Interface-Driven Two-Dimensional Superconductivity in Bilayers of BaBiO$_3$ and BaPbO$_3$

TL;DR

This study demonstrates two-dimensional superconductivity at the interfaces of BaBiO$_3$ and BaPbO$_3$ bilayers, with properties influenced by interface strain, advancing understanding of interface-driven superconductivity in oxide heterostructures.

Contribution

It reports the discovery of interface-driven 2D superconductivity in BaBiO$_3$/BaPbO$_3$ bilayers and elucidates the strain-induced nature of the superconducting state.

Findings

Superconductivity occurs at the interface of BaBiO$_3$ and BaPbO$_3$ bilayers.

Superconductivity exhibits characteristics of a Berezinskii-Kosterlitz-Thouless transition.

Transition temperature depends on the thickness of the BaPbO$_3$ layer.

Abstract

Besides the cuprate superconductors lead-doped barium bismuthate still attracts intense interest concerning its relatively high critical temperature and the nature of its superconductivity in vicinity to a charge density wave ordered topological insulator. Here we present bilayers of barium bismuthate and barium leadate and find two-dimensional superconductivity at their interfaces well described by current-voltage characteristics compatible with a Berezinskii-Kosterlitz-Thouless transition. Magneto-transport studies independently prove the two-dimensional character of the superconducting properties in these bilayers. The particular dependence of the superconducting transition temperature on the thickness of the barium leadate top layer suggests the formation of the superconducting state to be strain-induced through the interface.

Figures

Equations

$$\left|\frac{H_{c2}(\theta )\sin \theta }{H_{c2,\perp }}\right|+{\left(\frac{H_{c2}(\theta )\cos \theta }{H_{c2,\parallel }}\right)}^2=1.$$

$$d_{\mathrm{sc}}=\sqrt{\frac{6{\varphi }_0{H}_{c2,\perp }}{\pi H_{c2,\parallel }^2}},$$

Full text

Interfaces in oxide heterostructures serve as an inexhaustible source for the creation of new electronic phases well constrained on the nanoscale Mannhart and Schlom (2010). Specifically, superconductivity confined to an interface is of particular importance not only because it is easy to tune by external fields but especially because the interface electron system results from an electronic reconstruction in dependence on bulk states with their versatile ground states Hesper et al. (2000); Okamoto and Millis (2004); com (a); Zubko et al. (2011). The interface electron structure is controlled by bulk materials properties but also by the symmetry breaking at the edge of the respective bulk materials. The prominent oxide heterostructure of the two band insulators SrTiO3 (STO) and LaAlO3 (LAO) hosts such an interface-confined electron liquid Ohtomo and Hwang (2004, 2006); Breitschaft et al. (2010) showing two-dimensional (2D) superconductivity at temperatures below $\approx$ 300 mK Reyren et al. (2007); Caviglia et al. (2008). Structural inversion symmetry breaking at the interface introduces a sizable Rashba spin-orbit coupling Caviglia et al. (2010). Also cuprate bilayers present striking features of their superconducting states: a high-$T_{\mathrm{c}}$ state confined to 2–3 nm is formed between insulating La2CuO4 and metallic La1.55Sr0.45CuO4 Gozar et al. (2008), both of them not superconducting. Moreover, heterostructures built from the insulating oxides CaCuO2 and STO allow for a superconducting interface Di Castro et al. (2015).

Up to now, only few superconducting oxide interfaces have been realized. However it is an appealing challenge to identify further superconducting bilayers because different perovskite parent compounds account for novel characteristics of electronic states in proximity to the interface. For example, BaBiO3 (BBO) is predicted to be a large-energy gap topological insulator due to spin-orbit coupling (when electron doped) Yan et al. (2013), whereas the related compound BaPbO3 (BPO) is a bulk metal Ikushima and Hayakawa (1966). In fact, both BBO and BPO are expected to preserve a “hidden” topological insulator phase when electron or hole doped Li et al. (2015); com (b). Moreover, lead-doped bulk BBO is well-known to be superconducting Sleight (1974). That finding now incites the question of whether the interface between BBO and BPO is a 2D superconductor. If this is the case, do the topological surface states generate Majorana fermions Fu and Kane (2008) and is that modulated with the Berezinskiĭ-Kosterlitz-Thouless (BKT) transition which by itself is topologically driven? The potential realization of topologically protected edge states is certainly a strong motivation to explore the interfacial electronic system of BBO/BPO in detail, although here we keep our focus exclusively on establishing the formation of a 2D superconducting phase in bilayers of BBO and BPO.

