Absence of nesting in the charge-density-wave system $1{\text{T-VS}}_2$ as seen by photoelectron spectroscopy

We report on the electronic structure and Fermi surfaces of the transition-metal dichalcogenide $1{\text{T-VS}}_2$ in the low-temperature charge-density-wave (CDW) ordered phase. Using soft x-ray angle-resolved photoemission spectroscopy (ARPES), we investigate the in-plane and out-of-plane vanadium- and sulfur-derived band dispersions and identify $k_z$ dispersions in this layered system. Core-level photoemission and x-ray absorption spectroscopy show that vanadium electrons are in the $d^1$ configuration while $2p\text{−}3d$ resonant ARPES shows only $3d$-derived dispersive bands near the Fermi level. Comparison of energy- and angle-dependent data with band-structure calculations reveals renormalization of the $3d$ bands, but no lower Hubbard band, a signature of the rather weak electron-electron correlations in ${\text{VS}}_2$. High-resolution temperature-dependent low-energy ARPES measurements show the opening of an energy gap at the Fermi level that is attributed to the condensation of the CDW phase. The results indicate a CDW transition in the absence of nesting for $1{\text{T-VS}}_2$

Figure 1

(Color online) Left: electron-diffraction pattern obtained in a TEM of a ${\text{VS}}_2$ single crystal with the in-plane reciprocal space unit cell in the normal (black dashed lozenge) and CDW [yellow continuous small lozenge shifted on the (110) spot for clarity] phases. Right: schematic view of the reciprocal unit cells indicating that the experimental positions of the CDW-induced diffraction spots deviate from the commensurate superlattice case: the CDW vector is indicated by a fat red (or gray) arrow.

Figure 2

Magnetic susceptibility (dashed line) and electrical resistivity (continuous line) of the ${\text{VS}}_2$ single crystal. The CDW transition is signaled by the jump in the magnetic susceptibility and the electrical resistivity at 305 K (marked by the vertical line).

Figure 3

(a) XAS of ${\text{VS}}_2$ single crystal across the $L_3$ and $L_2$ absorption edges and (b) angle-integrated photoemission spectrum of the vanadium $2p$ core levels. The ARPES data presented in the next figure have been obtained fixing the photon energy to the value for which the XAS spectrum is maximum $\left(h\nu =516.1\text{eV}\right)$.

Figure 4

(Color online) (a) RPES data taken with $h\nu =516.1\text{eV}$ at the maximum of the vanadium $L_3$ absorption edge (as seen in Fig. 3); (b) Non-RPES data taken with $h\nu =510\text{eV}$ before the $L_3$ edge. The pink dashed and yellow continuous vertical lines in panels (a) and (b) mark the Brillouin-zone center and edge. (c) shows the reciprocal space in the repeated zone scheme together with the $k$ points probed as a function of the kinetic energy and wave vector: $h\nu =510\text{eV}$ black line, $h\nu =516.1\text{eV}$ red large dashed-dotted line, $h\nu =545\text{eV}$ pink short dashed-dotted line, $h\nu =590\text{eV}$, green dashed-double-dotted line. (d) Line profiles taken from panels (a) and (b) at $k$ points ranging from $k_{\parallel }=0{\text{Å}}^{-1}$ (bottom most) to $k_{\parallel }=1.12{\text{Å}}^{-1}$ (topmost) at steps of $0.28{\text{Å}}^{-1}$. At the bottom right of (a) the color scale (same also for the Figs. 5, 7, 8) is indicated.

Figure 5

(Color online) Band dispersion measured (a) along [with a $0.06{\text{Å}}^{-1}$ $k_z$ offset, as shown in Fig. 4c] the $\Gamma \text{M}$ $\left(h\nu =545\text{eV}\right)$ and (b) AL $\left(h\nu =590\text{eV}\right)$ directions. The black lines are the results of self-consistent band-structure calculations. (c) shows the bands near the Fermi level along $\Gamma \text{M}$ (black continuous curves) and AL (red dashed curves): the former do not disperse while the latter do disperse and cross $E_F$. The approximate band position is indicated by black and red arrows for the two directions and $k_F=-0.6{\text{Å}}^{-1}$ is indicated by a thicker arrow.

Figure 6

(Color online) First derivative image, $\frac{dI\left(\vec{k},E\right)}{dE}$ of the data of Fig. 5 near the Fermi level plotted in false color ranging from blue (large negative) to red (large positive). The white lines separating the red/blue features indicate the binding energies of the vanadium bands as functions of the wave vector. The blue/red feature is not caused by the derivative of the Fermi-Dirac step normally arising in the energy derivative of the photoemission data. As it is easy to see, the blue/red feature is at least 0.3 eV away from the Fermi level. Thus it is genuinely derived from band dispersion of the vandium $3d$ states.

Figure 7

(Color online) Unsymmetrized Fermi-surface mapping of ${\text{VS}}_2$ measured with $h\nu =545\text{eV}$ ($k_z$ indicated in Fig. 4) and right circular polarization (integrating over a 160 meV energy window about $E_F$), probing the $\Gamma \text{MK}$ plane of the Brillouin zone of the normal (black lines) or CDW (purple lines) phase. The green and pink arrows represent the experimental CDW vector at the $\Gamma$ point or translated to the normal-state Brillouin-zone edge.

Figure 8

(Color online) Angle-resolved photoemission maps taken with [(a) and (c)] helium lamp and [(b) and (d)] a laser source, for temperatures below and above the CDW transition temperature $\left(T_{\text{CDW}}=305\text{K}\right)$. In panels (e) and (f), a comparison of the EDCs extracted from the respective ARPES maps at the $\Gamma$ point are plotted to show the temperature-dependent spectral changes across the phase transition.