Enhancement of electron mobility at oxide interfaces induced by WO3 overlayers

TL;DR

This study demonstrates that amorphous WO3 overlayers can significantly enhance electron mobility at oxide interfaces by controlling defect formation, leading to high mobility and effective mass in LaAlO3/SrTiO3 heterostructures.

Contribution

Introduction of amorphous WO3 overlayers as a versatile method to improve electron mobility and control defects at oxide interfaces, independent of crystal symmetry constraints.

Findings

Electron mobility up to 80,000 cm²/Vs achieved.

Sharp insulator-to-metal transition observed.

High magnetoresistance of 900% at 10 T and 1.5 K.

Abstract

Interfaces between complex oxides constitute a unique playground for 2D electron systems (2DES), where superconductivity and magnetism can arise from combinations of bulk insulators. The 2DES at the LaAlO3/SrTiO3 interface is one of the most studied in this regard, and its origin is determined by both the presence of a polar field in LaAlO3 and the insurgence of point defects, such as oxygen vacancies and intermixed cations. These defects usually reside in the conduction channel and are responsible for a decreased electronic mobility. In this work we use an amorphous WO3 overlayer to control the defect formation and obtain an increased electron mobility and effective mass in WO3/LaAlO3/SrTiO3 heterostructures. The studied system shows a sharp insulator-to-metal transition as a function of both LaAlO3 and WO3 layer thickness. Low-temperature magnetotransport reveals a strong magnetoresistance reaching 900% at 10 T and 1.5 K, the presence of multiple conduction channels with carrier mobility up to 80 000 cm2/Vs and an unusually high effective mass of 5.6 me. The amorphous character of the WO3 overlayer makes this a versatile approach for defect control at oxide interfaces, which could be applied to other heterestrostures disregarding the constraints imposed by crystal symmetry.

Tables

Table 1. Table 1: Transport parameters. Mobility, carrier density, sheet resistance and mean free path of the conductive channels extracted from the fits in fig.   3b .

	$\mu$ (${\mathrm{cm}}^2{V}^{-1}{s}^{-1}$)	$n_{2D}$ (${\mathrm{cm}}^{-2}$)	${\rho }_0$ ($\Omega$)	$\lambda$ ($\mathrm{nm}$)
${(2,4)}_{\mathrm{𝙸𝙸}}$	$\mathrm{80\hspace{0.17em}000}$	$9.3\text{×}{10}^{12}$	$8$	$4100$
${(2,4)}_{𝙸}$	$3600$	$1.7\text{×}{10}^{13}$	$100$	$250$
${(4,0)}_{𝙸}$	$840$	$2.6\text{×}{10}^{13}$	$290$	$70$

Equations

$${\rho }_{xx}=\frac{(n_{\mathtt{I}}{\mu }_{\mathtt{I}}+n_{\mathtt{II}}{\mu }_{\mathtt{II}})+(n_{\mathtt{I}}{\mu }_{\mathtt{II}}+n_{\mathtt{II}}{\mu }_{\mathtt{I}}){\mu }_{\mathtt{I}}{\mu }_{\mathtt{II}}{B}^2}{(n_{\mathtt{I}}{\mu }_{\mathtt{I}}+n_{\mathtt{II}}{\mu }_{\mathtt{II}}{)}^2+(n{\mu }_{\mathtt{I}}{\mu }_{\mathtt{II}}B{)}^2}\cdot \frac{1}{e},$$

$${\rho }_{xy}=\frac{(\pm n_{\mathtt{I}}{\mu }_{\mathtt{I}}^2\pm n_{\mathtt{II}}{\mu }_{\mathtt{II}}^2)+n({\mu }_{\mathtt{I}}{\mu }_{\mathtt{II}}B{)}^2}{(n_{\mathtt{I}}{\mu }_{\mathtt{I}}+n_{\mathtt{II}}{\mu }_{\mathtt{II}}{)}^2+(n{\mu }_{\mathtt{I}}{\mu }_{\mathtt{II}}B{)}^2}\cdot \frac{B}{e},$$

$$\Delta {\rho }_{xx}=4{\rho }_{\mathrm{c}}{\mathrm{e}}^{-\alpha T_{\mathrm{D}}}\frac{\alpha T}{\sinh (\alpha T)}\sin \left(2\pi \frac{{\omega }_{\mathrm{SdH}}}{B}\right),$$

