Enhancing superconductivity in SrTiO₃ films with strain

A doubling of the superconducting transition temperature occurs in strained SrTiO₃ films, which are known to become ferroelectric.

Abstract

The nature of superconductivity in SrTiO₃, the first oxide superconductor to be discovered, remains a subject of intense debate several decades after its discovery. SrTiO₃ is also an incipient ferroelectric, and several recent theoretical studies have suggested that the two properties may be linked. To investigate whether such a connection exists, we grew strained, epitaxial SrTiO₃ films, which are known to undergo a ferroelectric transition. We show that, for a range of carrier densities, the superconducting transition temperature is enhanced by up to a factor of two compared to unstrained films grown under the same conditions. Moreover, for these films, superconductivity emerges from a resistive state. We discuss the localization behavior in the context of proximity to ferroelectricity. The results point to new opportunities to enhance superconducting transition temperatures in oxide materials.

INTRODUCTION

Although SrTiO₃ was the first oxide superconductor to be discovered (1), the nature of its superconducting state has been a longstanding subject of debate in the literature (2–10), reflecting in many ways the elusiveness of other families of superconductors, such as the cuprates. A striking feature is that superconductivity already appears at very low carrier densities (2, 11), when the Fermi temperature is lower than the Debye temperature, which is at odds with the Bardeen-Cooper-Schrieffer (BCS) theory. Bulk, undoped SrTiO₃ is an incipient ferroelectric for which quantum fluctuations suppress a low-temperature transition to a ferroelectric ground state at the lowest temperatures (12, 13). Several recent theoretical proposals have suggested that a connection between the ferroelectric and superconducting properties exists (14–17), providing strong motivation for developing experimental approaches that search for such a link.

The complex relationship between metallicity and ferroelectricity is one of the main challenges in experimental tests of the role of (incipient) ferroelectricity in the superconducting pairing mechanism of SrTiO₃. In particular, free carriers, needed for superconductivity, and ferroelectricity do not easily coexist. For example, sufficiently large concentrations of mobile carriers can screen the splitting of the transverse and longitudinal optical phonon modes (18, 19), which is essential for ferroelectricity in materials such as SrTiO₃ (20). Furthermore, conducting samples cannot sustain sufficiently large electric fields that are needed to switch a ferroelectric polarization. Thus, although there are no fundamental reasons why the two properties cannot coexist (21), practically, they are difficult to obtain within a homogeneous material.

Despite these challenges, several recent experiments have reported on the superconductivity of SrTiO₃ crystals that were tuned toward ferroelectricity by using approaches that were previously known (22–24) to stabilize ferroelectricity in insulating SrTiO₃. In particular, oxygen isotope doping (25) and alloying with Ca (26) were found to result in modest changes in T_C (superconducting transition temperatures) of doped single crystals.

Epitaxial coherency strains are well known to stabilize ferroelectricity in SrTiO₃ films (27–30). Films under different epitaxial strains thus offer an attractive platform to compare the superconducting properties of films poised to undergo a ferroelectric transition with those that remain paraelectric. Here, we show that doped, compressively strained SrTiO₃ films exhibit T_C values that are enhanced by a factor of two compared to unstrained films. Moreover, films with enhanced T_C exhibit a pronounced upturn in the normal state resistivity with decreasing temperature, which is highly unusual. In contrast, films with higher carrier densities remain metallic and do not exhibit enhanced T_C, although they are strained by the same amount. We discuss the implications of the results with regard to the connection between superconductivity and (incipient) ferroelectricity in SrTiO₃.

RESULTS

Electrical measurements were carried out on epitaxial SrTiO₃ films, which were grown on (001) LSAT [(LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7] and SrTiO₃ substrates using a hybrid molecular beam epitaxy (MBE) technique (31, 32). The films were doped with different amounts of Sm⁺³ to obtain a range of carrier densities.

