Experimental Evidence for Bright-to-Dark Exciton Transition in Anatase TiO₂

Anatase TiO₂ is a well-known indirect bandgap transition metal oxide, featuring high photocatalytic activity and excellent photoelectric properties, together with chemical stability and wide bandgap [1]. Very recently, further interesting properties, so far unexplored, have emerged. In particular, strongly bound excitons across the direct bandgap of the material have been highlighted. Bright, momentum-direct excitonic states have been predicted theoretically and observed experimentally. It was shown that the typical binding energy of these excitons is exceptionally large for a bulk solid, approaching 200 meV [2].<br/><br/>Given the indirect bandgap of anatase TiO₂, a further attractive property resides in the possibility of bound, momentum-indirect dark excitons. Such excitons are characterized by longer lifetimes compared to their bright counterpart, making them a possible platform for quantum information, Bose-Einstein condensation, and energy harvesting [3]. The possibility of momentum indirect excitonic states in TiO₂ has only been investigated theoretically quite recently [3] and remains without any experimental confirmation. An experimental proof of the existence of indirect excitons in anatase TiO₂would represent a relevant result, providing important information for fundamental research and technological applications.<br/><br/>Here, we report the first experimental evidence of a strongly bound, momentum-dark exciton at the indirect bandgap of anatase TiO₂. In this work, we employ deep-UV pump-probe spectroscopy in transient reflectivity (TR), with 20 fs time resolution and high sensitivity. We populate the bright excitonic state (3.8 eV) near the direct bandgap of the material and collect the transient reflectivity response over a broad photon energy range (from 2.5 to 4.85 eV) across the bandgap of TiO₂. We can thus detect the dark exciton and characterize its temporal evolution.<br/><br/>The TR spectra are characterized by a clear signal corresponding to the bright exciton<i>.</i> The main contributions to its spectral feature are given by a combination of phase space filling (PSF), coulomb screening (CS) and bandgap renormalization (BGR) [4]. Superimposed to this signal, We observe a weak spectral feature with derivative shape at photon energies around 3.4 eV, which is consistent with the theoretical estimation of the dark exciton. Moreover, this feature shows a well-defined rise time of approximately 200 fs. We also observe that this rise time matches the ultrafast decay component of the TR bright exciton signal. This is a clear indication of a transition from the lowest bright exciton at the direct bandgap of the material, to the dark, momentum indirect exciton, due to scattering events of charge carriers with phonons. The experimental timescale of this process agrees well with the theoretical predicitions, highlighting a clear dark-to-bright transition, driven by a strong hole-phonon scattering channel along the Γ-to-X direction taking place in 100 to 300 fs [3]. We postulate that the effects of PSF, CS, BGR on the dark excitonic state are sufficiently large to modulate the cross section of phonon-assisted light absorption, generating a faint spectral feature in the transient reflectivity spectra. The dependence of the scattering rate from the temperature is also considered.<br/><br/>In conclusion, using a high sensitivity setup for ultrafast spectroscopy in the deep UV spectral range, with a sufficiently high temporal resolution, we are able to detect the predicted dark exciton of anatase TiO₂. We thus shed light on the properties of this physically and technologically relevant material. This result also contributes to the general understanding of excitonic states in transition metal oxides, and wide bandgap indirect semiconductors.<br/><br/>[1] A. Fujishima et al., <i>Surf. Sci. Rep. </i><b>63</b>, 515–582 (2008)<br/>[2] E. Baldini et al., <i>Nat. Comm.</i> <b>8</b>, 13 (2017)<br/>[3] A. Wang et al., <i>PNAS</i> <b>120</b>, 47 (2023)<br/>[4] E. Baldini et al., <i>Phys. Rev. Lett</i>. <b>125</b>, 116403 (2020)