Full text

The formation of a two-dimensional electron system (2DES) at the interface between band insulators \ceSrTiO3 (STO) and \ceLaAlO3 (LAO) is among the most intriguing effects studied in oxide electronics Ohtomo and Hwang (2004). Gate tunable superconductivity Reyren et al. (2007); Caviglia et al. (2008), strong spin-orbit coupling Caviglia et al. (2010a); Diez et al. (2015) and magnetism Bert et al. (2011); Li et al. (2011) are some of the many phenomena observed. The origin of this 2DES is a long standing question in the solid state community and recent results indicate that a consistent picture should take into account both the built-in polar field and the presence of point defects Nakagawa et al. (2006); Gunkel et al. (2012); Yu and Zunger (2014). Among these, oxygen vacancies and cation off-stoichiometry in STO are capable of inducing a 2DES Kalabukhov et al. (2007); Warusawithana et al. (2013). However, defects residing in the conductive channel are usually responsible for a decreased electronic mobility Bristowe et al. (2011). In order to promote high electron mobility, it is crucial to confine donor sites away from the conducting plane, without preventing the 2DES formation in the STO top layers. Previous attempts to control the defect concentration profile and thus enhance the mobility involved the use of crystalline insulating overlayers Huijben et al. (2013); Chen et al. (2015), adsorbates Xie et al. (2013), amorphous materials Chen et al. (2013) and even thin metallic layers Wu et al. (2013); Lesne et al. (2014). A promising material to control defect formation is tungsten oxide \ceWO3. The several possible oxidations states of tungsten make \ceWO3 particularly active in undergoing redox reactions. For this reason this material is often utilized in electrochemical applications and electrochromic devices Deb (2008); Meng et al. (2015); Cong et al. (2016). Also, both crystalline and amorphous \ceWO3 can host vacancies and interstitial atoms, thus allowing cation accommodation and diffusion, with a tendency to form compounds such as tungsten bronzes Arab et al. (2013); He et al. (2016). Recent progress demonstrated the high-quality growth of \ceWO3 thin films on perovskite materials Du et al. (2014); Leng et al. (2015); Altendorf et al. (2016).

In this work we combine the use of a crystalline LAO/STO interface with the high reactivity of amorphous \ceWO3 to realise a high-mobility metallic 2DES in \ceWO3 / LAO / STO heterostructures. Our approach is based on the tendency of \ceWO3 to undergo redox reactions, whose contribution is primarily manifested by the reduction of the critical LAO thickness required for the formation of a 2DES. We characterise the transport properties of this system as a function of \ceWO3 and \ceLAO thickness and find multi-band conduction and an increased electron mobility up to $80\,000\text{\,}{\mathrm{cm}}^{2}\text{\,}{\mathrm{V}}^{-1}\text{\,}{\mathrm{s}}^{-1}$. The multi-band conduction leads to a remarkably strong classical magnetoresistance, which reaches 900% at $10\text{\,}\mathrm{T}$ and $1.5\text{\,}\mathrm{K}$. Furthermore, the analysis of Shubnikov-de Haas oscillations unveils an unusually large effective mass of the highly mobile electrons.

