FULL PAPER www.advancedscience.com Electron–Phonon Coupling and Electron–Phonon Scattering in SrVO3 Mathieu Mirjolet, Francisco Rivadulla, Premysl Marsik, Vladislav Borisov, Roser Valentí, and Josep Fontcuberta* ∗ band mass mband . Increasing further the Understanding the physics of strongly correlated electronic systems has been carrier density (n) or reducing the conduc- a central issue in condensed matter physics for decades. In transition metal tion band width (W), may eventually give oxides, strong correlations characteristic of narrow d bands are at the origin of rise to an emerging insulating state (Mott remarkable properties such as the opening of Mott gap, enhanced effective transition).[1–4] This framework has been used to mass, and anomalous vibronic coupling, to mention a few. SrVO3 with V4+ in rationalize the properties of correlated a 3d1 electronic configuration is the simplest example of a 3D correlated electronic systems, and particularly of tran- metallic electronic system. Here, the authors’ focus on the observation of a sition metal oxide (TMO) perovskites ABO3 (roughly) quadratic temperature dependence of the inverse electron mobility (B is a transition metal). The robustness of this seemingly simple system, which is an intriguing property shared by of the perovskite scaffolding (a 3D network of octahedrally coordinated BO6 polyhe- other metallic oxides. The systematic analysis of electronic transport in dra) allows multiple cation substitutions SrVO3 thin films discloses the limitations of the simplest picture at A/B sites that modify the electron fill- of e–e correlations in a Fermi liquid (FL); instead, it is shown show that the ing, and B─O bond distances and angles, quasi-2D topology of the Fermi surface (FS) and a strong electron–phonon achieving in some cases a band-filling and coupling, contributing to dress carriers with a phonon cloud, play a pivotal bandwidth-driven Mott transition.[5] role on the reported electron spectroscopic, optical, thermodynamic, and The complexity derived from the inter- play of all these parameters is schematized transport data. The picture that emerges is not restricted to SrVO3 but can be in the diagram below (Figure 1), where we shared with other 3d and 4d metallic oxides. take as example a TMO containing one sin- gle electron in a 3d1 band, for example, SrVO3 . In a cubic BO6 cage, the single elec- 1. Introduction tron of the transition metal M occupies the (dxy , dxz , dyz ) orbitals of 3d-t2g parentage. The resulting band Strong coulomb interaction characteristic of partially occupied (of width W), being partially occupied (1/6), will host a metal- narrow 3d bands renormalize the properties of charge carriers lic conductivity (Figure 1, center). Within the FL picture, the car- ∗ in Fermi liquids (FL), resulting, among other effects, in a large rier effective mass would be renormalized to mee , which will be ∗ ∗ increase of their effective mass mee , with respect to the effective larger than mband . Modification of the bond topology and charge M. Mirjolet, Prof. J. Fontcuberta Dr. P. Marsik Institut de Ciència de Materials de Barcelona (ICMAB-CSIC) Department of Physics Campus UAB Faculty of Science and Medicine Bellaterra 08193, Spain University of Fribourg E-mail: fontcuberta@icmab.cat Fribourg CH-1700, Switzerland Dr. F. Rivadulla Dr. V. Borisov CIQUS Department of Physics and Astronomy Centro de Investigación en Química Biolóxica e Materiais Moleculares, Uppsala University and Departamento de Química-Física Box 516, Uppsala SE-75120, Sweden Universidade de Santiago de Compostela Prof. R. Valentí Santiago de Compostela 15782, Spain Institut für Theoretische Physik Goethe-Universität Frankfurt am Main The ORCID identification number(s) for the author(s) of this article Frankfurt am Main 60438, Germany can be found under https://doi.org/10.1002/advs.202004207 © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. DOI: 10.1002/advs.202004207 Adv. Sci. 2021, 8, 2004207 2004207 (1 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 1. (Center) Partially occupied t2g (dxy, dxz , dyz ) orbitals, (1/6) in the sketch, are responsible for metallic behavior. Electron–electron correlations may increase carrier effective mass (m∗ee ) and among other consequences, reduce the plasma frequency (bottom illustration) or, eventually, open a Mott gap (top illustration). In cubic metal-oxide surrounding, the symmetry of the (dxy , dxz , dyz ) orbitals produces a quasi 2D cylindrical Fermi surface (right). Charge carriers in an ionic lattice are dressed with a lattice polarization cloud (left illustration), enhancing also the effective mass (m∗e−ph ). distribution within the t2g band, may promote the opening of a mer el al.[11] ), and in some high-TC superconductors (HTS), and Mott gap. Vanadium 3d1 oxides such as (Sr, Ca)VO3 or VO2 fit oxyselenides.[12] It has been emphasized that although 𝜇 ≈ T−2 in this picture, as recently overviewed by Brahlek et al.[6] Accord- may be consistent with the picture of e–e scattering in a FL, the ing to that, the red-shifted plasma frequency (𝜔∗p ∝ (n∕m∗ )1∕2 ) of dependence of the amplitude of this scattering term on carrier (Sr, Ca)VO3 can be attributed to a large effective mass m* aris- density sharply contradicts expectations based on the FL descrip- ing from e–e correlations (Figure 1, bottom). In the same vein, tion of interacting electron systems.[11,13] Therefore, the whole an abrupt metal insulator transition occurs in VO2 upon cooling scenario should be revisited. due to the opening of a Mott gap (Figure 1, top). The properties In this regard, we suggest that the topology of the Fermi sur- of these materials are thus described within a purely electronic face (FS) could be an important ingredient to this picture, previ- model including correlation effects (Figure 1, bottom–top). ously overlooked. Along the Γ-X direction, only (dxy , dxz ) orbitals Although the success of this approach has been tremendous, overlap and therefore the FS consists of a 2D cylinder. A similar some properties of metallic oxides cannot be described within situation occurs along the orthogonal directions, and thus the FS this framework. For instance, it has been repeatedly reported is formed by three interpenetrated cylinders (Figure 1, right). The that the resistivity (𝜌) and the inverse carrier mobility (𝜇 −1 ) of relevance of a quasi-2D FS on the carrier mobility is not minor: SrVO3 (SVO) follow a nearly T2 temperature dependence.