Figure 1A shows the resistivities (ρ) of strained Sm:SrTiO₃ films grown on LSAT with different carrier densities, measured between 300 and 2 K. Here, the resistivities were determined from the sheet resistance and film thickness (200 nm) measured by cross-sectional transmission electron microscopy. The highest doped film (n_3D = 2.8 × 10²⁰ cm⁻³ at 300 K, where n_3D is the carrier density determined from Hall measurements) shows metallic behavior, $\frac{\mathit{d}\mathrm{\rho }}{\mathit{d}\mathit{T}}>0$, down to 1.8 K. In contrast, lower doped films (n_3D = 2 × 10¹⁹, 6 × 10¹⁹, and 1.4 × 10²⁰ cm⁻³) exhibit a crossover to $\frac{\mathit{d}\mathrm{\rho }}{\mathit{d}\mathit{T}}<0$ upon lowering the temperature. The transition temperatures, defined as$\frac{\mathit{d}\mathrm{\rho }}{\mathit{d}\mathit{T}}=0$, for films with n_3D = 6 × 10¹⁹ and 1.4 × 10²⁰ cm⁻³ are ~110 and ~60 K, respectively (see arrows). The lowest doped film with n_3D = 2 × 10¹⁹ cm⁻³ not only demonstrates an upturn in resistivity at low temperatures but also shows a more complicated temperature dependence. All films exhibit an abrupt decrease in the Hall carrier density upon lowering the temperature (Fig. 1B). Roughly the same mobile carrier density (4 × 10¹⁹ to 7 × 10¹⁹ cm⁻³) is lost in all films.

Fig. 1. Transport properties in the normal state.

(A) Resistivity as a function of temperature (T) for compressively strained Sm-doped SrTiO₃ on LSAT substrates with different carrier densities (the legend states the carrier densities at 300 K). Upturns in the resistivity are indicated by arrows. (B) Hall carrier densities (n_3D) as a function of temperature. Lines are a guide for the eye.

Figure 2 shows ρ between 1 K and 10 mK. All films become superconducting at low temperatures. Taking T_C as the temperature for which ρ corresponds to$\frac{{\mathrm{\rho }}_{\mathrm{n}}}{\mathit{e}}$, where ρ_n is the normal state value and e is Euler’s number, the values for T_C are 0.37, 0.60, 0.67, and 0.16 K for films with n_3D = 2 × 10¹⁹, 6 × 10¹⁹, 1.4 × 10²⁰, and 2.8 × 10²⁰ cm⁻³, respectively.

Fig. 2. Superconducting transitions for strained Sm-doped SrTiO₃ films with different carrier densities.

The resistivity as a function of temperature between 1 K and 10 mK without an applied magnetic field is shown. The legend indicates the Hall carrier densities measured at 300 K. Lines are a guide for the eye.

Figure 3 compares the T_C values for the films shown in Fig. 2 with those of other SrTiO₃ samples with similar carrier densities reported in the literature, including SrTiO₃ crystals that were tuned toward ferroelectricity using the approaches mentioned in the Introduction (11, 25, 26, 33, 34). The T_C of the Sm:SrTiO₃ film with the highest doping density, which remains metallic, is comparable to previous reports. In contrast, films with lower doping densities have a substantially increased T_C, which reaches almost a factor of two near the peak of the superconducting dome (“optimal doping”). Thus, the enhancement of T_C is seen for underdoped and optimally doped films but not on the overdoped side of the superconducting dome of SrTiO₃. For direct comparison with unstrained films grown by the same MBE method and T_C defined in the same way, Fig. 3 also shows T_C of unstrained Sm- and La-doped SrTiO₃ thin films grown on SrTiO₃ substrates, which show T_C similar to La-doped SrTiO₃ crystals reported in the literature (34). All samples shown in Fig. 3, except for the three lower doped films on LSAT, which have enhanced T_C, exhibit metallic behavior.

Fig. 3. Comparison of T_C of strained and unstrained SrTiO₃.

T_C values of strained and unstrained La- and Sm-doped SrTiO₃ films with different carrier densities grown on LSAT and SrTiO₃ substrates, respectively (filled circles), are shown. T_C values of SrTiO₃ crystals taken from the literature are also shown, some of which were tuned toward a ferroelectric transition (triangles). Literature data are from Lin et al. (11), Stucky et al. (25), Rischau et al. (26), Koonce et al. (33), and Suzuki et al. (34). Lines are a guide for the eye.