Ultra-thin heterostructures of amorphous \ceWO3 and crystalline LAO are grown on \ceTiO2-terminated STO (001) substrates by pulsed laser deposition (details on the growth are provided in the supplementary information). We denote by $(m,n)$ the crystalline equivalent number of unit cells (u.c.) of \ceWO3 and LAO, respectively, that form the heterostructure. To investigate structurally the \ceWO3 / LAO / STO heterostructure, we perform high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). The HAADF-STEM images in figs. 1a and 1b acquired from a $(4,2)$ heterostructure show uniform layers of amorphous \ceWO3 corresponding to 4 u.c. in thickness, followed by 2 u.c. of crystalline LAO. Due to the atomic number difference between La and Sr, the HAADF signal from the LAO is more intense than from the underlying STO substrate, as expected. To further confirm the growth of LAO, electron energy loss spectroscopy (EELS) is subsequently performed. With an energy dispersion of $0.25\text{\,}\mathrm{eV}\mathrm{/}\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{l}$, the Ti-L2,3 and La-M4,5 edges are recorded simultaneously, providing atomic-resolution Ti and La elemental maps as presented in figs. 1c, 1d and 1e. By averaging the La map parallel to the interface in fig. 1f, two clear peaks are shown for La, consistent with the growth of 2 LAO layers in our heterostructure. However, significant diffusion of La into the \ceWO3 is also observed. The surface of all heterostructures is additionally measured by atomic force microscopy (fig. 1g), revealing the same regular steps and terraces of the underlying STO substrate, indicating uniform film growth.

The series of resistance versus temperature curves of $(m,n)$ heterostructures in fig. 2a, shows a sharp tickness-dependent insulator-to-metal transition. The transport measurements are performed in a Van der Pauw configuration (see methods for details). For different $(m,n)$ combinations the samples show either insulating (orange curves) or metallic (blue curves) character, with a sharp transition between the two regimes as function of layer thickness. This can be noted comparing the $(4,1)$ and $(4,2)$ curves, where a variation of a single u.c. of the LAO interlayer determines a three orders of magnitude resistivity difference at room temperature, which diverges upon cooling. It is noteworthy that the onset of the metallic state corresponds to the sheet resistance value $h/e^{2}$ (dotted line in fig. 2a) which is the quantum limit for metallicity in 2D Mott (1985), suggesting this electronic system has a two-dimensional nature.

The interplay between \ceWO3 and LAO thicknesses is summarised in the phase diagram of fig. 2b, where we indicate with a shaded orange background the $(m,n)$ combinations resulting in insulating samples. For LAO-only films $(0,n)$ we reproduce the well-known critical thickness for metallicity of 4 unit cells in crystalline \ceLAO / STO interfaces, while samples with only \ceWO3 $(m,0)$ are always insulating. Heterostructures with 1 u.c. of LAO $(m,1)$ show an insulating state, independently of the \ceWO3 layer thickness. When $n=2$ the insulating state persists for \ceWO3 thickness $m\leq 2$ only, above which a metallic state is induced. With 3 cells of LAO a single layer of \ceWO3 is enough to trigger the metallic state. We can compare the metallicity of the conducting heterostructures by evaluating their residual resistivity ratio, defined as $\mathrm{RRR}=\rho_{xx}($300\text{,}\mathrm{K}$)/\rho_{xx}($1.5\text{,}\mathrm{K}$)$. Higher RRR values indicate more pronounced metallic behaviour and are represented by the colour map in fig. 2b. Our reference \ceLAO / STO heterostructure $(0,4)$ has $\mathrm{RRR}=110$, similarly to previous reports Gariglio et al. (2009); Warusawithana et al. (2013). In the \ceWO3 / LAO / STO system we find higher values for decreasing thickness of the LAO interlayer. As an example, the $(4,2)$ combination shows $\mathrm{RRR}=700$. A simple interpretation for this trend can be provided by considering two competing effects. On the one hand the spatially closer the amorphous \ceWO3 overlayer is to the STO, the more effective it is in controlling defect formation and maintaining a clean conductive channel. On the other hand a sufficiently thick LAO interlayer is required to provide the polar electric field necessary for driving charge carriers at the \ceLAO / STO interface. The optimal balance of these two effects seems to be achieved for 2 u.c. of LAO, where we measure the highest RRR value. In this picture we are thus able to combine the mobility enhancement provided by the amorphous overlayer with the advantage of a crystalline conductive interface.