[7–10] in anisotropic metals with quasi-cylindrical FS branches, e–ph In fact, 𝜇(T) ≈ T−2 is commonly observed in doped Mott insu- scattering promotes a distinctive ≈T−2 temperature dependence lators, such as LaTiO3 or SmTiO3 , in doped band insulators (e.g. of the carrier mobility, early described in great detail for Bi.[14] SrTiO3−x and (Gd, La, Nb):SrTiO3 as recently reviewed by Stem- The second feature to consider is that carriers in a 3d1 TMO Adv. Sci. 2021, 8, 2004207 2004207 (2 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com a) b) c) 250 100 150 STO P(Ar) = 0 mbar t = 10 nm LSAT P(Ar) = 0.03 mbar t = 20 nm 200 NGO 80 P(Ar) = 0.2 mbar t = 70 nm ρ (μΩ cm) ρ (μΩ cm) ρ (μΩ cm) LAO P(Ar) = 0.3 mbar 100 150 60 100 40 50 50 20 0 0 0 0 100 200 300 0 100 200 300 0 100 200 300 T (K) T (K) T (K) Figure 2. Temperature dependence of 𝜌(T) of selected series of SVO samples, plotted versus T. a) Films of 70 nm gown at P(Ar) = 0 mbar on various substrates. b) Films of 70 nm on NGO grown at various P(Ar). c) Films of different thickness, on NGO grown at P(Ar) = 0 mbar. move within an ionic lattice background. This implies that the lat- 2. Results tice can be polarized around the moving charge. Carriers, in this scenario (Figure 1, left) are dressed with a lattice distortion, that 2.1. Temperature Dependence of the Electrical Resistivity ∗ translates into an effective mass (me−ph ) related to the coupling of the electrons to the lattice (e–ph) coupling. Films were grown on different cubic substrates (LaAlO3 (LAO), In view of the two above-mentioned aspects, SVO is at the NdGaO3 (NGO), LSAT, and SrTiO3 (STO)) which have different crossroad of e–e correlations, e–ph strong coupling, and low di- structural mismatch with SVO. Depending on film thickness (t), mensional FS (Figure 1), whose interplay requires renewed at- substrates may impose tensile (STO) or compressive (LAO) epi- tention. An important general question is whether the quadratic taxial strain on nominally cubic (bulk) SVO, promoting a tetrag- temperature dependence of the resistivity is indeed an undis- onal distortion (c/a ≠ 1, where (a, c) are the cell parameters) as putable fingerprint of e–e correlations, or if other scenarios determined by X-ray diffraction (Section S1, Supporting Infor- should be envisaged. mation). Growth rate and carrier concentration were adjusted by Here, we aim at revising some of these issues by reporting on growth atmosphere. Figure 2a,b displays some 𝜌(T) curves, rep- electric transport data (resistivity, magnetoresistance, Hall, and resentative of films on different substrates, all having a t ≈ 70 nm Seebeck coefficients) of a large set of SrVO3 (SVO) epitaxial films and grown at different P(Ar). Although the growth pressure has a deposited on different substrates and with different growth con- major effect on 𝜌(T), all films show a metallic-like resistivity, and ditions, selected to tune the lattice distortions and, expectedly, the the 𝜌(300 K) ≈ 85–100 µΩ cm for films grown on LSAT, NGO, and lattice dynamics. LAO is similar to state-of-the-art data.[8–10,20–22] The resistivity of It will be first shown that all films have roughly 𝜇(T) ≈ T−2 the SVO film on STO is vertically shifted due to the presence of and 𝜌(T) ≈ A T2 ; these temperature dependences are consistent planar defects associated to the large tensile mismatch of SVO with earlier findings,[7–10] where A was identified as the coeffi- with the STO substrate,[23] although its slope remains similar to cient corresponding to the temperature-dependent e–e scatter- the other films. In Figure 2c, we show 𝜌(T) of SVO films of dif- ing rate (Aee ) in a FL, that is, A ≡ Aee .[15–17] However, from the ferent thicknesses on NGO; the resistivity of the films gradually analysis of the magnitude of A and its carrier density depen- increases as thickness reduces, as commonly found in SVO.[8–10] dence, we conclude that the temperature dependence of 𝜇(T), The residual resistivity ratio (RRR) (Section S2, Supporting Infor- in contrast to earlier views, may not originate from e–e scatter- mation) is as high as ≈12, among the highest values ever reported ing in a FL. Instead, we show that 𝜌(T) can be well described for pulsed laser deposition (PLD)-grown SVO films,[24] in opti- by a polaronic model (Figure 1, left panel), where the relevant mally grown films (70 nm; P(Ar) = 0.2–0.3 mbar), and decreases phonon energy can be tuned ad-hoc by epitaxial strain and sub- down to RRR ≈ 2 in films grown on poorly matched substrates sequent lattice distortion. We also show that e–ph scattering in and/or too-high or too-low P(Ar). Thus, the RRR is used in the a cylindrical 2D FS (Figure 1, right panel) can contribute to the following as a label for film quality.[9,22,25,26] observed 𝜇(T) ≈ T−2 . The e-ph coupling and topology of the FS All 𝜌(T) data in Figure 2a–c displays a characteristic non- account for the temperature-dependent Seebeck coefficient S(T), linearity.[8–10,21,22] Data can be roughly described as 𝜌(T) = 𝜌0 + the observed magnetoresistance and its Kohler’s scaling. We thus AT2 and can be fitted to extract (𝜌0 , A) (see fits in Figure 5 below). conclude that e–e interactions and e–ph coupling in 3d1 TMOs In Figure 3a, we show the obtained A values for all samples as a should be taken on an equal footing to account for the experi- function of the carrier concentration (n), determined from room- mental mass renormalization, as found in other oxides,[18,19] and temperature Hall effect measurements. It can be appreciated that that the 2D character of the FS should be explicitly considered A varies within the ≈(3 × 10−10 – 4 × 10−9 ) Ω cm K−2 range to build a comprehensive view of the carrier transport in these when the carrier density (n) varies within the ≈(3 × 1021 – 2 × seemingly most simple metallic oxides. 