Microscopic evidence for strong periodic lattice distortion in two-dimensional charge-density wave systems

In quasi-two-dimensional electron systems of layered transition metal dichalcogenides (TMDs) there is still controversy about the nature of the transitions to charge-density wave (CDW) phases, i.e., whether they are described by a Peierls-type mechanism or by a lattice-driven model. By performing scanning tunneling microscopy experiments on canonical TMD-CDW systems, we image the electronic modulation and the lattice distortion separately in $2\mathrm{H}\text{−}\mathrm{Ta}{\mathrm{S}}_2$, $\mathrm{Ta}{\mathrm{Se}}_2$, and $\mathrm{Nb}{\mathrm{Se}}_2$. Across the three materials, we found dominant lattice contributions instead of the electronic modulation expected from Peierls transitions, in contrast to the CDW states, which show the hallmark of contrast inversion between filled and empty states. Our results imply that periodic lattice distortion plays a vital role in the formation of CDW phases in TMDs and illustrate the importance of taking into account the more complicated lattice degrees of freedom when studying correlated electron systems.

Figure 1

(a) Atomically resolved topographic image of 2H-${\mathrm{TaS}}_2$ with CDW modulation ($3\times 3$ superstructure). This image was obtained at 60 K and with setup conditions of $-$100 mV and 200 pA. Inset: Zoom-in showing the atomic structure of the $3\times 3$ unit cell, with lighter (red) spheres indicating sulfur atoms. (b) Crystal structure of trigonal prismatic (2H) TMD. Lighter (red) spheres are chalcogen atoms; black spheres, metal atoms. The dotted horizontal line is where it cleaves. (c) Fourier transform of (a). Inner (blue) circles [outer (red) circles] indicate the primary peaks of CDW [atomic] modulation, and ${\mathbf{b}}_{\mathbf{1}}$ and ${\mathbf{b}}_{\mathbf{2}}$ are the atomic lattice reciprocal vectors.

Figure 2

Topographic images showing sym-metrization and antisymmetrization on 2H-${\mathrm{TaS}}_2$ at 52 K: (a) $-50$ mV and 100 pA; (b) +50 mV and 100 pA. These two images were individually corrected for drift and aligned with subatomic precision. (c, d) Symmetrized [$\mathrm{S}=(a+b)/2$] and antisymmetrized [$\mathrm{AS}=(a-b)/2$] images of (a) and (b). The contrast in (d) is much smaller compared to (c). (e) Line profiles in (a–d) indicated by colors.

Figure 3

Topographic images of ${\mathrm{NbSe}}_2$ and ${\mathrm{TaSe}}_2$ at 5 K. (a, b) ${\mathrm{NbSe}}_2$ with $-100$ mV and 100 pA (a) and with +100 mV and 100 pA (b). (e, f) ${\mathrm{TaSe}}_2$ with $-50$ mV and 40 pA (e) and with $+$50 mV and 30 pA (f). (c, g) Symmetrized and antisymmetrized images of (a, e); (d, h) symmetrized and antisymmetrized images of (b, f). The contrast of (c, g) is much larger than that of (d, h), as for ${\mathrm{TaS}}_2$.