Figure 4 shows the superconducting upper critical magnetic field, H_C2, as a function of temperature. Data follow the relation${\mathit{H}}_{\mathrm{C}2}={\mathit{H}}_{\mathrm{C}2}(0)\frac{1-{\mathit{t}}^2}{1+{\mathit{t}}^2}$, where t = T/T_C, which is shown as dashed lines, similar to the behavior observed in La-doped films (35). The values of H_C2 (i.e., 1.75 T at 50 mK for the film with n_3D = 6 × 10¹⁹ cm⁻³) are comparable with those reported for La-doped SrTiO₃ films (35). Table 1 lists quantities derived from the data, including the values for the BCS superconducting gap, Δ = 1.75 k_BT_C, where k_B is Boltzmann’s constant, and the superconducting coherence length, ${\mathrm{\xi }}_0=\sqrt{{\mathrm{\varphi }}_0/2\mathrm{\pi }{\mathit{H}}_{\mathrm{C}2}}$, where ϕ₀ is the magnetic quantum flux. Here, films with n_3D = 2 × 10¹⁹ and 1.4 × 10²⁰ cm⁻³, despite having different critical temperatures, show relatively similar H_C2 at low temperatures. Thus, T_C peaks near n_3D = 1.4 × 10²⁰ cm⁻³, while H_C2 peaks near n_3D = 6 × 10¹⁹ cm⁻³. The behavior of H_C2 might be related to the multiband nature of this superconductor (36) and requires further investigations beyond the scope of the present study.

Fig. 4. Dependence of the upper critical field H_C2 at different temperatures.

The dashed lines are fits to the data (see text for details).

Table 1. Values for T_C, H_C2, Δ, and ξ for Sm-doped SrTiO₃ films on LSAT with different carrier densities.

n3D at 300 K (cm−3)	TC (K)	HC2 at 50 mK (T)	Δ (μeV)	ξ (nm)
2 × 1019	0.37	0.83	56	18
6 × 1019	0.6	1.75	90	14
1.4 × 1020	0.67	0.91	100	19
2.8 × 1020	0.16	0.07	20	67

DISCUSSION

To briefly summarize the results, our main findings are as follows: (i) There is an enhancement in T_C of compressively strained SrTiO₃ films up to a factor of two, and (ii) the increase in T_C depends on the carrier density and (iii) it is connected to the presence of a crossover in the resistivity in the normal state to $\frac{\mathit{d}\mathrm{\rho }}{\mathit{d}\mathit{T}}<0$ at low temperatures.

The first important conclusion from these results is that the increase in T_C is caused not simply by the epitaxial strain, such as strain-induced modification of phonon modes. If this were the case, then all films, independent of their carrier density, should exhibit enhanced T_C, because they are all under the same epitaxial film strain. Instead, the carrier density dependence of the enhancement in T_C and the resistivity upturn point to a direct connection between a (proximal) ferroelectric state and the modified superconducting properties.

As mentioned above, SrTiO₃ films grown on LSAT substrates are known to transition to a ferroelectric state as a result of the epitaxial coherency strain (27–30). Even SrTiO₃ films containing substantial amounts of carriers (on the order of 10¹⁹ cm⁻³) were found to undergo a ferroelectric transition around 140 K (29). Thus, the films in the present study are, at minimum, in proximity to a ferroelectric transition.

Beyond this, the observed crossover in the temperature dependence of the resistivity also hints at the emerging ferroelectric or polar nature of the films. The behavior is in marked contrast to unstrained SrTiO₃ films grown on SrTiO₃ [Fig. 3; see also (37) for more data] or bulk crystals of SrTiO₃ (38), which remain metallic even with orders of magnitude lower carrier densities. The reason is the high dielectric constant of SrTiO₃. The Mott criterion (39) for metallic behavior, ${\mathit{n}}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\mathit{a}}_{\mathrm{B}}\approx 0.25$, where a_B is the Bohr radius, is thus easily exceeded, even if we assume a substantially reduced dielectric constant (~1000), which is more typical for ferroelectric SrTiO₃ (29). While carrier localization can be caused by disorder or traps, unstrained films with similar dopant densities and disorder remain metallic. Screening of a polar charge is a reasonable explanation for the observed localization of a fixed amount of the mobile charge density (Fig. 1B). Remotely doped ferroelectric BaTiO₃ films undergo a transition that is very similar to the one observed here (40). In contrast, T_C is not increased at higher carrier densities on the overdoped side of the superconducting dome, which remains metallic. At high carrier densities, we expect the long-range interactions needed for ferroelectricity to be screened (20). While there is currently no agreement in the literature as to the pair-breaking mechanism that causes T_C to decrease on the overdoped side, it is expected to play a role here as well.

