Semimetal-to-semiconductor transition and charge-density-wave suppression in $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ single crystals

The transition-metal dichalcogenide $1T-{\mathrm{TiSe}}_2$ is a quasi-two-dimensional layered material with a phase transition towards a commensurate charge-density wave (CDW) at a critical temperature $T_c\approx 200\mathrm{K}$. The relationship between the origin of the CDW instability and the semimetallic or semiconducting character of the normal state, i.e., with the nonreconstructed Fermi-surface topology, remains elusive. By combining angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and density functional theory (DFT) calculations, we investigate $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ single crystals. Using STM, we first show that the long-range phase-coherent CDW state is stable against S substitutions with concentrations, at least, up to $x=0.34$. The ARPES measurements then reveal a slow but continuous decrease in the overlap between the electron and the hole ($e-h$) bands of the semimetallic normal state well reproduced by DFT and related to slight reductions of both the CDW order parameter and $T_c$. Our DFT calculations further predict a semimetal-to-semiconductor transition of the normal state at a higher critical S concentration of $x_c=0.9\pm 0.1$ that coincides with a suppressed CDW state in TiSeS as measured with STM. Finally, we rationalize the $x$ dependence of the $e-h$ band overlap in terms of isovalent substitution-induced competing chemical pressure and charge localization effects. Our study highlights the key role of the $e-h$ band overlap for the CDW instability.

Figure 1

Constant current ($I=0.15\mathrm{nA}$) STM images of $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ recorded at $T=4.5\mathrm{K}(15\times 15{\mathrm{nm}}^2)$. Applied bias voltage is $V_{\mathrm{bias}}=+0.6\mathrm{V}$ for (a) and (b). The insets show a line profile from image (a) and the normalized radial distribution function $g\left(r\right)$ of sulfur atoms from image (b). (c) and (d) Same surface regions as (a) and (b) with $V_{\mathrm{bias}}=+0.15\mathrm{V}$ in order to highlight the $2\times 2$ charge-density modulation. (e) and (f) Comparison of DFT-simulated and experimental $5\times 3-{\mathrm{nm}}^2$ STM images with sulfur substitutions for $V_{\mathrm{bias}}=+0.6\mathrm{V}$ (e) and $V_{\mathrm{bias}}=+0.1\mathrm{V}$ (DFT) and +0.15 V (STM) (f). The arrows on (e) and (f) show the location of one S substitution.

Figure 2

(a) $1T-{\mathrm{TiSe}}_2$ bulk and surface Brillouin zones. (b) DFT electronic band structure along the $\mathrm{\Gamma }-A-L$ path in the normal phase. (c) and (d) RT momentum distribution curve- (MDC-) normalized ARPES spectra of pristine $1T-{\mathrm{TiSe}}_2$ at the $\overline{\mathrm{\Gamma }}$ and $\overline{M}$ points of the surface BZ, respectively. (e) ARPES spectra of $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ crystals for $x=0,0.14$, and 0.34 (from left to right) displaying the valence band at $\overline{\mathrm{\Gamma }}$. (f) RT ARPES spectra of the conduction band recorded at $\overline{M}$ as a function of $x$ (from left to right). (g) $A-L$ gap and $\mathrm{\Gamma }-L$ overlap values obtained from DFT simulations and ARPES measurements at room temperature as a function of the sulfur concentration $x$. The $\mathrm{\Gamma }-L$ experimental values (red markers) are obtained by shifting the experimental $A-L$ values (in gray) by the energy difference in DFT between the top of the hole pockets at $\mathrm{\Gamma }$ and $A$ as illustrated by the black arrow. Negative and positive values, respectively, refer to $e-h$ band overlap and band gap. (h) Top view of the $1T-{\mathrm{TiSe}}_2$ structure and lattice deformation associated with the CDW.

Figure 3

(a)–(c) ARPES spectra of $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ for $x=0,0.14$, and 0.34 recorded at low temperatures ($T=46\pm 5\mathrm{K}$) and displaying the valence band at $\overline{\mathrm{\Gamma }}$. (d)–(f) Low-temperature ARPES spectra measured at $\overline{M}$ where the backfolded band is well visible. The two lines on each spectrum (a)–(f) indicate the determined valence- and conduction-band extrema at room (upper lines) and low (lower lines) temperatures. (g)–(i) Evolution of the conduction-band minimum and the backfolded weight maximum as a function of the temperature for the three crystals. (j)–(l) energy distribution curves (EDCs) taken on spectra at $\overline{M}$ as a function of temperature for $x=0,0.14$, and 0.34. The markers indicate the position of the backfolded spectral weight maximum, and the green EDCs correspond to the maximum temperature at which it can still be identified [the corresponding extracted positions on (g)–(i) are indicated by the green arrows].

Figure 4

(a)–(c) $T$ dependence of the CDW order parameter $\mathrm{\Delta }$ deduced from ARPES for $x=0,0.14$, and 0.34, respectively. For each sample, $\mathrm{\Delta }\left(T\right)$ is fitted with a BCS-like power law given by $\mathrm{\Delta }\left(T\right)\propto \tanh \left(A\sqrt{T_c/T-1}\right)+\mathrm{\Delta }\left(T_c\right)$, where $A=0.9$ is a proportional constant. (d) $x$ dependence of the order parameter at $T=0\mathrm{K},\mathrm{\Delta }\left(0\right)$. The black dashed line is a mean-field-like fit of $\mathrm{\Delta }$ vs $x$ given by $\mathrm{\Delta }/{\mathrm{\Delta }}_{x=0}={(1-x/x_c)}^{1/2}$, based only on the three ${\mathrm{\Delta }}_{x=0}$ values extracted from (a)–(c). The shaded area displays the possible range of values obtained from the upper and lower fits. In (d), the blue dot is excluded from the fit and indicates that the $2\times 2$ charge modulation is not observed with STM measurements for $x\approx 1$.

Figure 5

(a) Constant current ($I=0.10\mathrm{nA}$) STM image of $1T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ with $x\approx 1$ recorded at $T=4.5\mathrm{K}$ with applied bias voltage $V_{\mathrm{bias}}=+0.05\mathrm{V}(11\times 11{\mathrm{nm}}^2)$. The inset shows line profiles of fast-Fourier-transform (FFT) spots taken on the FFT-amplitude plots (b)–(d) obtained from STM images of the $11T-{\mathrm{TiSe}}_{2-x}{\mathrm{S}}_x$ crystals in Figs. 1 and 1(d) for $x=0.14,0.34$, and in Fig. 5 for $x\approx 1$, respectively. The white circles show the extra spots originating from the CDW. For $x\approx 1$, the extra spots coming from the $2\times 2$ charge modulation are not present.

Figure 6

Energy difference between the electron band minimum at $L$ and the hole band maximum at $\mathrm{\Gamma }\left(E_g\right)$ as obtained by DFT for $x=0$, 0.125, 0.25, 0.375, and 0.5 and lattice parameters $a$ and $c$ fixed at their experimental values taken from [16] (green circles). $E_g<0$ and $E_g>0$, respectively, refer to semimetallic and semiconducting normal state. The $E_g$ values obtained by substituting S atoms in the DFT superstructure but keeping $a=3.54$ and $c=6.01\AA$ fixed are displayed by the orange triangles. Inversely, the $E_g$ values corresponding to $x=0$ but decreasing lattice parameters $a$ and $c$ are depicted by the blue triangles. The dashed lines are linear fits to the $E_g$ values that have been all shifted to match our ARPES-extracted values.