BBO crystallizes at room and low temperatures in perovskite related monoclinic structures Sleight (2015). The underlying octahedral distortion leads to symmetric breathing-mode displacements forcing the Bi3+ and Bi5+ ions to distinct crystal sites forming a bond-order charge density wave (CDW) Cox and Sleight (1976, 1979); Varma (1988); Kim (1996). The charge-ordered state can be altered by, e. g., substituting the metal cations in BBO giving rise to tremendeous changes in the structural and electronic properties of this very special perovskite: in homogeneosly doped bulk samples of BaBi1-xPbxO3 (BBPO) three-dimensional superconductivity is observed for doping ranges of $0.65<x<0.95$ with a maximum superconducting transition temperature of $T_{\mathrm{c}}\approx 13$ K for $x$ near 0.75 Sleight et al. (1975); Than et al. (1980); Batlogg (1984); Climent-Pascual et al. (2011); Giraldo-Gallo et al. (2012). The onset of superconductivity is attributed to the formation of a bimorphic phase consisting of orthorhombic and tetragonal polymorphs in BBPO Climent-Pascual et al. (2011); Giraldo-Gallo et al. (2012); Balachandran and Rondinelli (2013); Giraldo-Gallo et al. (2015). By substituting barium by potassium, bulk samples of Ba1-xKxBiO3 yield maximum critical temperatures of $T_{\mathrm{c}}\approx 30$ K for a potassium concentration of $x=0.4$ Cava et al. (1988). The high-$T_{\mathrm{c}}$ superconductivity of these compounds was recently linked to correlation-enhanced electron-phonon coupling Yin et al. (2013). After the discovery of superconductivity in bulk samples, thin films of BBPO were soon realized by different growth techniques including sputtering Gilbert et al. (1978); Suzuki et al. (1980); Hidaka et al. (1983) and pulsed laser deposition (PLD) Zaitsev-Zotov et al. (1983).

Inspired by the discovery of a superconducting state at LAO/STO interfaces, we investigated BBO/BPO bilayers (BLs) in expectation to identify 2D superconductivity non-existent in both parent compounds. Thin films of nominal BaBi0.25Pb0.75O3, BBO, BPO, and BBO/BPO BLs were grown by PLD using commercially available, stoichiometric targets with purities of at least 99.9% at maximum reachable density. We used single crystalline (001) oriented STO crystals as substrates, which we cleansed in acetone and isopropyl prior to deposition. HF buffering STO substrates Kawasaki et al. (1994); Koster et al. (1998) had no significant impact on the results. The deposition temperatures were $\approx$ 635℃ for BaBi0.25Pb0.75O3 thin films and $\approx$ 552℃ for BBO, BPO thin films and BBO/BPO BLs controlled by laser-heating and monitored by pyrometers. The background pressure of pure oxygen was kept mass-flow controlled at $\approx$ 1 mbar during growth. Our PLD system is equipped with a KrF laser having a fluency of $\approx$ 2 J/cm2. We used laser pulse energies in the range of 550–750 mJ and laser pulse frequencies of 3–5 Hz. After deposition the samples were cooled to $\approx$ 400℃ within three minutes and annealed at a background pressure of oxygen of $\approx$ 400 mbar for at least 17 minutes before the vacuum chamber was evacuated again.

For BaBi0.25Pb0.75O3 thin films we used 1000 laser pulses (LP) resulting in film thicknesses of $\approx$ 420 nm. For thin films of BBO and BPO we used 50–150 LP corresponding to film thicknesses of $\approx$ 25–75 nm for BBO and $\approx$ 17–50 nm for BPO. Concerning the BBO/BPO BLs we kept the thickness of the BBO starting layer constant (always 100 LP) and only varied the number $N$ of LP of the BPO top layer.