The characteristics of this metallic state are investigated by performing magnetotransport measurements on a $(4,2)$ heterostructure, which shows a high RRR value. In fig. 3a we present its magnetoresistance (MR) which is defined as $\mathrm{MR}=\frac{\rho_{xx}(B)-\rho_{0}}{\rho_{0}}$, where $\rho_{0}$ is the sheet resistance at $B=0$ and the magnetic field is applied perpendicular to the interface plane. At $1.5\text{\,}\mathrm{K}$ the MR is positive and reaches 900% at $10\text{\,}\mathrm{T}$, corresponding to one order of magnitude increase in sheet resistance. This response is very different from what is usually observed in LAO/STO heterostructures $(0,n)$ as can be seen from the comparison with a $(0,4)$ sample in fig. 3a. The LAO/STO, in fact, shows a positive MR of only $12\text{\,}\mathrm{\char 37\relax}$ at $10\text{\,}\mathrm{T}$.

The Hall resistance of the $(4,2)$ heterostructure(fig. 3b) is negative, indicating electronic transport, with a kink at about $1\text{\,}\mathrm{T}$. A non-linear component in the Hall effect is typically related to multiple conduction channels contributing to the transport. In the simplest approximation of two independent channels in parallel, the classical magnetoresistance and the Hall resistance are given by

[TABLE]

where $n_{i}$, $\mu_{i}$ are the carrier density and mobility of the $i$-th channel, $n=(\pm n_{\mathtt{I}}\pm n_{\mathtt{II}})$ and the $\pm$ sign indicates hole or electron carriers, respectively. We use eq. 1b to fit with good agreement the $(4,2)$ Hall data (dashed line in fig. 3b) and extract in table 1 the corresponding transport parameters (see methods for details). The $(4,2)$ heterostructure presents two channels of electrons: one with lower-mobility $\mu_{\mathtt{I}}=$3600\text{,}{\mathrm{cm}}^{2}\text{,}{\mathrm{V}}^{-1}\text{,}{\mathrm{s}}^{-1}, $n_{\mathtt{I}}=$1.7\text{\times}{10}^{13}\text{\,}{\mathrm{cm}}^{-2} and one with higher mobility $\mu_{\mathtt{II}}=$80,000\text{,}{\mathrm{cm}}^{2}\text{,}{\mathrm{V}}^{-1}\text{,}{\mathrm{s}}^{-1}, $n_{\mathtt{II}}=$9.3\text{\times}{10}^{12}\text{\,}{\mathrm{cm}}^{-2}. Higher mobility values are observed for lower carrier densities, consistent with previous studies of STO-based 2DES Gunkel et al. (2016). We note that the sheet resistance of the higher-mobility channel $\rho_{\mathtt{II}}$ is one order of magnitude smaller than $\rho_{\mathtt{I}}$, suggesting that it dominates the low-temperature transport. The $(4,2)$ mobility is about two orders of magnitude higher than what observed in the reference $(0,4)$ sample ($\mu_{\mathtt{I}}=$840\text{,}{\mathrm{cm}}^{2}\text{,}{\mathrm{V}}^{-1}\text{,}{\mathrm{s}}^{-1}$$). The absence of a higher-mobility channel is coherent with the higher resistivity at $1.5\text{\,}\mathrm{K}$ and the lower RRR value usually found in \ceLAO/STO heterostructures.

Using $n_{i}$, $\mu_{i}$ extracted from the Hall effect we calculate with eq. 1a the classical two-channels MR (dashed line in fig. 3a). The resulting curve accounts for a good extent of the measured signal, which is thus the dominant MR contribution, in particular for small magnetic fields. The residual MR can arise from the presence of further conduction channels or disorder (Supplementary Figure 5). Quantum corrections might also be present, but considering their typical magnitude, they are negligible compared to the other contributions.