1022 ) cm−3 range (Sections S3 and S4, Supporting Information). Adv. Sci. 2021, 8, 2004207 2004207 (3 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com a) b) SVO/STO PO2 (this work) 1E-4 SVO/LSAT PO2 (this work) 1E-8 SVO/LSAT P(Ar) (this work) 1E-5 SVO/NGO P(Ar) (this work) A ~ 1/n A (Ω cm K-2) A (Ω cm K-2) 1E-6 1E-7 A ~ 1/n5/3 1E-9 A ~ 1/n 1E-8 Gd:SrTiO3 Ca1-xSrxVO3 (Inoue et al.) La:SrTiO3 SVO/LSAT (Zhang et al.) 1E-9 SrTiO3-x (Lin et al.) SVO/LSAT (Gu et al.) Nb:SrTiO3 (Lin et al.) 1E-10 SVO/STO (Fouchet et al.) Nb:SrTiO3 (Van der Marel et al.) 1E-10 1E21 1E22 1E17 1E18 1E19 1E20 1E21 1E22 1E23 -3 n (cm ) n (cm-3) Figure 3. a) Coefficient A of 𝜌(T) = 𝜌0 + A T2 versus carrier density (n), as extracted from Hall measurements, for some SVO films. Data from literature refs. [7–10] are also included. b) Comparison of present A values with available literature values for SVO films and related metallic oxides (Adapted with permission from Mikheev et al.[30] and Stemmer et al.,[11] including data of Gd:SrTiO3 from Moetakef et al.,[27] La:SrTiO3 from Cain et al.,[29] Nb:SrTiO3 from Van der Marel et al.,[28] and SrTiO3−x and Nb:SrTiO3 from Lin et al.[13] ). Dashed lines indicate A ≈ n𝛼 power dependences with 𝛼 = −1 and −5/3. In Figure 3a we also include the A values reported in the litera- 1022 cm−3 , reducing slightly (≈12%) at 5 K. The mobility rapidly ture for Ca1−x Srx VO3 polycrystalline samples (4.2 × 10−10 – 9.1 × decays with increasing temperature. As shown in Figure 4b, 10−10 Ω cm K−2 )[7] as well as for SVO thin films (2.5 × 10−10 – 5 × 𝜇 −1 (T) ≈ T2 which is similar to 𝜌(T), implying that 𝜇(T) governs 10−10 Ω cm K−2 ).[8–10] The close similarity of all available data is 𝜌(T). Therefore, we indistinctly refer to the quadratic temperature worthy of note. To set in an appropriate context the large varia- dependence of 𝜌(T) or 𝜇 −1 (T). tion in magnitude of A, in Figure 3b we display the A values for Details of 𝜌(T) = 𝜌0 + A T2 fits can be appreciated in Figure 5 SVO and related oxide materials. We have selected oxides where where we show (dashed red) illustrative fits on samples having the conduction band is mainly formed by partially occupied 3d- large RRR = 9.6 and small RRR = 2.1 (Figure 5a,b, respectively). t2g orbitals, either intrinsic (SVO case) or obtained by electron It is obvious that 𝜌(T) data of optimal films (Figure 5a) show a doping of Mott insulators (e.g., Sr:GdTiO3 )[27] or band insulators clear departure from the T2 dependence, most noticeable at T ≲ (La:SrTiO3 , Nb:SrTiO3 , or SrTiO3−x ),[13,28,29] as first summarized 180 K (dashed vertical line). Importantly, the deviation from T2 by Mikheev et al.[30] and Stemmer et al.[11] It is remarkable that becomes least perceptible in films with lower RRR (Figure 5b). A can be varied by about five orders of magnitude when the car- Including a phonon-like T5 term did not improve fits and did not rier concentration changes by about five orders of magnitude; we affect the extracted A parameter. Fits to other samples, residual conclude that A ≈ n−1 over a very wide range of carrier concen- fit differences and fits including additional T5 terms are shown tration, as indicated by the dashed line in Figure 3a,b. in Section S4, Supporting Information. The temperature-dependent carrier mobility 𝜇(T) (𝜇 = To explore the origin of the departure of 𝜌(T) from T2 ob- (𝜌 n e)−1 ) was determined from n(T), extracted from Hall ef- served in the films with the largest RRR, we consider that the fect measurements, and 𝜌(T). Illustrative n(T) and 𝜇(T) data are dynamics of the d1 electron, moving in the narrow 3d-t2g band shown in Figure 4a. It can be appreciated that n(300 K) ≈ 2.5 × within an ionic matrix (O2− /V4/5+ ), bears some similitude to a) b) 100 40 0.15 2.3 80 1/μ (cm-2 V1 s1) 30 μ (cm2 V-1 s-1) n (x1022 cm-3) 2.2 0.10 ρ (μΩ cm) 60 SVO//NGO 20 SVO//NGO 2.1 t ≈ 70 nm 40 t ≈ 70 nm P(Ar) = 0.2 mbar P(Ar) = 0.2 mbar 0.05 2.0 10 20 1.9 0 0 0.00 0 100 200 300 0 2 4 6 8 10 T (K) T 2 (x 104 K2) Figure 4. a) Temperature-dependent carrier concentration (left axis) and mobility (right axis) of an illustrative SVO film (70 nm thick, deposited on NGO at P(Ar) = 0.2 mbar). b) Resistivity (left axis) and inverse mobility (right axis) versus T2 of the same film. Adv. Sci. 2021, 8, 2004207 2004207 (4 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 5. a,b) Illustrative 𝜌(T) data of SVO films on NGO substrates (70 nm, grown at different P(Ar)) largely differing in RRR, as indicated. c–e) 𝜌(T) data of SVO films (10 nm, P(Ar) = 0 mbar) grown on substrates imposing tensile (STO, NGO) or compressive strain (LAO) on SVO. The dashed red line is the fit to the T2 dependence. Dashed vertical black lines indicate the temperature where noticeable departure from the quadratic T-dependence is observed. The dashed green line is the fit to the polaronic model. Insets are zooms of the low temperature region. polaronic motion. Indeed, it has been early suggested that pola- where Ae−ph encapsulates the e–ph coupling strength and the ef- ∗ ronic carrier motion could be of relevance in itinerant-electron fective mass of the polaron (me−ph ) and kB is the Boltzmann con- systems approaching the localized edge, including CaVO3 ,[31] stant. Assuming that Ae−ph in Equation (2) is temperature inde- weakly-doped Ln:STO (where Ln is a lanthanide), orthorhom- pendent, by combining all parameters, Equation (1) can be rewrit- bic manganites La1−x Cax MnO3 ,[32,33] La0.7 Sr0.3 MnO3 ,[34] and ten as: La2/3 (Ca1−x Srx )1/3 MnO3 ,[5] or in doped LaTiO3 and NdTiO3 .[35,36] Within this framework, the carrier mobility is determined by ∗ Ae−ph × 𝜔0 their coupling to some low energy phonons. The polaronic re- 𝜌 (T ) = 𝜌0 + ( ) (3) ℏ𝜔 sin h2 2k 0T sistivity is given by:[33,37] B ℏ 2 1 ∗ where Ae−ph is given by: 𝜌 (T ) = 𝜌0 + × (1) ne2 a2 tp 𝜏 ∗ ℏ2 where tp is the hopping amplitude for polarons, a the cell param- Ae−ph = × Ae−ph (4) ne2 a2 tp eter, n the carrier density, and 𝜌0 is the residual resistivity. 