Electron-Phonon Interaction and Charge Carrier Mass Enhancement in SrTiO 3

International audienceWe report a comprehensive THz, infrared and optical study of Nb-doped SrTiO 3 as well as dc conductivity and Hall effect measurements. Our THz spectra at 7 K show the presence of an unusually narrow (< 2 meV) Drude peak. For all carrier concentrations the Drude spectral weight shows a factor of three mass enhancement relative to the effective mass in the local density approximation, whereas the spectral weight contained in the incoherent midinfrared response indicates that the mass enhancement is at least a factor two. We find no evidence of a particularly large electron-phonon coupling that would result in small polaron formation. Electron-phonon coupling in the perovskites is a subject of much recent interest due to the controversy over its relevance in the phenomena of multiferroicity, ferroelec-tricity, superconductivity, and colossal magnetoresistance [1-5]. Despite much progress, full understanding of the physics of electron-phonon coupling in perovskites is still lacking because of additional crystallographic complexities of many materials involved (breathing, tilting and rotational distortions, ferroelectric symmetry breaking), magnetism, complex electronic effects (strong correlations), and also because of the lack of high-accuracy spectroscopic measurements specifically designed to probe electron-phonon coupling. With this in mind, we have studied a prototypical pe-rovskite oxide, SrTi 1ÿx Nb x O 3 with 0 x 0:02. SrTiO 3 is an insulator (ˆ 3:25 eV) with the conduction band formed by the Ti 3d states. These are split by the crystal field so that the three t 2g states become occupied when the material is electron doped by substituting pentavalent Nb for tetravalent Ti. For 0:0005 x 0:02 SrTi 1ÿx Nb x O 3 becomes superconducting at a T c of typically 0:3 K [6], and at most 1.2 K [5]. Characterized by the threefold degeneracy of the conduction bands and the high lattice polarizability, electron-doped SrTiO 3 provides a perfect opportunity for the study of electron-phonon coupling and polaron formation in an archetypal perovskite [7,8]. One of the fingerprints of an ultrastrong electron-phonon coupling is the formation of small polarons, which is observable in the form of a gigantic electron mass renor-malization. The renormalized mass can be obtained by measuring the optical spectral weight of the Drude peak, which is equal to ne 2 =2m †. Besides renormalizing the ''coherent'' (Drude) part of the spectrum, the electron-phonon coupling is responsible for ''incoherent'' contributions at higher energies, resulting in multiphonon absorption bands in the midinfared range. To address these issues, we have measured the optical reflectivity and transmission of double side polished, 5 5 mm 2 [(100) face] single crystals of SrTi 1ÿx Nb x O 3 between 300 K and 7 K by time-domain THz spectroscopy (TPI spectra 1000, TeraView Ltd.), Fourier transform in-frared spectroscopy, and photometric IR-UV spectroscopy, in the range from 0.3 meV to 7 eV. To obtain a detectable transmission, we have used for each composition several samples of different thicknesses (8-60 m), adopted to the spectral range and value of the optical transmission. The Hall carrier concentrations were 0.105%, 0.196%, 0.875%, and 2.00% at 7 K, which were within 5% of those measured by the wavelength-dispersive x-ray spectroscopy, and within 12% of the Nb concentration specified by the supplier (0.1%, 0.2%, 1.0%, and 2.0%, respectively, Crystec, Berlin). Compared to earlier measurements [9-13], we expand the lower limit of the spectral range from 1.2 meV [11] to 0.3 meV. The real and imaginary part of ˆ 0 ‡ 4=!†i 1 were obtained from inversion of the Fresnel equations of transmission and phase (below 12 meV for the samples with x ˆ 0:001 and 0.002), from inversion of the Fresnel equations of reflection and transmission coefficients (above 0.1 eV), and from Kramers-Kronig analyses of the reflectivity spectra (2-80 meV) with Drude-Lorentz fits [14] to aforementioned reflectivity, transmission, and phase spectra up to 7 eV, and dc. The gap of SrTiO 3 is revealed as the sharp onset of the optical conductivity at 3.3 eV in all samples (Fig. 1). The absorption peak at 2.4 eV, with intensity proportional to the charge carrier density, reveals optical excitation of the doped t 2g states to the empty e g states. The only subgap contributions to the optical conductivity of undoped SrTiO 3 (Fig. 1) are the three infrared active phonons at 11.0, 21.8, and 67.6 meV (at room temperature). The lowest one exhibits a strong redshift upon cooling, and saturates at about 2