A better insight into the effects of these parallel conduction channels is given by tracking the resistivity and Hall coefficient as a function of temperature. The measurements are performed in a $100\text{\times}500\text{\,}\mathrm{\SIUnitSymbolMicro m}$ Hall bar geometry (inset of fig. 4a), where the conductive regions are defined using an insulating \ceAl2O3 hard mask, as described in the methods. In fig. 4a we compare the resistivity versus temperature curve measured with a magnetic field of $0\text{\,}\mathrm{T}$ and $12\text{\,}\mathrm{T}$ applied perpendicular to the interface plane. At $1.5\text{\,}\mathrm{K}$ the curves are well separated, underscoring a strong positive MR of $200\text{\,}\mathrm{\char 37\relax}$. On warming, the MR decreases and disappears below our measurement limit around room temperature.

By tracking the Hall effect as a function of temperature (Supplementary Figure 4) we can investigate the temperature dependence of $n_{i}$, $\mu_{i}$ for the different channels. A non-linear Hall effect is observed between $1.5\text{\,}\mathrm{K}$ and $30\text{\,}\mathrm{K}$, while a linear trend is seen at higher temperatures. The extracted mobilities and carrier densities are presented in figs. 4b and 4c. In this patterned sample we measure $\mu_{\mathtt{I}}=$2500\text{,}{\mathrm{cm}}^{2}\text{,}{\mathrm{V}}^{-1}\text{,}{\mathrm{s}}^{-1} and $\mu_{\mathtt{II}}=$27\,000\text{\,}{\mathrm{cm}}^{2}\text{\,}{\mathrm{V}}^{-1}\text{\,}{\mathrm{s}}^{-1} at $1.5\text{\,}\mathrm{K}$. With increasing temperature, at first $\mu_{\mathtt{I}}$ retains an almost constant value while $\mu_{\mathtt{II}}$ decreases. Above $30\text{\,}\mathrm{K}$ the high-mobility channel disappears and the Hall effect becomes linear, signalling the cross-over to single channel transport. At higher temperatures $\mu_{\mathtt{I}}$ decreases several orders of magnitude and reaches $\mu_{\mathtt{I}}=$7\text{,}\mathrm{c}\mathrm{m}\mathrm{{}^{2}}\mathrm{/}\mathrm{V}\mathrm{s}$$ at room temperature. This trend is similar to what has previously been reported for LAO/STO heterostructures Fête et al. (2015).

The strong MR in our system can be explained by considering the peculiar characteristics of the two conduction channels. In general, the classical theory of MR gives a strong resistivity increase with applied magnetic field whenever the charge carriers possess high mobility. To observe high MR in systems with multiple channels it is also required that the high mobility channel is dominant in the electronic conduction (i.e. $\rho_{\mathtt{II}}/\rho_{\mathtt{I}}\ll 1$). Both conditions are met in our \ceWO3 / LAO / STO system, where we find a direct correlation between the ratio $\rho_{\mathtt{II}}/\rho_{\mathtt{I}}$ and the MR magnitude at $10\text{\,}\mathrm{T}$: with $\rho_{\mathtt{II}}/\rho_{\mathtt{I}}\sim${10}^{-1}\text{,} in [fig. 3](#S0.F3) we measure $\mathrm{MR}\sim 900\%$, and with $\rho_{\mathtt{II}}/\rho_{\mathtt{I}}\sim 1$ in [fig. 4](#S0.F4) we have a lower $\mathrm{MR}\sim 200\%$. A further confirmation of this behaviour is given by considering that $\rho_{\mathtt{I}}$ values in [fig. 4a](#S0.F4.sf1) well represent the resistivity versus temperature curve at $B=$12\text{\,}\mathrm{T}. This indicates that the high-mobility channel is suppressed in the transport at high magnetic field.