All grown BaBi0.25Pb0.75O3 thin films show an increase in resistance with decreasing temperature and a superconducting transition at $T_{\mathrm{c,ip}}\approx 8$ K, which is determined at the inflection point (ip) of $R(T)$ at the transition (see Fig. 1, blue filled triangles facing right).

BBO and BPO thin films display peaks consistent with only (00$l$) oriented planes in routinely taken x-ray diffraction (XRD) experiments. BBO thin films are insulating with resistances ranging from M$\Omega$ to G$\Omega$ over the whole accessible temperature range. Pure BPO thin films instead turn out to be metallic (see Fig. 1, gray hexagons).

BBO/BPO BLs reveal only peaks classified by (00$l$) orientation in XRD studies separated in individual reflexes for BBO and BPO, respectively. Peaks assigned to a homogeneously doped BaBi1-xPbxO3 phase could not be identified (see Supplemental Material sup , Fig. S1). BLs with $N=30$ are semiconducting at all accessible temperatures, BLs with $N=40$ show semiconductor-to-superconductor transitions with $T_{\mathrm{c,ip}}\approx 3.0$ K (see Fig. 1, pink filled squares). An increase of the BPO thickness ($N=60$) shifts the superconducting transition temperature to values as high as $T_{\mathrm{c,ip}}=3.5$ K (see Fig. 1, red diamonds). Interestingly, with further increase of $N$ we observe a dramatic reduction of the critical temperature ($N=\{80,100\}$) and no superconducting transition for samples with $N=150$. The observation of an optimal BPO thickness to reach maximum $T_{\mathrm{c}}$ and the suppression of superconductivity beyond this thickness indicates that the BL superconductivity is related to the interface (see below) and may also be dependent on the thickness of the BBO starting layer (in the case of atomically thin BBO layers which is not investigated here).

If the superconducting transition is really driven by the interface, then a likely scenario is that a 2D superconducting sheet is formed within the bilayered samples. Such behavior is described by a BKT transition Berezinskiĭ (1971, 1972); Kosterlitz and Thouless (1973); Kosterlitz (1974). A convenient experimental method to characterize the transition into the algebraically ordered state is the familiar progression of current-voltage (IV) characteristics taken at temperatures around $T_{\mathrm{c}}$: the applied voltage $V$ breaks vortex-antivortex pairs and yields at $T=T_{\mathrm{BKT}}$ the well-known $V=I^{\alpha}$ behavior with $\alpha=3$, whereas the current $I$ responds linear in $V$ for a state with free vortices above $T_{\mathrm{BKT}}$ Halperin and Nelson (1979). A direct validation of this observation can be made by analyzing the $R(T)$ dependence. For a BKT transition, the resistance follows $R\propto R_{\mathrm{n}}\exp(-b/\sqrt{t})$ Kosterlitz and Thouless (1973) near $T_{\mathrm{BKT}}$ with $b$ being a material parameter in the order of unity Halperin and Nelson (1979) and $t=T/T_{\mathrm{BKT}}-1$. Our data yield $b=1.22$ and $T_{\mathrm{BKT}}=3.26$ K matching the value $T_{\mathrm{BKT}}=3.19$ K obtained independently from the IV measurements (see Supplemental Material sup , Fig. S2). The perfect agreement of our results (see Fig. 2) with the BKT predictions signifies unambiguously that indeed a 2D superconducting sheet is formed through the interface. The ohmic regime observed below $T_{\mathrm{BKT}}$ for small currents is attributed to be responsible for the deviations from the fits due to finite size effects Medvedyeva et al. (2000).

An estimate of the thickness of the superconducting sheet can be retrieved by measuring the magneto-transport properties of our BLs. Such measurements are evaluated in the Ginzburg-Landau (GL) regime for magnetic fields up to $H_{\mathrm{c2}}$. They also act as an independent proof for the observed 2D superconductivity given that the sheet thickness $d_{\mathrm{sc}}$ is comparable to or smaller than the GL coherence length $\xi_{\mathrm{GL}}$ Tinkham (1996); De Gennes (1999). Fig. 3 exemplarily summarizes the observed dependence of the upper critical magnetic field $H_{\mathrm{c2}}$ of a BL with $N=60$ on the angle $\theta$, in respect to the sample plane of the externally applied swept magnetic field. As expected for a 2D superconductor the in-plane field $H_{\mathrm{c2,\parallel}}$ ($\theta=0$°) is much higher than the out-of-plane field $H_{\mathrm{c2,\perp}}$ ($\theta=90$°). Following Tinkham’s analysis Tinkham (1963, 1964); Harper and Tinkham (1968) both magnetic fields can be experimentally determined on the basis of the relation:

