Photoemission and optical studies of $\mathrm{Zr}{\mathrm{Se}}_3$, $\mathrm{Hf}{\mathrm{Se}}_3$, and $\mathrm{Zr}{\mathrm{S}}_3$

Angle-resolved photoemission spectroscopy (ARPES) and optical measurements were performed on single crystal samples of $\mathrm{Zr}{\mathrm{Se}}_3$, $\mathrm{Hf}{\mathrm{Se}}_3$, and $\mathrm{Zr}{\mathrm{S}}_3$, which belong to the class of low-dimensional band insulators. By ARPES, we traced the dispersion of the ($\mathrm{S}3p$, $\mathrm{Se}4p$) $p$-derived valence states. In all cases, the topmost band exhibits energy splitting increasing from S to Se, which we attribute to the spin-orbit interaction, similar to recent observations in the related layered dichalcogenides. The combination of optical and photoemission results allows us to address the issue of the gap feature in the absorption spectra and to characterize the electronic and vibrational properties of $\mathrm{Zr}{\mathrm{Se}}_3$, $\mathrm{Hf}{\mathrm{Se}}_3$, and $\mathrm{Zr}{\mathrm{S}}_3$.

Figure 1

(Top) The three-dimensional $\mathrm{Zr}{\mathrm{Se}}_3$ crystal structure, where infinite parallel chains of $M{X}_6$ prisms run along the $b$ direction. The filled circles indicate the $M$ cations. (Bottom, left) LEED image of the (001) cleavage plane. The arrows indicate the surface reciprocal lattice vectors. (Bottom, right) The three-dimensional Brillouin zone.

Figure 2

Angle-integrated photoemission spectra of the valence bands of $\mathrm{Zr}{\mathrm{Se}}_3$, $\mathrm{Hf}{\mathrm{Se}}_3$, and $\mathrm{Zr}{\mathrm{S}}_3$ $(h\nu =21.2\mathrm{eV})$. The energy zero for each compound coincides with the estimated valence band maximum $E_V$.

Figure 3

ARPES spectra $(h\nu =21.2\mathrm{eV})$ of $\mathrm{Zr}{\mathrm{Se}}_3$ (left) and $\mathrm{Hf}{\mathrm{Se}}_3$ (right) measured along the chain direction. The energy zero coincides with the Fermi level. Each curve refers to a different polar emission angle, and the angular step is 1°. Values of the wave vector $k_y$ along the chains, evaluated at $E=E_F$, are indicated, with “0” corresponding to normal emission. Thick solid and dashed gray lines highlight the dispersion of two closely spaced subbands.

Figure 4

(a) ARPES intensity map of $\mathrm{Hf}{\mathrm{Se}}_3$, corresponding to the data in Fig. 3b. (b) ARPES spectra $(h\nu =21.2\mathrm{eV})$ of $\mathrm{Hf}{\mathrm{Se}}_3$ measured along the $a$ axis, perpendicular to the chain direction. (c) A two-dimensional constant energy slice near the center of the Brillouin zone at $E=-1.4\mathrm{eV}$ [dashed line in (a)].

Figure 5

(Color online) (Left) ARPES intensity map of $\mathrm{Zr}{\mathrm{S}}_3$ along the $\overline{\Gamma Y}$ chain direction $(h\nu =21.2\mathrm{eV})$. (Right) The dispersion of the top valence subbands in the chain direction, as determined from the ARPES data: $\mathrm{Hf}{\mathrm{Se}}_3$ (solid lines), $\mathrm{Zr}{\mathrm{Se}}_3$ (red dashed lines), and $\mathrm{Zr}{\mathrm{S}}_3$ (dotted line).

Figure 6

(Color online) (a) Optical reflectivity $R\left(\omega \right)$ at $300\mathrm{K}$ along both polarization directions for $\mathrm{Zr}{\mathrm{S}}_3$. The inset shows the FIR spectral range with the IR active phonon modes. [(b) and (c)] ${\sigma }_1\left(\omega \right)$ of $\mathrm{Zr}{\mathrm{S}}_3$ for light polarized parallel and perpendicular to the chains, respectively, with the total Lorentz fit and the corresponding components (see text). The insets in (b) and (c) are a blowup of the FIR spectral range.

Figure 7

(Color online) (a) Optical reflectivity $R\left(\omega \right)$ at $300\mathrm{K}$ along both polarization directions for $\mathrm{Zr}{\mathrm{Se}}_3$. The inset shows the FIR spectral range with the IR active phonon modes. [(b) and (c)] ${\sigma }_1\left(\omega \right)$ of $\mathrm{Zr}{\mathrm{Se}}_3$ for light polarized parallel and perpendicular to the chains, respectively, with the total Lorentz fit and the corresponding components (see text). The insets in (b) and (c) are a blowup of the FIR spectral range.

Figure 8

(Color online) ${\sigma }_1\left(\omega \right)$ at $300\mathrm{K}$ for $\mathrm{Zr}{\mathrm{Se}}_3$, $\mathrm{Hf}{\mathrm{Se}}_3$, and $\mathrm{Zr}{\mathrm{S}}_3$ for light polarized (a) along and (b) perpendicular to the chains, respectively. The arrows indicate ${\omega }_{\mathit{max}}$ (see text and Table ).

Figure 9

(Color online) Comparison of the optical energy scale ${\omega }_{\mathit{max}}$ for both polarizations and the quantities $(E_F-E_V)$ and $2(E_F-E_V)$ from ARPES (see text). The lines are guides for the eyes.