The carrier density of the two conduction channels present opposite trends as a function of temperature. At $1.5\text{\,}\mathrm{K}$ we find that the lower-mobility channel has a higher density $n_{\mathtt{I}}=$2.2\text{\times}{10}^{13}\text{,}{\mathrm{cm}}^{-2}, and the higher-mobility has a lower-density $n_{\mathtt{II}}=$2.4\text{\times}{10}^{12}\text{\,}{\mathrm{cm}}^{-2}. Upon warming, $n_{\mathtt{I}}$ maintains an almost constant value, while $n_{\mathtt{II}}$ undergoes a sharp drop above $10\text{\,}\mathrm{K}$ and subsequently disappears. This disappearance might be due to the activation of interband scattering processes at higher temperatures, which cause a mixing of $\rho_{\mathtt{I}}$, $\rho_{\mathtt{II}}$, so that their populations cannot be independently resolved in Hall effect measurements Gunkel et al. (2016). Another possible interpretation for this trend is that the two conduction channels are situated in STO at two different distances from the interface. The first channel might be spatially closer to the LAO layer, where electrons experience more defects and a stronger polar electric field, resulting in lower mobility and higher carrier density. The second channel, instead, could be further away from the interface, where a less-defected STO determines a higher electron mobility. In this picture, the depopulation of $\rho_{\mathtt{II}}$ might be linked to the drop of the STO dielectric constant upon warming Sakudo and Unoki (1971) (Supplementary Fig. 6).

The electronic state confined in our \ceWO3 / LAO / STO heterostructures shows Shubnikov-de Haas (SdH) oscillations superimposed on the background of strong positive MR. The SdH as a function of temperature are shown in fig. 5a, where their signal was extracted by fitting the background with a 3rd order polynomial (dashed line in fig. 5b). The oscillations disappear when the magnetic field is applied parallel to the interface plane, as expected for a two-dimensional system. SdH oscillations in 2DES can be modelled by

[TABLE]

where $\rho_{\mathrm{c}}$ is the classical sheet resistance in zero magnetic field, $\alpha=2\pi^{2}k_{\mathrm{B}}/\hbar\omega_{\mathrm{c}}$ with cyclotron frequency $\omega_{\mathrm{c}}=eB/m^{*}$, Boltzmann’s constant $k_{B}$, reduced Planck’s constant $\hbar$, carrier effective mass $m^{*}$ and Dingle temperature $T_{D}$. Fourier analysis in fig. 5c reveals that the oscillations are periodic in $B^{-1}$, with a single frequency peak at $\omega_{\mathrm{SdH}}=$49\text{,}\mathrm{T}. Assuming a 2DES with circular sections of the Fermi surface, we can estimate the carrier density as $n_{\mathrm{SdH}}=\omega_{\mathrm{SdH}}\nu_{\mathrm{s}}e/h$, where $\nu_{\mathrm{s}}$ indicates the spin degeneracy. By considering $\nu_{\mathrm{s}}=2$ we find $n_{\mathrm{SdH}}=$2.4\text{\times}{10}^{12}\text{\,}{\mathrm{cm}}^{-2}. We note that even if Hall effect measurements indicate the presence of two conduction channels (values in fig. 5a), only one channel contributes to the quantum oscillations. Furthermore, the obtained $n_{\mathrm{SdH}}$ is lower than both $n_{\mathtt{II}}$, $n_{\mathtt{I}}$ for this sample, so that it is not possible to associate the SdH oscillation to one specific channel. A discrepancy between $n_{\mathrm{SdH}}$ and $n_{\mathrm{Hall}}$ in \ceLAO/STO interfaces has already been reported and its origin remains unknown Caviglia et al. (2010b); Shalom et al. (2010).