[TABLE]

The GL theory for thin superconducting sheets allows to express both magnetic fields in terms of the magnetic flux quantum $\phi_{0}$, the thickness $d_{\mathrm{sc}}$ of the 2D superconducing sheet, the product of the penetration depth and the thermodynamic critical field Ginzburg and Landau (1950). Eliminating last said quantity the thickness $d_{\mathrm{sc}}$ can be calculated Harper and Tinkham (1968) with the help of experimentally obtained values of $H_{\mathrm{c2,\parallel}}$ and $H_{\mathrm{c2,\perp}}$ via

[TABLE]

supporting a thickness of the 2D superconducting sheet to be in the range of $d_{\mathrm{sc}}\approx 11.8$ nm being clearly smaller than the nominal thickness of the BPO top layer. The calculated thickness $d_{\mathrm{sc}}$ is robust against different experimental determination of $H_{\mathrm{c2}}$ (see Supplemental Material sup , Fig. S3). In contrast, $d_{\mathrm{sc}}$ of a nominal BaBi0.25Pb0.75O3 thin film (60 LP) is of the same size as the overall thickness of the thin film (see Supplemental Material sup , Fig. S4).

The coherence length of the BL ($N=60$) is estimated to be $\xi_{\mathrm{GL}}\approx 11.0$ nm, the value of which we extracted from the temperature dependence of the upper critical magnetic field obtained from $R(T,H)$ measurements (see Supplemental Material sup , Fig. S5). This is consistent with the prerequisites of the GL theory Tinkham (1996).

We suggest that the occurrence of 2D superconductivity in BBO/BPO BLs results from a strained growth of BPO on top of BBO possibly also affecting the crystallographic phase of BBO at the interface. Reciprocal space maps, which were taken for BLs with $N=50$ and $N=150$ (see Fig. 4a and 4b), prove that BBO grows epitaxially and fully relaxed on STO substrates consistent with domain-matched expitaxy Zheleva et al. (1994); Narayan and Larson (2003). BPO however grows strained on top of BBO for thin layers ($N=50$, Fig 4a) and relaxes more and more for thicker layers ($N=150$, Fig. 4b). We studied the strain effect in more detail in XRD $\theta/2\theta$ measurements taken for several BLs with different $N$ (see Fig. 4c). With increasing $N$ the $2\theta$ position of the (004) peak of BPO shifts towards larger angles supporting a relaxation of interface-induced strain in the on-growing lattice of BPO. For BLs with $N=\{80,100,150\}$ the peak position of BPO stabilizes serving as an indication for reaching a relaxed state.

These observations aid the idea of a strain-only effect at the interface: as BLs with $N=50$ become superconducting, whereas those with $N=150$ stay metallic in the accessible temperature range, a possible existence of an established homogeneously doped region equal to BaBi1-xPbxO3 is hardly conceivable. Ultimately a most favorable thickness of the BPO film exists to assign a robustly induced superconducting phase with maximum $T_{\mathrm{c}}$.

In this study we have shown that BLs of BBO and BPO become superconducting depending on the thickness of the BPO top layer with transition temperatures as high as $T_{\mathrm{c,ip}}=3.5$ K for our given sample layout. The electrical transport characterization clearly revealed a BKT transition identifying a 2D superconducting state within the BLs. Magneto-transport investigations independently provide evidence for the two-dimensionality of the superconducting sheet estimating the thickness of the sheet to be $d_{\mathrm{sc}}\approx 11.8$ nm. X-ray studies suggest an interface-driven epitaxial-matched strain effect at the interface between BBO and BPO responsible for the occurrence of the observed 2D superconducting state. The encountered transition in BBO/BPO bilayers is a remarkable further precedent of interface driven ground-state variance. With the identification of a robust superconducting state at the interface of two “hidden” topological insulators Li et al. (2015) it will be compelling to determine the surface states of the superconducting sheet in future work.