𝜏 −1 is the polaron relaxation rate, which is dictated by the e–ph coupling In Figure 5a,b (dashed green lines), we include the fits of the to some phonon modes. In the simplest assumption of polaron 𝜌(T) data using Equation (3), that allow to extract the phonon fre- coherent motion, in which a single optical phonon mode (h̄𝜔0 ) quency 𝜔0 . We observe that data are well reproduced in all tem- dominates the polaron relaxation rate, 𝜏 −1 is given by:[33] perature range (5–300 K), including the low temperature region 1 Ae−ph × 𝜔0 (<180 K), where the quadratic fit failed. Residual fit differences = ( ) (2) are reduced by about 90% compared to T2 fits and similar excel- 𝜏 ℏ𝜔 sinh2 2k 0T B lent fits have been obtained for all samples, and fitted parameters Adv. Sci. 2021, 8, 2004207 2004207 (5 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 6. a) Dependence of the phonon energy (h̄𝜔0 ) extracted from 𝜌(T) using the polaronic model (Equation (3)) of SVO films as a function of their tetragonal cell distortion (c/a). Films were grown on NGO (red spheres), LSAT (blue), STO (green), and LAO (violet), at different P(Ar) (as indicated by the labels; units are mbar). All films are 70 nm, except some few as indicated by the additional label in parenthesis. Decorared sphere symbols correspond to films on STO, NGO and LAO of indentical thickness and grown under nominally identical conditions. b) Left axis (full spheres): Dependence of A∗e−ph on the phonon energy (h̄𝜔0 ). Right axis (empty circles): Electron–phonon coupling parameter Ae−ph calculated from the experimental A∗e−ph as described in the text (Equation (4)). In (a,b) we also include (light blue spheres) the corresponding data points extracted from reported resistivity data of SVO films deposited on LSAT by h-MBE, by Zhang et al. (20 and 45 nm thick)[9] and by Moyer et al. (50 nm thick).[25] Errors bars for fit-extracted 𝜔0 and A∗e−ph in (a,b) are smaller than the symbol size (S4, Supporting Information). √ are robustly obtained irrespectively of fitting procedures (see Sec- the actual n, the mean cell parameter a = 3 Vuc (Vuc is the mea- tion S4, Supporting Information). ∗ sured unit cell volume) and the experimental Ae−ph values of all Aiming at exploring changes of the phonon frequency (𝜔0 ) samples. These data provide a transparent view of the variations with lattice distortion, we first concentrate on fully strained films of the strength of the e–ph coupling with the phonon frequency. grown on substrates where epitaxial strain dictates different c/a Within the polaronic framework, Ae−ph is proportional to the ef- ratios. One expects that phonons in SVO films are sensitive to fective mass of polarons, which data in Figure 6b, indicatethat it tetragonal distortions of the VO6 octahedra which can be quan- becomes larger when phonons harden. tified by the c/a ratio extracted from XRD. In Figure 5c,d,e we show the 𝜌(T) data of SVO (≈10 nm, P(Ar) = 0 mbar) films on STO, NGO, and LAO. As observed, the polaronic model leads 2.2. Temperature and Magnetic Field Dependent to excellent fits. The extracted h̄𝜔0 values are around 20.6 meV Magnetoresistance (STO), 12.7 meV (NGO), and 10.7 meV (LAO), which indicates a clear softening under compressive distortion of the SVO lat- In Figure 7a we display the magnetoresistance MR(H) = tice (from c/a < 1 to c/a > 1). Figure 6a (decorated sphere sym- [R(H)−R(H=0)]/R(H=0) of a representative SVO film (70 nm, bols) shows the observed h̄𝜔0 and its variation with c/a. We also NGO, P(Ar) = 0.2 mbar), recorded at various temperatures. The include in Figure 6a the phonon energy h̄𝜔0 extracted from the resistance R(H, T) is measured with the magnetic field H per- fits of SVO films on optimally matched substrates (LSAT, NGO) pendicular to the film plane and the current is transverse to H. grown at different pressures (0–0.3 mbar) and thicknesses (10– In a conventional metal MR ≈ (𝜔c 𝜏)2 = (𝜇𝜇 0 H)2 , where 𝜔c and 𝜏 70 nm). For completeness, we have also included (light blue are the cyclotron frequency and scattering time respectively, and spheres) the h̄𝜔0 data extracted from fits to digitized 𝜌(T) data 𝜇 and 𝜇 0 are the mobility and the vacuum permeability, respec- of films grown by hybrid-MBE (h-MBE),[9,25] which nicely fall tively. Our experimental data show that MR of SVO is positive, on top of our data (fits are shown in Figure S4c, Supporting parabolic on H and rather small (<2% at 5 K), decreasing with Information). increasing temperature. Fitting the parabolic MR(H) gives 𝜇 ≈ In Figure 6b (left axis, full spheres), we explore a possible cor- 30 cm2 V−1 s−1 at 300 K, increasing up to 𝜇 ≈ 160 cm2 V−1 s−1 at ∗ relation between the e–ph coupling related Ae−ph parameter and 5 K (inset in Figure 7a). This increase of mobility upon cooling the phonon energy h̄𝜔0 . We also include data from literature[9,25] is consistent with Hall measurements (included also in inset in ∗ (light blue spheres) that follow the same Ae−ph (h̄𝜔0 ) trend: the e– Figure 7a), although its value is somewhat smaller in the latter, as often observed.[39] ph coupling strength increases with h̄𝜔0 . To get an insight into On the other hand, as stated by the Kohler’s rule,[40] MR(H) the implications of data in Figure 6b, we evaluate Ae−ph from ∗ data recorded at different temperatures should be a unique func- Ae−ph using Equation (4). A rough estimate of Ae−ph can be ob- tion F(x), with x = [𝜇 0 H/R(H=0)], as shown in Figure 7b. The tained using n ≈ 2 × 1022 cm−3 , a ≈ 4 Å, and tp ≈ 0.6 eV (we Kohler’s rule is expected to hold irrespectively on the carrier use here the DFT calculated hopping integral for electrons [not nature (e.g., correlated electrons or polarons) and scattering polarons] in SVO[38] ) and a typical value of Ae−ph ∗ from Figure 6b mechanism.[41] −20 (≈1 × 10 Ω m s). It turns out that Ae−ph ≈ 7. In Figure 6b (right Here it is relevant to emphasize that, in a non-magnetic sys- axis) we show the Ae−ph values (empty circles) calculated using tem, MR is non-zero only if different carriers participate in the Adv. Sci. 2021, 8, 2004207 2004207 (6 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Figure 7. a) Magnetoresistance MR = [R(H) − R(H=0)]/R(H) of SVO film (70 nm thick; deposited on NGO substrate; P(Ar) = 0.2 mbar) recorded with magnetic field perpendicular to the film surface, at various temperatures (5, 50, 100, 200, and 300 K). Data display a clear parabolic dependence MR ≈ H2 . Inset: Carrier mobility extracted from Hall effect and magnetoresistance measurements as indicated. b) Kohler plot of MR(H) measured at 5, 50, 100, 200, and 300 K, illustrating the expected collapsing. transport, and this has to happen if the FS is constituted by inter- and increases linearly (in modulus) when increasing tempera- penetrated cylinders as in the present case. ture, as expected for band transport of electrons in which S(T) is Indeed, first principles calculations (DFT) of the electronic given by:[15] structure of bulk SVO clearly indicate that the FS has a multi- band character, dominated by the dxy , dxz , and dyz orbitals, al- [ ] −𝜋 2 k2B g (E ) 𝜕 though a non-vanishing contribution ≈20% (in terms of the den- S (T ) = T + ln [𝜏 (E )] (5) 3e n 𝜕E E=EF sity of states) of the oxygen 2p states is apparent. These orbitals determine a cylindrical FS along three-perpendicular directions (Figure 8). Calculations were performed for bulk SVO, using the where g(E) is the density of states, n the carrier density, and EF cell parameters of tensely and compressively strained (10 nm) the Fermi energy. 