To extract the mass of the electrons showing the SdH effect, in fig. 5d we track the oscillation amplitude at $B=$11.85\text{,}\mathrm{T}$$ as a function of temperature (similar results are obtained using different values of $B$). Fitting the trend with eq. 2, we find a surprisingly high value $m^{*}=5.6\,m_{\mathrm{e}}$. Considering the enhanced mobility of carriers in the \ceWO3 / LAO / STO system, in fact, one would expect a decreased effective mass, while in this case $m^{*}$ is three times larger than typical observations in \ceLAO / STO heterostructures Chen et al. (2013); McCollam et al. (2014).

A possible explanation of this electron mass renormalization can be lead back to strong electron-phonon coupling, which is enhanced by the tight spatial confinement of the 2DEG. Such coupling was previously found to produce large phonon-drag Pallecchi et al. (2015, 2016) and polaronic effects in both \ceLAO / STO interfaces and amorphous \ceWO3 thin films Cancellieri et al. (2016); Berggren et al. (2001). Another possibility is that the modified defect profile with respect to conventional \ceLAO / STO interfaces determines a mass enhancement of the 2DES bands Wunderlich et al. (2009).

Finally, from the Dingle plot in fig. 5e we extract $T_{D}=$0.45\text{,}\mathrm{K}. This value points to an ordered electronic system with sharp Landau levels, considering that their energy smearing $k_{\mathrm{B}}T_{\mathrm{D}}\sim$40\text{\,}\mathrm{\SIUnitSymbolMicro eV} is much smaller than their spacing $\hbar\omega_{\mathrm{C}}\sim$250\text{,}\mathrm{\SIUnitSymbolMicro eV}. The extracted value $\rho_{\mathrm{C}}=$14\text{\,}\mathrm{\SIUnitSymbolOhm}\mathrm{/}\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} is in good agreement with $\rho_{0}=$35\text{,}\mathrm{\SIUnitSymbolOhm}\mathrm{/}\mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e}, corroborating the performed analysis. Using $T_{D}=\hbar/2\pi k_{\mathrm{B}}\tau$ and $\tau=m^{*}\mu_{\mathrm{SdH}}/e$ we calculate the elastic scattering time $\tau=$2.7\text{\,}\mathrm{ps} and the quantum mobility $\mu_{\mathrm{SdH}}=$851\text{,}{\mathrm{cm}}^{2}\text{,}{\mathrm{V}}^{-1}\text{,}{\mathrm{s}}^{-1}$$. Even though $\mu_{\mathrm{SdH}}$ is lower than both the Hall effect values $\mu_{\mathtt{II}}$, $\mu_{\mathtt{I}}$, it further confirms the formation of a high mobility 2DES in the \ceWO3 / LAO / STO heterostructure.

To conclude, we have demonstrated that amorphous \ceWO3 is an effective overlayer to form 2DES with enhanced mobility and effective mass at \ceLAO / STO interfaces. Reducing the crystalline \ceLAO critical thickness from 4 to 2 unit cells, the \ceWO3 overlayer determined a metallic system with high RRR and increased electron mobility. We ascribed the insurgence of a strong classical magnetoresistance to the peculiar characteristics of the multiple conduction channels observed in the system. Quantum oscillations of conductance confirmed the realisation of high-quality \ceWO3 / LAO / STO heterostructures, where a strong two-dimensional confinement of carriers is achieved. All these results are achieved using an amorphous \ceWO3 overlayer, which does not require crystal matching. Our work thus demonstrates a new approach for defect control at oxide interfaces, which can be exploited to induce high-mobility 2DES in a broad variety of oxide materials.

