Unique Gap Structure and Symmetry of the Charge Density Wave in Single-Layer ${\mathrm{VSe}}_2$

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer ${\mathrm{VSe}}_2$, which shows a ($\sqrt{7}\times \sqrt{3}$) CDW in contrast to the ($4\times 4$) CDW for the layers in bulk ${\mathrm{VSe}}_2$. Angle-resolved photoemission spectroscopy from the single layer shows a sizable ($\sqrt{7}\times \sqrt{3}$) CDW gap of $\sim 100\mathrm{meV}$ at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.

Figure 1

Film structure, electronic band structure, and STM images of single-layer ${\mathrm{VSe}}_2$. (a) Atomic structure of single-layer 1 T ${\mathrm{VSe}}_2$. (b) A RHEED pattern taken at room temperature after single-layer ${\mathrm{VSe}}_2$ film growth. (c) A STM topographic image taken from single-layer ${\mathrm{VSe}}_2$ at 77 K revealing ($\sqrt{7}\times \sqrt{3}$) CDW modulation, as indicated by the blue solid line unit cell. The experimental conditions are size $9.9\times 6.2\mathrm{nm}$, sample bias $-0.5\mathrm{V}$, and tunneling current 0.5 nA. (d) Fourier transform of the STM image in (c). The ($1\times 1$) zone and the ($\sqrt{7}\times \sqrt{3}$) reciprocal lattice vectors are indicated. (e) Brillouin zones of the ($1\times 1$) and ($\sqrt{7}\times \sqrt{3}$) structures are outlined in blue and red, respectively. ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$ are ($\sqrt{7}\times \sqrt{3}$) primitive reciprocal lattice vectors. (f) An ARPES map along $\overline{\mathrm{\Gamma }M}$ taken at 10 K. (g) Calculated band dispersion relations for the ($1\times 1$) structure without spin polarization.

Figure 2

Fermi surfaces of single-layer and bulk ${\mathrm{VSe}}_2$ in the CDW and normal phases. (a) Measured Fermi surface contours of single-layer ${\mathrm{VSe}}_2$ in the normal phase at 300 K obtained by integrating the ARPES intensity over $\pm 10\mathrm{meV}$ around the Fermi level. The blue hexagon indicates the first Brillouin zone; ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$ indicate the ($\sqrt{7}\times \sqrt{3}$) CDW wave vectors. (b) Fermi contours for the CDW phase at 10 K. Dark spots spanned by ${\mathbf{q}}_1$ are caused by nesting and CDW gap formation. [(c) and (d)] Fermi surface maps of bulk ${\mathrm{VSe}}_2$ in the normal phase at 300 K and the CDW phase at 10 K, respectively.

Figure 3

CDW gap opening in single-layer ${\mathrm{VSe}}_2$. (a) ARPES spectra along $\overline{MK}$ for single-layer ${\mathrm{VSe}}_2$ in the normal phase at 300 K (upper panel) and the CDW phase at 10 K (lower panel). (b) Corresponding ARPES maps symmetrized in energy about the Fermi level show a gap in the CDW phase. The nesting vector ${\mathit{q}}_1$ is shown as a red arrow. (c) Calculated band structure in the normal and CDW phases. The CDW gap is indicated. An enlarged plot is shown at the bottom to show details. (d) ARPES spectra along the $MK$ direction for bulk ${\mathrm{VSe}}_2$ at 10 K (top panel). The symmetrized map (bottom panel) shows no gap.

Figure 4

Temperature dependence of the CDW gap and the transition temperature. (a) Symmetrized EDCs at the gap location at selected temperatures between 10 and 300 K. The evolution of the line shape is consistent with a peak splitting into two peaks separated by the CDW gap, while simultaneously the peak width diminishes because of reduced broadening at lower temperatures. The energy gap is extracted by fitting each symmetrized EDC with a phenomenological self-energy formula [26]. (b) An example of the fit shown as a red curve for the EDC obtained at 10 K. (c) The extracted temperature dependence of the square of the CDW gap. The blue curve is a fit using a mean-field equation. Transition temperature $T_c$ is labeled.