𝜏(E) is an energy dependent scattering time, SVO films. They indicate that the fine details of the covalent mix- which in general can be written as 𝜏 ≈ E𝛼 where 𝛼 is related to ing are somehow modified by strain, but the main features of the the scattering mechanism. Within the simplest parabolic band FS are fully preserved. Combination of three orbitals and the hy- approximation and for 𝜏 ≈ E−1 (𝛼 = −1), as deduced from optical bridization between the three FS sheets results in the obtained measurements by Makino et al.,[42] S(T) reduces to: picture, where the outer sheet has a quasi-2D character and dif- ferent carriers contribute to them, which can account for the ob- −𝜋 2 k2B T S (T ) = (6) served magnetoresistance. 6e EF The slope dS(T)/dT allows to extract EF and, using the car- 2.3. Seebeck Coefficient rier density n deduced from Hall measurements (n = 2.13 × 1022 cm−3 ), the transport effective mass m* can be deter- In Figure 9, we display the temperature dependence of the See- mined. From Figure 9, dS(T)/dT = − 0.0211 µV K−2 and us- beck coefficient S(T) of an illustrative SVO film (70 nm, LSAT, ing Equation (6) we obtain EF = 0.58 eV and m* ≈ 4.8 me P(Ar) = 0.03 mbar; similar data obtained for other samples are (me is the free electron mass). Angle-resolved photoemission shown in Section S5, Supporting Information). S(T) is negative spectroscopy (ARPES) measurements indicate a Fermi energy at Figure 8. Fermi surface of cubic SVO determined from first principles. Three sheets of the Fermi surface are shown. The aspect ratio of the quasi- cylindrical first band is 1:2.1. Adv. Sci. 2021, 8, 2004207 2004207 (7 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com 1 For a spherical FS EF = (h̄2 /2m)(3𝜋 2 n)2/3 and 𝜌(T) = (2m2 kB 2 )/(e2 h̄3 (3𝜋 2 )2/3 n5/3 ) T2 ≈ n−5/3 T2 .[51] Mobility data in Fig- Seebeck coeff. S (μV K-1) Exp. data set 1 0 Exp. data set 2 ure 4a,b as well as 𝜌(T) in Figure 2a–c are roughly consistent with this T2 dependence. However, the A(n) data shown in Figure 3a,b Linear fit (set 1): -1 is better described by A ≈ n−1 over a large range of carrier concen- slope = -0.0211 μV K-2 tration, rather than A ≈ n−5/3 (dashed lines in Figure 3b). In the -2 simplest view, A ≈ n−1 would imply that 1/𝜏 (and therefore 1/𝜇) would not depend on carrier density, which is at odds with ex- -3 pectations for a FL model. As recently emphasized by Stemmer et al.,[11,30] this discrepancy holds for a large number of oxides -4 at the verge of a metal–insulator transition, although it is worth SVO//LSAT noticing that the predicted A ≈ n−5/3 dependence had been ob- -5 P(Ar) = 0.03 mbar served in other systems, such as TiS2 .[52] t ≈ 70 nm The magnitude of the A coefficient in 𝜌(T) ≈ A T2 signals an- -6 other discrepancy. As shown in Figure 3a, we obtained A ≈ (1 × 0 100 200 300 10−10 – 1 × 10−9 ) Ω cm K−2 , which are similar values to those re- T (K) ported by Inoue et al. (4.2 × 10−10 Ω cm K−2 ).[7] Within the e–e scattering model, A ≡ Aee is given by: Figure 9. Temperature dependence of the Seebeck coefficient S measured on a SVO film (70 nm thick; deposited on LSAT). Open blue symbols (data 2m2 k2B set 1) are data measured when ramping the temperature. Solid red sym- Aee = (7) bols (data set 2) are data determined in a different temperature run, by e2 ℏ3 (3𝜋 2 )2∕3 n5∕3 setting the temperature before measuring the Seebeck voltage. Using as typical parameters (n = 2 × 1022 cm−3 and mee ∗ ≈ 4 me ) one gets: A ≈ 1 × 10−11 Ω cm K−2 , which is almost two orders of about ≈0.5 eV[43] which is in excellent agreement with our See- magnitude smaller than the measured values. beck data. Summarizing, the observation that A ≈ n−1 , suggesting that 𝜇 Therefore, we conclude that transport in SVO is ruled by does not depend on n, and the severe discrepancy between mea- carriers having a large effective mass. Within the scope of the sured and expected A values, question the e–e scattering in a FL Brinkman–Rice model,[44] m* ≈ 4.8 me would indicate that the scenario as the origin of the roughly quadratic temperature de- system is close to the metal–insulator transition. More elaborate pendence of resistivity. Next, we investigate the role of the e–ph ab initio calculations for bulk SVO including only electronic cor- scattering. relation effects within dynamical mean field theory also find a significant mass enhancement.[45−47] This scenario has been pro- posed to account for the observation of a metal–insulator transi- 3.2. Electron–Phonon Scattering in Cylindrical Fermi Surfaces tion in ultrathin SVO films[8,10,48] and in irradiated SVO films.[49] However, as we argue in the following, the mass enhancement We first notice that the temperature dependence of 1/𝜏 is primar- can also be contributed by e–ph coupling, as the polaronic fits ily due to scattering events with phonons. At high temperature, suggest. all phonon branches are equally populated and the phonon num- ber increases linearly with T, therefore 1/𝜏 ≈ T and 𝜌(T) ≈ T, as 3. Discussion frequently observed. However, at lower temperature the differ- ent phonon occupation of different phonon branches leads to a We have first shown that the temperature-dependent 𝜌(T) data more complex situation, which becomes particularly remarkable of SVO films can be roughly described by either a quadratic T2 for anisotropic FSs. Indeed, it was long ago recognized that e–ph dependence that we recall is commonly taken as a signature of scattering in metals with cylindrical FSs (e.g., Bi[14] ) leads to 1/𝜏 ≈ e–e scattering in correlated electronic systems, or by a polaronic 𝜌(T) ≈ T2 in some temperature range. As recently emphasized by model. However, we have demonstrated that the quality of fits, Snyder et al., the topological 2D feature of the FS in some metallic performed in a wide temperature range (5–300 K), is significantly oxides can be at the origin of 1/𝜏 ≈ 𝜌(T) ≈ T2 .