Giant Exciton Mott Density in Anatase ${\mathrm{TiO}}_2$

Elucidating the carrier density at which strongly bound excitons dissociate into a plasma of uncorrelated electron-hole pairs is a central topic in the many-body physics of semiconductors. However, there is a lack of information on the high-density response of excitons absorbing in the near-to-mid ultraviolet, due to the absence of suitable experimental probes in this elusive spectral range. Here, we present a unique combination of many-body perturbation theory and state-of-the-art ultrafast broadband ultraviolet spectroscopy to unveil the interplay between the ultraviolet-absorbing two-dimensional excitons of anatase ${\mathrm{TiO}}_2$ and a sea of electron-hole pairs. We discover that the critical density for the exciton Mott transition in this material is the highest ever reported in semiconductors. These results deepen our knowledge of the exciton Mott transition and pave the route toward the investigation of the exciton phase diagram in a variety of wide-gap insulators.

Figure 1

(a) Schematic illustration of the electronic band structure of anatase ${\mathrm{TiO}}_2$, as obtained from $GW$ calculations. The direct gap around the $\mathrm{\Gamma }$ point is determined in experiments to be $\sim 3.98\mathrm{eV}$ [14]. The violet arrows indicate the single-particle states that contribute to building up the $a$-axis bound exciton transition. (b) Reflectivity spectrum of anatase ${\mathrm{TiO}}_2$ at RT with the light electric field polarized along the $a$ axis. Peak I is the 2D bound exciton, whereas peak II is a high-energy resonant exciton. The data, measured by spectroscopic ellipsometry, and their assignment are obtained from Ref. [14]. The pump photon energy of 4.10 eV used for the pump-probe experiment is indicated by the blue arrow and the probed region is highlighted as a grey shaded area. The inset shows the wave function of the bound 2D exciton around 3.79 eV. The isosurface representation shows the electronic configuration when the hole of the considered excitonic pair is localized close to one oxygen atom. The colored region represents the excitonic squared modulus wave function.

Figure 2

(a) Imaginary part of the $a$-axis dielectric function of anatase ${\mathrm{TiO}}_2$, calculated by solving the Bethe-Salpeter equation for pristine and $n$-doped ${\mathrm{TiO}}_2$. The optical response of the $n$-doped crystal with $n=1.4\times {10}^{19}{\mathrm{cm}}^{-3}$ (not shown) overlaps almost completely that of the pristine case, indicating that this doping level does not affect the exciton peak energy. Only when $n>$ $10\times {10}^{19}{\mathrm{cm}}^{-3}$, does the exciton blueshift. The vertical lines represent the quasiparticle gap energy at each doping level. The Mott transition occurs at $n_M\sim 35\times {10}^{19}{\mathrm{cm}}^{-3}$; i.e., it occurs when the quasiparticle gap matches the exciton peak energy. (b) Doping dependence of $E_B$, estimated from the energy difference between the quasiparticle gap energy and the exciton peak energy. An abrupt change is observed around $n>$ $10\times {10}^{19}{\mathrm{cm}}^{-3}$ and the bound states are lost at $n_M$.

Figure 3

(a) Color-coded map of $\mathrm{\Delta }R/R(\omega ,\mathrm{t})$ as a function of probe photon energy and time delay between pump and probe. (b) Spectral evolution of $R(\omega ,\mathrm{t})$, obtained by combining the steady-state $R(\omega )$ and the $\mathrm{\Delta }R/R(\omega ,\mathrm{t})$ data in the time window 700 fs–1 ns. The R of the unperturbed system is displayed as a dashed blue line. (c) Spectral evolution of $\alpha (\omega ,\mathrm{t})$, obtained as a result of the Lorentz fit in the time window 700 fs–1 ns. The $\alpha$ of the unperturbed system is displayed as a dashed blue line. (d)–(f) Temporal evolution of (c) the oscillator strength, (d) the linewidth, and (e) the peak energy of the bound exciton upon photoexcitation.