In summary, our experimental results, especially the carrier density dependence of the observed T_C enhancement, should be of interest for testing the different theoretical models that have been proposed in the literature that relate superconductivity in SrTiO₃ to a (proximal) ferroelectric state (14–17). Independent of the precise mechanism, the results point to opportunities to enhance T_C by searching for superconducting oxides that are in proximity to ferroelectricity. It would also be interesting to explore whether similar enhancement could be obtained in superconducting/ferroelectric composite structures.

Last, we would like to note that, during the preparation of this article, we became aware of a recent report of increased T_C in SrTiO₃ crystals under uniaxial tensile strain (41). The increase in T_C was attributed to a strain-induced modification of phonon modes, suggesting that other promising approaches to enhance T_C exist for SrTiO₃.

MATERIALS AND METHODS

Epitaxial SrTiO₃ films, which were doped with Sm⁺³, were grown by a hybrid MBE technique described elsewhere (31, 32). The LSAT substrate temperature was 900°C (thermocouple reading), and the growth rate was ~130 nm/hour. The carrier density scaled with the Sm flux during growth, consistent with all Sm dopants acting as donors (+3 formal valence state). The lattice mismatch results in compressive in-plane film strains (~1%), and lightly doped films are known to show a ferroelectric transition at ~140 K on this substrate (29). The film thickness was ~200 nm. This thickness is below the critical thickness of SrTiO₃ on LSAT (42) while being sufficiently thick to avoid substantial carrier depletion from the well-known surface depletion of SrTiO₃ (43). A combination of high-resolution x-ray diffraction (see fig. S1) and reflection high-energy electron diffraction oscillations was used to calibrate the film thickness. Laue thickness fringes were visible in x-ray diffraction and confirmed the film thickness. Reciprocal space mapping (see fig. S2) was carried out around the 113 reflection of SrTiO₃ and used to determine the in- and out-of-plane lattice parameters of the film and to confirm that the films remained coherently strained to the LSAT. Cross-sectional high-angle annular dark-field (HAADF) imaging in scanning transmission electron microscopy (STEM) was also used to determine the film thickness and structural quality (fig. S3). We also investigated unstrained Sm-doped SrTiO₃ and La-doped SrTiO₃ films on (001) SrTiO₃ substrates grown under the same conditions.

Temperature-dependent measurements of the longitudinal and Hall resistances were carried out using a Quantum Design Physical Property Measurement System. The Hall carrier densities extracted from the Hall measurements, n_3D = −1/(teR_H), where t is the thickness of the Sm_xSr_1−xTiO₃ thin film, e is the electron charge, and R_H is the Hall coefficient R_H = dR_xy/dB, were extracted from linear fits to the transverse resistance R_H(B) with the magnetic field (B). Magnetotransport measurements below 1 K were carried out in a dilution refrigerator (Triton, Oxford Instruments Group). Transport measurements were carried out in van der Pauw geometry with square-shaped samples (5 mm × 5 mm). Ohmic contacts (40-nm Ti/400-nm Au) were deposited on the sample corners (<0.5 mm × 0.5 mm) through a shadow mask using an electron beam evaporation. The superconductivity measurements were carried out using a lock-in amplifier (SR830, Stanford Research Systems) in AC mode with an excitation current of 1 μA and a frequency of 33.33 Hz. The critical field was obtained from measuring the longitudinal resistance while sweeping an out-of-plane magnetic field at different temperatures (see fig. S4).

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/4/eaaw0120/DC1

Fig. S1. 2θ-ω scan of a SrTiO₃ film on LSAT near the 001 reflections.

Fig. S2. RSM of a SrTiO₃/LSAT heterostructure around the 113 reflection.

Fig. S3. Cross-sectional HAADF-STEM images.

Fig. S4. Magnetic field dependence of the superconducting transition.

Fig. S5. Superconducting transitions for Sm- and La-doped SrTiO₃ films grown on SrTiO₃ substrates.

Fig. S6. Resistivity as a function of temperature for Sm-doped SrTiO₃ films grown on SrTiO₃ substrates.