[53,54] Indeed, a cylin- improved using a polaronic model. In the following, we carefully drical FS of SVO has been observed by ARPES.[43,55–57] The recent revise the implications of these findings. observation of a similar T2 -dependent resistivity in Bi2 O2 Se oxy- selenides, where the FS is an elongated ellipsoid,[12] may point to 3.1. The Quadratic Temperature Dependence of the Resistivity a common origin. According to Kukkonen,[14] the electrical resistivity of metals The quadratic temperature dependence of 𝜌(T) in metals is a with cylindrical FS display a genuine T2 temperature dependence common observation.[50] The e–e scattering rate is given by in a temperature region bounded by Tp < T < Tk . The tempera- 1/𝜏 = Bee (kB T)2 /(h̄EF ), where Bee is a dimensionless con- ture limits Tp and Tk are determined by the dimensions of the FS stant of order unity.[15] The electrical resistivity is given by 𝜌 = through the relation Tp = 2h̄vS pF /kB and Tk = 2h̄vS kF /kB where (m/ne2 )(1/𝜏) and, if only the scattering time is temperature de- pF (respectively kF ) is the diameter (respectively the height) of the pendent, it follows that 𝜌(T) ≈ 1/𝜏 ≈ T2 . Accordingly, 𝜌(T) ≈ T2 cylindrical FS and vS the sound velocity.[14,58] In the SVO case, by can be viewed as a signature of FL. approximating the FS to a cylinder, using pF ≈ 0.5(𝜋/a) and kF Adv. Sci. 2021, 8, 2004207 2004207 (8 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com ≈ (𝜋/a), as deduced from ARPES experiments[43] and our calcu- < 11, depending on the tetragonality ratio c/a. Therefore, there is lations (Figure 8), and using the experimental transverse sound a dramatic enhancement of the electron effective mass via e–ph velocity vS ≈ 4000 m s−1 ,[59] we get Tp ≈ 239 K, and Tk ≈ 478 K. ∗ dressing. The large me−ph ∗ /mband effective mass derived from the We notice that the estimated low-temperature limit (≈ 239 K) for polaronic fit is consistent with the large effective mass derived 𝜌 ≈ T2 , is somewhat higher than the low temperature experimen- above from Seebeck data. Moreover, we notice that similar values tal bound for the quadratic T2 term (≈ 180–200 K), below which have been reported in nickelates (m*/mband ∗ ≈ 6–7).[69] a clear departure from T2 is observed (Figure 5a,c). To what ex- Search for direct evidences of e–ph coupling in HTS was of tent this discrepancy is related to limitations of the anisotropic paramount relevance in the quest for a microscopic mechanism scattering model of Kukkonen[14] (such as the assumption of a for e–e pairing. Lanzara et al.[68] used ARPES to show that, in single band carriers and absence of phonon drag), or is linked to some cuprates, electrons experience an abrupt change of its the present approximation of a (interpenetrated) cylindrical FS velocity and scattering rate at some well-defined energy (50– for SVO, remains to be solved. 80 meV) that was interpreted as a fingerprint of e–ph coupling. Therefore, one could tentatively conclude that the 𝜌(T) ≈ T2 de- Interestingly, recent ARPES data in SVO,[43,55] showed similar pendence may result from e–ph scattering in the quasi-2D cylin- features at ≈60 meV, that were also attributed to the coupling drical FS characteristic of 3d-t2g metal oxides. Magnetoresistance of electrons with these phonons. In principle, this conclusion data would be also compatible with this picture. would be in agreement with the polaronic model discussed here, although the significant difference on the energy of most 3.3. Polaronic Transport relevant phonons for dc conductivity and ARPES remains to be elucidated. Landau first suggested the possibility for lattice distortions to Finally, we mention that Mirjolet et al.[23] and Zhang et al.[9] re- trap electrons by means of an intrinsic modification of the lattice ported ellipsometric measurements to deduce the effective mass phonon-field induced by the electron itself. The resulting e–ph of carriers in SVO films, and obtained m*/me ≈ 3–5 (depend- quasiparticle (the polaron) is a coupled e–ph system in which the ing on the substrates and growth conditions). Ellipsometric mea- polarization generated by the lattice distortions acts back on the surements have also been performed in some of the films of this electron, renormalizing its properties, for instance the effective manuscript, to determine the plasma frequency and consistent mass. m*/me ≈ 4.1 values have been obtained (Section S8, Support- ∗ At low temperature, (small) polarons may display a coherent ing Information). It is also enlightening to notice that m*/mband band-like transport, where the phonon-mediated scattering rules values extracted from specific heat coefficient (𝛾) and magnetic their mobility.[60,61] As the phonon number decreases with tem- susceptibility (𝜒) data of ceramic SVO samples differ by about perature, the resistivity decreases upon lowering temperature a factor RW ≈ 1.6 (Wilson ratio), which also suggests that e–ph and small polarons behave as heavy particles with effective mass coupling to be relevant.[7] ∗ me−ph . In this regime, 𝜌(T) is given by Equations (1) − (4). As To gain some perspective, it may be useful to point out that it has been recently shown that bosonic modes largely contribute shown, data can be well reproduced by these expressions. As em- to effective mass renormalization in SrRuO3 oxide. SrRuO3 is a phasized by Van der Marel et al.,[28] this 𝜌(T) dependence is ex- metallic and ferromagnetic (<150 K) 4d system (Ru4+ : d4 : (t2g 3↑ , pected to hold for small polarons; but on the other hand, Devreese t2g 1↓ )) that had been commonly assumed to be a strongly cor- et al.[62] also signaled that, even in one of the most studied pola- related metallic system.[70,71] However, detailed calculations[72] ronic materials (Nb:SrTiO3 ), the distinction between small and have lately suggested correlations to be weaker than expected and large polarons is not that sharp. We will not attempt to dig here ARPES data have provided strong evidence of e–ph coupling.[19] into this distinction. The fact that in both SrVO3 and SrRuO3 , the itinerant elec- Instead, we note that in recent years, the small polaron trons (3d-t2g 1 and 4d-(t2g 3↑ , t2g 1↓ ), respectively) reside in a quasi- scenario has been used to describe 𝜌(T) of heavily doped degenerate t2g band may be instrumental on the enhanced rele- manganites[33,63] or doped Mott insulators LaTiO3 [35,36] and vance of e–ph coupling. NdTiO3 .