergoing a commensurate $2\times 2\times 2$ charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below $\approx 200\mathrm{K}$. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows us to go beyond the usual spatial resolution of STM and to intimately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric achiral nature of the CDW in the $z$ direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds.

Figure 1

(a) Simulation of the CDW as observed in STM at $V_{\mathrm{bias}}=100\mathrm{mV}$ with indication of three minima and one maximum of the charge modulation composing the $2\times 2$ surface unit cell. The black and the dashed rhombi indicate the $1\times 1$ and $2\times 2$ unit cells, respectively. (b) Side view of two $1T\text{−}{\mathrm{TiSe}}_2$ layers separated by a van der Waals (vdW) gap. The out-of-plane $c_0$ lattice constant of the $1\times 1\times 1$ unit cell is also shown. (c) Schematic top view of the $2\times 2\times 2$ PLD corresponding to the two adjacent layers shown in (b). The arrows indicate the directions of displacement of the atoms after transition to the CDW state. The underlaying modulation shows the registry of the minima and maxima of the ${\mathrm{Se}}_{\mathrm{up}}$ layer with respect to the PLD. The two possible orientations of displacement are denominated right-handed and left-handed, respectively.

Figure 2

(a) $40\times 17{\mathrm{nm}}^2$ constant current STM image of the $700°\mathrm{C}$-grown $1T\text{−}{\mathrm{TiSe}}_2$ sample with 5% additional Ti in the growth tube. $V_{\mathrm{bias}}=150\mathrm{mV}$, $I=0.2\mathrm{nA}$. Native defects are labeled $A–D$ according to Ref. [27]. The new defect is labeled $E$. An inset showing the DFT-simulated STM image from Fig. 1 is added as an eye guide; note that the image has been rotated by 30° with respect to Fig. 1. (b),(c) Enlargements on one defect of type $D$ and $E$, respectively. Dotted triangles are added for highlighting the orientation of three Se atoms concerned with the electronic signatures of the defects.

Figure 3

(a) Side view of the DFT-calculated relaxed structure with an interstitial Ti atom. (b) DFT-simulated STM image at $V_{\mathrm{bias}}=150\mathrm{mV}$. White circles mark the CDW maxima and arrows show the direction of simulated PLD displacements according to Di Salvo et al. [17] of the ${\mathrm{Se}}_{\mathrm{up}}$ atoms concerned with the electronic perturbation of the defect. (c)–(e) Enlargements on three defects of type $E$ from Fig. 2 with three different orientations. White circles again mark the CDW maxima extended from the defect-free region and arrows show the direction of PLD displacements deduced from (b).

Figure 4

(a) $20\times 10{\mathrm{nm}}^2$ constant current STM image at $V_{\mathrm{bias}}=150\mathrm{mV}$ and $I=0.1\mathrm{nA}$ of two adjacent $1T\text{−}{\mathrm{TiSe}}_2$ layers. (Inset) Height difference of approximately 6 Å corresponding to the separation between two Se-Ti-Se sandwiches obtained along the profile represented by the blue dotted line. Two white rectangles indicate the presence of two defects induced by interstitial Ti, one on each layer. (b),(c) Enlargements on the defects of the bottom and top layer, respectively, with white circles indicating the position of the maxima of the CDW charge modulation and black arrows indicating the corresponding PLD-induced atomic displacements. (d),(e) $2.8\times 2.8{\mathrm{nm}}^2$ enlargements showing the CDW modulation in the bottom and top layer, respectively, with arrows indicating the orientations of the CDW $q$ vectors. (f),(g) FFT-amplitude plots obtained from (d) and (e) with blue circles highlighting the extra spots originating from the CDW charge modulation.