Electronic structure of commensurate, nearly commensurate, and incommensurate phases of $1T-\mathrm{Ta}{\mathrm{S}}_2$ by angle-resolved photoelectron spectroscopy, scanning tunneling spectroscopy, and density functional theory

The electronic structure of $1T-\mathrm{Ta}{\mathrm{S}}_2$ showing a metal-insulator transition and a sequence of different charge density wave (CDW) transformations was discussed in the frame of variable temperature angle-resolved photoelectron spectroscopy (ARPES), scanning tunneling spectroscopy (STS), and density functional theory (DFT) calculations. For the commensurate charge density wave phase (CCDW) the Mott gap was estimated to be 0.4 eV and energy gaps ${\mathrm{\Delta }}_{\text{CCDW},1},{\mathrm{\Delta }}_{\text{CCDW},2},{\mathrm{\Delta }}_{B3-\mathit{HHB}},{\mathrm{\Delta }}_{B4-B3}$ were observed. For the nearly commensurate charge density wave phase (NCCDW), the reminiscent of higher and lower Hubbard bands and a very pronounced electronic state associated with the parabolic band at the $\overline{\mathrm{\Gamma }}$ point in the Brillouin zone were identified. The incommensurate charge density wave phase (ICCDW) showed a high value of local density of states at the Fermi level and a very pronounced edge of the metallic surface state located in the range of 0.15–0.20 eV above the Fermi level. The obtained STS and ARPES results were consistent with our theoretical calculations performed within DFT formalism including spin-orbit coupling.

Figure 1

LEED patterns, raw STM topographies, FFT power spectra of the raw STM topographies, selected frequencies for the calculation of the FFT filtered topographies, and Fourier filtered STM topographies for the UHV cleaved $1T-\mathrm{Ta}{\mathrm{S}}_2$ sample: (a)–(e) the CCDW phase at 110 K; (f)–(j) the NCCDW phase at 293 K; (k)–(o) the ICCDW phase at 400 K.

Figure 2

(a)–(d) Raw STM topographies and FFT power spectra for the UHV cleaved $1T-\mathrm{Ta}{\mathrm{S}}_2$ sample at 293 K. (e) High-resolution FFT filtered STM topography for the $1T-\mathrm{Ta}{\mathrm{S}}_2$ sample at 293 K. (f)–(h) DFT maps of electron density of states calculated for different energies relative to the Fermi level for the CCDW phase. (i)–(l) Raw STM topographies and FFT power spectra for the UHV cleaved $1T-\mathrm{Ta}{\mathrm{S}}_2$ sample at 400 K.

Figure 3

ARPES measurements recorded at three different phases of $1T-\mathrm{Ta}{\mathrm{S}}_2$ measured along the $\overline{\mathrm{\Gamma }}-\overline{M}$ and $\overline{\mathrm{\Gamma }}-\overline{K}$ directions [see Fig. 4 for indication of the direction]. (a), (d) The CCDW phase at 130 K; (b), (e) NCCDW at 293 K; (c), (f) ICCDW at 400 K. The gaps denotation is taken from the paper given by Sohrt et al. [15].

Figure 4

ARPES measurements recorded at three different phases of $1T-\mathrm{Ta}{\mathrm{S}}_2$ measured along the $\overline{K}-\overline{\mathrm{\Gamma }}-\overline{M}$ direction. (a) The CCDW phase at 130 K; (b) NCCDW at 293 K; (c) ICCDW at 400 K. (d), (e) Band structure calculated for bulk $1T-\mathrm{Ta}{\mathrm{S}}_2$ with PLD representative for the presence of the CCDW phase. (f)–(h) Surface and bulk Brillouin zones of $1T-\mathrm{Ta}{\mathrm{S}}_2$ with marked high-symmetry points. (i,j) Band structure calculated for bulk $1T-\mathrm{Ta}{\mathrm{S}}_2$ without PLD representative for the presence of the ICCDW phase.

Figure 5

ARPES measurements in the form of $E(k_x,k_y)$ maps at different temperatures and energies grouped into three columns. Column (a) temperature 130 K; column (b) temperature 293 K; column (c) temperature 400 K. $k_x$ span along the $\overline{\mathrm{\Gamma }}-\overline{M}$ direction. Energy relative to the Fermi level is labeled at each map. Negative energies mean electronic states above the Fermi level.

Figure 6

Integrated energy distribution curves. (a) IEDCs for three different temperatures integrated in the wave-vector range: $-0.1{\AA }^{-1}$ up to $0.1{\AA }^{-1}$. (b) IEDCs for three different temperatures integrated in the wave-vector range: $-0.1{\AA }^{-1}$ up to $1.0{\AA }^{-1}$.

Figure 7

LDOS maps and corresponding $\mathit{dI}/\mathit{dV}$ profiles: (a), (b) at 130 K for the CCDW phase; (c), (d) at 293 K for the NCCDW phase; (e), (f) at 400 K for the ICCDW phase. On the LDOS map blue color corresponds to low value of LDOS, while red color corresponds to high value of LDOS.

Figure 8

Schematic model of DOS structure of the (a) CCDW, (b) NCCDW, and (c) ICCDW phases. Please note that the energy scales for CCDW, NCCDW, and ICCDW are not the same. Yellow color denotes occupied states.

Figure 9

(a), (b) $\mathit{dI}/\mathit{dV}$ curve and its normalized form ($\mathit{dI}/\mathit{dV}$)/($I/V$) for the NCCDW phase recorded at 1.5 V around the Fermi level. (c), (d) $\mathit{dI}/\mathit{dV}$ curve and its normalized form ($\mathit{dI}/\mathit{dV}$)/($I/V$) for the NCCDW phase recorded at 2 V around the Fermi level.

Figure 10

(a), (c) Normalized LDOS map and (b), (d) ($\mathit{dI}/\mathit{dV}$)/($I/V$) curves recorded at 400 K for the ICCDW phase. On the LDOS map blue color corresponds to the very low value of LDOS, while red color corresponds to the very high value of LDOS.

Figure 11

Total and partial density of states calculated for bulk $1T-\mathrm{Ta}{\mathrm{S}}_2$ without periodic lattice distortion representative for the presence of the ICCDW phase. The densities of states were calculated based on the band structure presented in Figs. 3 and 3. (a) Total density of states and partial density of states for electrons localized on Ta and S atoms. (b) Partial density of states for tantalum $s, p, d$ orbitals and sulfur $s, p$ orbitals. (c) Partial density of states in logarithmic scale for different total angular momentum.