[36] We focus now our attention on the relevant phonon We end by noticing that it has been recently reported that, be- energies (h̄𝜔0 ≈ 5–25 meV ≈ 60–290 K) extracted from the fits yond the original Kadowaki–Woods plot, there is a kind of uni- of 𝜌(T) of our films (Figure 6a) and the observed variation with versal link between the Fermi energy and the prefactor A of the the tetragonal distortion c/a. Preliminary calculations in SVO T2 resistivity, which persists across various FLs,[12] that remain (Section S6, Supporting Information) allow to identify phonons to be explained. Our data also nicely fall within this scaling (see in this energy range that soften when increasing c/a, as ob- Section S8, Supporting Information). served experimentally (Figure 6a). Phonons within the same en- ergy range were extracted from 𝜌(T) data in manganites,[5,33,64] LaTiO3 [35] and Ba1−x Kx BiO3 .[65,66] Therefore, we propose that 4. Conclusion similar phonons may govern the dynamics of dressed electrons We have analyzed transport properties of epitaxial SrVO3 thin in SVO films. films, where V4+ ions have a single 3d1 electron in a t2g orbital The e–ph coupling implies an enhanced effective mass triplet. First, we have shown that 𝜌(T) displays roughly a T2 de- ∗ (me−ph ). Therefore, following Zhao et al.,[33] we identify in Equa- pendence (𝜌(T) ≈ 𝜌0 + A T2 ) which is in agreement with earlier tion (2), Ae−ph ≡ 𝜆 where 𝜆 = [(me−ph ∗ ∗ /mband ) − 1],[67,68] and we findings. However, the fit quality is unsatisfactory; the observed use 𝜆 as a measure of e–ph coupling. It follows from the data dependence of A(n) is not that expected in a FL and the mag- in Figure 6b, that 5 < 𝜆 < 10, and accordingly, 6 < me−ph ∗ ∗ /mband nitude of the A coefficient differs by two orders of magnitude Adv. Sci. 2021, 8, 2004207 2004207 (9 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com from expectations for e–e scattering. This disconformity appears Structural Characterization: X-ray diffraction (XRD) techniques (𝜃–2𝜃 not only in SVO (intrinsic metal) but, as earlier pointed out, is symmetric scans and reciprocal space maps) had been used to determine shared by other conducting oxides (mainly doped semiconduc- the in-plane (a) and out-of-plane (c) cell parameters of the epitaxial films. Illustrative XRD patterns, extracted (a, c) parameters and tetragonal dis- tors). We emphasize here that this discrepancy is common to ox- tortion (c/a ratio) are shown in Figure S1, Supporting Information. The ides having a low occupation of narrow 3d-t2g bands. Two differ- film thickness was determined by X-ray reflectivity and/or by fitting of the ent scenarios have been considered to account for the available Laue fringes (when present). In agreement with previous reports,[23,24] it experimental data. We first note that the FS of these 3dx (x ≤ 1) is was found that the c/a ratio in SVO thin films differs from bulk SVO due to mostly formed by three interpenetrated cylinders oriented along epitaxial strain and growth-induced defects. Indeed, in SVO films grown the three principal axis and thus the FS has a 2D character. As on LSAT or NGO, the tetragonal c/a ratio varies systematically (0.986 < c/a < 1.006) with P(Ar), typically increasing when reducing P(Ar) as a result of argued, the extreme anisotropy of the FS has a profound impact the out-of-plane unit cell expansion in films grown at the lowest pressures. on the temperature dependence of the electron–phonon scatter- Electrical Characterization: Electrical measurements on the films had ing and a 𝜌(T) ≈ T2 dependence was predicted in some temper- been performed by using four-probe Van der Pauw contact configuration. ature range, which is roughly in agreement with observations in Hall effect and magnetoresistance were recorded by using magnetic fields SVO. For a 3d1 TMO, the FS includes up to three sheets, imply- up to ± 9 T applied perpendicular to sample surface. Illustrative Hall effect ing multiband conduction, which is consistent with the observed measurements are shown in Figure S3, Supporting Information. In agree- magnetoresistance. ment with earlier findings, the carrier density extracted from Hall effect, as- suming a single band, varied within the n ≈ (1.8 × 1022 – 2.6 × 1022 ) cm−3 Second, a polaronic (or vibronic) scenario has been explored. range depending on film thickness, substrate and growth conditions. The It has been shown that, assuming a single phonon mode (h̄𝜔0 ) to carrier density roughly coincided with the expected carrier density of SVO be relevant for the e–ph coupling, 𝜌(T) can be excellently fitted in (1 electron per unit cell). The carrier density of all films is included in Sec- all temperature range (5–300 K). It is observed that the frequency tion S3, Supporting Information. For the measurements of the Seebeck of the relevant phonon can be tuned by the tetragonal distortion coefficient, two Cr/Pt (5/50 nm) lines with four contacts (1 mm × 50 µm, in SVO imposed by epitaxial strain and growth conditions. 2 mm apart) were deposited by optical lithography on top of the film. After deposition, a current of 1 mA was driven through the Pt lines at room tem- Moreover, it is found that h̄𝜔0 and the e–ph coupling strength perature during 5 min to favor the recrystallization of Pt. The temperature (𝜆) both systematically increase under a tensile deformation of dependence of the resistivity of each Pt line was measured in several cool- the lattice (c/a < 1) and subsequently, the polaron effective mass, ing/heating ramps, until obtaining a reproducible result. The Pt resistivity also increases. was finally recorded on a heating ramp at 0.5 K min−1 and the recorded val- In summary, the results indicate that e–e scattering in a FL ues were used as local thermometers. Before each Seebeck measurement, alone does not account for the observed temperature dependence the sample was stabilized at the base temperature for at least 15 min to ensure the absence of spurious thermal gradients that could influence the of resistivity, mobility, and magnetoresistance in these transition determination of the intrinsic