Temperature-dependent photoemission on $1T{\text{-TiSe}}_2$: Interpretation within the exciton condensate phase model

The charge-density-wave phase transition of $1T{\text{-TiSe}}_2$ is studied by angle-resolved photoemission over a wide temperature range. An important chemical-potential shift which strongly evolves with temperature is evidenced. In the framework of the exciton condensate phase, the detailed temperature dependence of the associated order parameter is extracted. Having a mean-field-like behavior at low temperature, it exhibits a nonzero value above the transition, interpreted as the signature of strong excitonic fluctuations, reminiscent of the pseudogap phase of high-temperature superconductors. Integrated intensity around the Fermi level is found to display a trend similar to the measured resistivity and is discussed within the model.

Figure 1

(Color online) (a) In-plane $\left(\perp c\right)$ resistivity of $1T{\text{-TiSe}}_2$ as a function of temperature (Ref. 7). (b) Brillouin zone of $1T{\text{-TiSe}}_2$ with its high symmetry points. (c) Left: constant energy map near $E_F$ of $1T{\text{-TiSe}}_2$ in planes parallel to the $\Gamma \text{MK}$ plane with electron pockets at $\text{L}\left(\overline{\text{M}}\right)$ produced by the conduction band. In parenthesis the surface Brillouin-zone notation is indicated for high symmetry points. Right: the valence bands have their maxima at $\Gamma$ and the conduction band has its minimum at L.

Figure 2

(Color online) Photoemission intensity maps, as false color plots (dark colors represent strong intensity), measured along $\overline{\Gamma }\overline{\text{K}}$ (see text for an explanation of this notation) at three different temperatures corresponding, from left to right, to situations well below $T_c$, around $T_c$ and well above $T_c$, respectively.

Figure 3

(Color online) (a) Left: EDCs measured exactly at $\overline{\text{M}}$, as a function of temperature [for the dotted (blue) EDC, $T=200\text{K}$]. Right: the corresponding false color plot with the dashed line at $T=200\text{K}$. (b) Integrated intensity around $E_F$ (over $\pm 50\text{meV}$) for each measured photoemission intensity map, as a function of temperature. (c) Inverse integrated intensity.

Figure 4

(Color online) (a) Position of contributions A, B, and C as a function of temperature, obtained by fitting EDCs, and with their error bars. (b) Order parameter of the exciton condensate phase. The continuous (blue) line is a fit with a mean-fieldlike function. The dashed (blue) line is a similar fit, after subtraction of the chemical-potential shift (see text for more details). (c) Chemical-potential shift obtained from our data. The dotted-dashed line represents the extrapolation of a linear fit to the high-temperature part. (d) Calculated chemical-potential shift from previous work (Ref. 24) (see text).

Figure 5

Renormalized dispersions at L calculated by the spectral function derived for the exciton condensate phase for (a) the normal phase, $\Delta =0\text{meV}$, (b) a weak CDW phase, $\Delta =25\text{meV}$, and (c) a well-established CDW phase, $\Delta =100\text{meV}$. The spectral weight is rendered by the grayscale (the darker the color, the higher the spectral weight).

Figure 6

(Color online) (a) Near $E_F$ dispersions around L of $1T{\text{-TiSe}}_2$ calculated within the exciton condensate phase model for an order parameter $\Delta =100\text{meV}$. (b) Corresponding (calculated) photoemission intensity map (as a false color plot), where the spectral weight has been added to the dispersions. (c) Integrated intensity around $E_F$ (over $\pm 50\text{meV}$) for each calculated photoemission intensity map, as a function of temperature. (d) False color plot made of the collection of calculated EDCs at different temperatures and at L for the case of a nonzero chemical-potential shift and a nonzero order parameter.