Revealing Charge Density Wave Formation in the ${\mathrm{LaTe}}_2$ System by Angle Resolved Photoemission Spectroscopy

We present the first direct study of charge density wave (CDW) formation in quasi-2D single layer ${\mathrm{LaTe}}_2$ using high-resolution angle resolved photoemission spectroscopy and low energy electron diffraction. CDW formation is driven by Fermi surface (FS) nesting, however, characterized by a surprisingly smaller gap ($\approx 50\mathrm{meV}$) than seen in the double layer $R{\mathrm{Te}}_2$ compounds, extending over the entire FS. This establishes ${\mathrm{LaTe}}_2$ as the first reported semiconducting 2D CDW system where the CDW phase is FS nesting driven. In addition, the layer dependence of this phase in the tellurides and the possible transition from a stripe to a checkerboard phase is discussed.

Figure 1

(a) Unsymmetrized FS map (integrated between $+50\mathrm{meV}$ above to $-100\mathrm{meV}$ below the chemical potential, $\mu$) at $T=180\mathrm{K}$. White represents maximum intensity and black zero intensity with beam polarization displayed in the inset. The non-CDW LDA band structure at $E_F$ [25] is shown as yellow lines. (b) MDCs through the inner diamond, along $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}M$ directions. (c) Raw MDCs spectra near $\mu$ for cuts parallel to the $\Gamma \mathrm{\text{−}}X$ direction (1–9) as shown in the inset of the same figure, where the first derivative of the FS is shown. Each curve is shifted in $k$ space by a constant.

Figure 2

(a) EDCs stack taken along the green line ($\Gamma \mathrm{\text{−}}M$) in the inset. (b) Symmetrized EDC stack at $k_F$ along one quarter of the outer band contour as indicated in the inset of (a), with $T=50\mathrm{K}$. (c) Unsymmetrized constant energy cut at 450 meV showing evidence of shadow bands indicated by black arrows, where black represents maximum intensity and white zero intensity. (d) MDC cut taken along the dashed line in panel c showing two peaks associated with the main band (MB) and the shadow band (SB). The inset illustrates how the shadow bands (gray line) arise by shifting the inner diamond by the nesting vector ${\mathbf{q}}_N$ (red arrow).

Figure 3

(a–f) First derivative with respect to $k_y$ of the unsymmetrized constant energy maps over energies 200 to 820 meV at $T=180\mathrm{K}$. (g),(h) Image plots taken along the high symmetry directions: $X\mathrm{\text{−}}\Gamma \mathrm{\text{−}}X$ and $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}M$, respectively. The lower panels show the LDA band structure. The suggested renormalization of the LaTe block bands with respect to their original energies (gray dashed lines) is shown by black arrows. (i) Cartoon illustrating the experimental FS structure of Fig. 1a (black curves) shifted by ${\mathbf{q}}_2$ (red arrow and blue dashed lines) indicating a lack of any obvious nesting by this wave vector for the data. This is compared to (j) where the band structure is shifted by ${\mathbf{q}}_1$ and shows the nestable regions examined in Fig. 1c.

Figure 4

(a) LEED measurements of sample surface using 95 eV electrons at 160 K. The $\mathbf{q}=0.6{\mathbf{a}}^{*}\mathrm{\text{−}}0.2{\mathbf{b}}^{*}$ superstructure is indicated by white arrows. (b) Unsymmetrized constant energy map integrated over 100–160 meV at 50 K. The anomalous bands are indicated by red arrows.