Seebeck voltage. Different currents were in- metal oxides. Instead, other factors need to be invoked. The jected through the heater until a constant temperature difference between cylindrical 2D-like nature of the FS of SVO and the e–ph cou- the Pt thermometers was achieved. The voltage between the Pt lines was pling giving rise to a polaronic transport, appear to be necessary measured at the same position with a switch. Fitting the voltage versus ingredients to account for available transport, calorimetric and temperature difference provides an accurate measurement of the Seebeck spectroscopic data. SVO and presumably other 3dx (x ≤ 1) oxides coefficient. An example of measurement procedure is given in Figure S5, may share a similar e–ph coupling that has remained largely un- Supporting Information. Optical Measurements: Spectroscopic ellipsometry measurements explored. These findings may have some practical consequences. (Figure S7, Supporting Information) were done in the far-infrared (FIR) To mention one, in the search for transparent conducting oxides, and mid-infrared (MIR) using an IR spectroscopic ellipsometer, based on where focus was on correlated electronic systems, the present Bruker Vertex 70v FTIR spectrometer, similar to one described in ref. [73]. findings suggest that enhanced e–ph coupling could be an Near-infrared to UV part of the spectrum was determined with Woollam efficient tool to bring the plasma frequency to the infrared VASE (variable angle of incidence spectroscopic ellipsometer). region. First Principles Calculations: The electronic structure of bulk SrVO3 was calculated using density functional theory (DFT),[74,75] as available in the all-electron full-potential localized orbitals basis set code.[76] The generalized-gradient approximation[77] was chosen for the exchange- 5. Experimental Section correlation energy and the summation in the Brillouin zone was performed Samples Preparation: SVO films of thickness 10–70 nm had been on the (20 × 20 × 20) k-mesh. The Fermi surface was determined based grown on single crystalline SrTiO3 (STO), (LaAlO3 )0.3 (Sr2 TaAlO6 )0.7 on the band energies calculated on the (50 × 50 × 50) k-mesh. The struc- (LSAT), NdGaO3 (NGO), and LaAlO3 (LAO) substrates by PLD, as de- tural parameters of bulk SrVO3 were taken from reported data for the bulk scribed in detail elsewhere.[23] Bulk SVO is cubic with cell parameter material (lattice parameter of 3.842 Å) and the measured (a, c) param- aSVO = 3.842 Å. The (pseudo)cubic cell parameters of the substrates (aS ) eters of the films were used when appropriate. In order to calculate the were: 3.905 Å (STO), 3.868 Å (LSAT), 3.863 Å (NGO), and 3.791 Å (LAO). phonon properties, the density functional perturbation theory as avail- The corresponding structural mismatch parameters (defined as f = (aS − able in the Quantum Espresso package was used.[78] In the first step, aSVO )/aS ) were: +1.59%, +0.65%, +0.52% and −1.37%, respectively. It is the electronic structure was determined self-consistently using the density known that the residual resistivity (𝜌0 ≈ 𝜌(5 K)) and the residual resistivity functional theory[74] within the PBE parametrization of the generalized- ratio (RRR = 𝜌(300 K)/𝜌(5 K)) both depend on growth conditions, namely gradient approximation. The electronic wavefunctions were represented gas pressure. Consequently, films had been grown at various Ar pressure by plane waves with an energy cutoff of 80 Ry. For the electronic density, (P(Ar) = 0 – 0.3 mbar).[24] Earlier experiments had shown that optimal larger cutoff of 320 Ry was used. The smearing for the electronic occu- SVO films can be grown at 750 °C, and this temperature had been kept pations was set to 0.02 Ry and the integration in the Brillouin zone was fixed for all films reported here.[23,24] To further modulate the carrier den- done on the Gamma-centered (10 × 10 × 10) k-mesh. The calculation of sity, another series of films had been deposited at various oxygen pressure the electron–phonon interaction was based on a denser (20 × 20 × 20) k- PO2 (from the base pressure of the chamber, that is, ≈ 4 × 10−7 mbar, to mesh and the phonon modes at the Gamma point were determined with 2 × 10−5 mbar). For growth details, see Mirjolet et al.[23] the threshold 10−16 . Adv. Sci. 2021, 8, 2004207 2004207 (10 of 12) © 2021 The Authors. Advanced Science published by Wiley-VCH GmbH www.advancedsciencenews.com www.advancedscience.com Supporting Information [13] X. Lin, B. Fauqué, K. Behnia, Science 2015, 349, 945. [14] C. A. Kukkonen, Phys. Rev. B 1978, 18, 1849. Supporting Information is available from the Wiley Online Library or from [15] N. W. Ashcroft, N. D. Mermin, Solid State Physics, Harcourt College the author. Publishers, San Diego, CA 1976. [16] N. F. Mott, Metal-Insulator Transitions, Taylor and Francis, London 1990. Acknowledgements [17] N. F. Mott, Rev. Mod. Phys. 1968, 40, 677. [18] M. Brühwiler, S. M. Kazakov, J. Karpinski, B. Batlogg, Phys. Rev. B Financial support from the Spanish Ministry of Science, Innovation and 2006, 73, 094518. Universities, through the “Severo Ochoa” Programme for Centres of Excel- [19] D. E. Shai, C. Adamo, D. W. Shen, C. M. Brooks, J. W. Harter, E. J. lence in R&D FUNFUTURE (CEX2019-000917-S) and the MAT2017-85232- Monkman, B. Burganov, D. G. Schlom, K. M. Shen, Phys. Rev. Lett. R (AEI/FEDER, EU), from Generalitat de Catalunya (2017 SGR 1377), 2013, 110, 087004. and from Deutsche Forschungsgemeinschaft (DFG), through TRR 288– [20] B. Bérini, V. Demange, M. Bouttemy, E. Popova, N. Keller, Y. Dumont, 422213477 (A05), is acknowledged. The authors would also like to ac- A. Fouchet, Adv. Mater. Interfaces 2016, 3, 1600274. knowledge the Computer Center of the Goethe University Frankfurt for [21] J. Wang, G. Rijnders, G. Koster, Appl. Phys. Lett. 2018, 113, 223103. providing the computational resources. The work of M.M. has been done [22] L. Shoham, M. Baskin, M. G. Han, Y. Zhu, L. Kornblum, Adv. Electron. as a part of the Ph.D. program in Physics at Universitat Autònoma de Mater. 2020, 6, 1900584. Barcelona, and was financially supported by the Spanish Ministry of Sci- [23] M. Mirjolet, H. B. Vasili, L. l. López-Conesa, S. Estradé, F. Peiró, J. ence, Innovation and Universities (BES-2015-075223). 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