I Experimental Section

Samples growth: \ceWO3 / LaAlO3 / SrTiO3 heterostructures were grown by pulsed laser deposition on commercially available $5\text{\times}5\text{\,}\mathrm{mm}$ \ceSrTiO3 (001) substrates, with \ceTiO2 surface termination. The laser ablation was performed using a KrF excimer laser (Coherent COMPexPro 205, $\lambda=$248\text{,}\mathrm{nm}$$) with a $1\text{\,}\mathrm{Hz}$ repetition rate and $1\text{\,}\mathrm{J}\text{\,}{\mathrm{cm}}^{-2}$ fluence. The target-substrate distance was fixed at $55\text{\,}\mathrm{mm}$. For the \ceLaAlO3 thin films a crystalline target was employed and the deposition performed at $800\text{\,}\mathrm{\SIUnitSymbolCelsius}$ substrate temperature and $3\text{\times}{10}^{-5}\text{\,}\mathrm{mbar}$ oxygen pressure. \ceLaAlO3 film thickness was monitored in-situ during growth by intensity oscillations of reflection high-energy electron diffraction (RHEED). The samples were annealed for $1\text{\,}\mathrm{h}$ at $600\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in $300\text{\,}\mathrm{mbar}$ of \ceO2 atmosphere to compensate for the possible formation of oxygen vacancies. The amorphous \ceWO3 thin films were deposited from a \ceWO3 sintered target at $500\text{\,}\mathrm{\SIUnitSymbolCelsius}$ substrate temperature and $5\text{\times}{10}^{-3}\text{\,}\mathrm{mbar}$ oxygen pressure. \ceWO3 film thickness was calibrated by depositing crystalline \ceWO3 on \ceSrTiO3 and monitoring the growth by RHEED. The thickness value was then confirmed by X-ray diffraction and transmission electron microscopy measurements (results to be published elsewhere). At the end of the growth the heterostructures were cooled down to ambient temperature in $5\text{\times}{10}^{-3}\text{\,}\mathrm{mbar}$ oxygen pressure (further details in Supplementary Figure 1).

Hall bar geometry fabrication: \ceSrTiO3 substrates were patterned prior to \ceWO3 / LaAlO3 thin films deposition with standard e-beam lithography followed by the evaporation of an insulating \ceAl2O3 mask. The mask was deposited at room temperature by RF sputtering in a $5\text{\,}\mathrm{\SIUnitSymbolMicro bar}$ \ceAr atmosphere, resulting in amorphous alumina.

Electrical measurements: The measurements in figs. 2 and 3 were carried out in van der Pauw configuration, while for the ones in figs. 4 and 5 a Hall bar geometry was used. In both measurement configurations the metallic interface was directly contacted by ultrasonically wire-bonded \ceAl.

*Non-linear Hall effect fits: The fits are performed with the least squared method using data in the magnetic field range $-4\text{\,}\mathrm{T}4\text{\,}\mathrm{T}$. The constraint $1/\rho_{0}=1/\rho_{\mathtt{I}}+1/\rho_{\mathtt{II}}$ is applied to the fitting parameters, and $\rho_{0}$ is extracted from the $\rho_{xx}(B)$ measurement. With the assumption $1/\rho_{i}=n_{i}e\mu_{i}$, only three free parameters among $\rho_{i}$, $n_{i}$, $\mu_{i}$, with $i={\mathtt{I},\mathtt{II}}$, are varied in the fitting procedure. *

II Acknowledgments

We thank P. Zubko for valuable feedback and for performing XRD measurements; Y. M. Blanter and D. J. Groenendijk for fruitful discussions. This work was supported by The Netherlands Organisation for Scientific Research (NWO/OCW) as part of the Frontiers of Nanoscience program (NanoFront), the Dutch Foundation for Fundamental Research on Matter (FOM), the European Research Council under the European Union’s H2020 programme/ ERC GrantAgreement n. [677458] and the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1120296). The FEI Titan Themis 300 TEM was acquired through NSF-MRI-1429155, with additional support from Cornell University, the Weill Institute and the Kavli Institute at Cornell. A. F. thanks TU Delft and Kavli Institute for the access to Computing Center resources, and computational support from the CRS4 Computing Center (Piscina Manna, Pula, Italy).

Appendix A Supplementary Information