Abstract
Low dimensionality, broken symmetry and easilymodulated carrier concentrations provoke novel electronic phase emergence at oxide interfaces. However, the spatial extent of such reconstructions  i.e. the interfacial “depth”  remains unclear. Examining LaAlO_{3}/SrTiO_{3} heterostructures at previously unexplored carrier densities n_{2D} ≥ 6.9 × 10^{14} cm^{−2}, we observe a Shubnikovde Haas effect for small inplane fields, characteristic of an anisotropic 3D Fermi surface with preferential d_{xz,yz} orbital occupancy extending over at least 100 nm perpendicular to the interface. Quantum oscillations from the 3D Fermi surface of bulk doped SrTiO_{3} emerge simultaneously at higher n_{2D}. We distinguish three areas in doped perovskite heterostructures: narrow (<20 nm) 2D interfaces housing superconductivity and/or other emergent phases, electronically isotropic regions far (>120 nm) from the interface and new intermediate zones where interfacial proximity renormalises the electronic structure relative to the bulk.
Introduction
Ever since the discovery of a conducting channel in LaAlO_{3}/SrTiO_{3}^{1} and the subsequent observations of magnetism^{2} and superconductivity^{3}, the vast majority of oxide interface research has focussed on synthesising intrinsicallydoped heterostructures featuring narrow conducting channels () with twodimensional carrier densities n_{2D} in the 10^{12}–10^{14} cm^{−2} range^{4,5,6,7,8,9}. At such interfaces, it has been shown^{4,10,11,12,13,14} that symmetrylowering and quantum confinement lift the Ti t_{2g} degeneracy, so that the d_{xy} orbital lies at lower energy than the d_{xz,yz} orbitals. Xray absorption spectroscopy^{4} reveals a band splitting of ~50 meV for n_{2D} ~ 10^{13} cm^{−2} and theoretical approaches indicate that this increases with n_{2D}, reaching ~0.25 eV at 3 × 10^{14} cm^{−2}^{12}. Regardless of the total n_{2D}, the splitting should gradually vanish below the interface, until the electronic structure resembles that of bulk SrTiO_{3} with degenerate d_{xy,xz,yz} orbitals creating a Fermi surface at the centre of the Brillouin zone^{15}. The lengthscale over which this degeneracy is regained  i.e. the total distance over which the interface induces electronic reconstruction  remains unknown, despite being a vital prerequisite for building layered 3D oxide devices.
Probing this lengthscale requires the synthesis of LaAlO_{3}/SrTiO_{3} heterostructures with significantly more carriers (and correspondingly deeper conducting channels) than the norm. Previously, high n_{2D} heterostructures have only been grown in reducing environments^{16,17}, creating bulklike conducting layers hundreds of microns thick (n_{2D} ≥ 10^{16} cm^{−2}) in which the broken symmetry of the interface plays no role. However, interfaces with have until now remained unexplored: at these intermediate n_{2D}, electrons “spill over” from the interface and begin to occupy states lying deeper within the SrTiO_{3}. The principal focus of our work is therefore to track the evolution of the electronic structure and its crossover from 2D interfacial to 3D bulklike behaviour within this range of carrier densities. For n_{2D} ≥ 6.9 × 10^{14} cm^{−2}, we report the first instance of Shubnikovde Haas (SdH) oscillations from an ultrahigh mobility electron gas (μ_{H} ~ 10^{4} cm^{2}V^{−1}s^{−1}) for small magnetic fields parallel to the interface. The absence of such oscillations from the lowfield perpendicular magnetoresistance indicates that these carriers originate from an anisotropic 3D Fermi surface (FS); our firstprinciples calculations of the subinterfacial electronic structure reveal dominant d_{xz,yz} orbital occupancy, which is consistent with our experimental data. Superconductivity remains confined within 20 nm of the interface, while the 3D FS characteristic of bulk doped SrTiO_{3} gradually emerges with increasing n_{2D}. Together, our results imply the existence of a region below the interface whose electronic structure differs from that of the bulk, with a minimum thickness of 100 nm imposed by the cyclotron radius. This discovery has important implications for oxide devices seeking to functionalise interfacial electronic reconstructions.
Results
During sample growth, three mechanisms exist for carrierdoping the LaAlO_{3}/SrTiO_{3} interface: (a) intrinsic selfdoping via the polar catastrophe^{18} (leading to a maximum n_{2D} = 3.3 × 10^{14} cm^{−2}), (b) oxygen vacancy doping^{19} (contributing 2e^{−} per O^{2−} vacancy) and (c) cation intermixing^{9} (an unbalanced switching of La^{3+} for Sr^{2+} and Al^{3+} for Ti^{4+}). Since our principal aim is to explore the evolution of the electronic structure for n_{2D} > 5 × 10^{14} cm^{−2} (far beyond the upper limit imposed by the polar catastrophe) and cation intermixing is difficult to control in a pulsed laser deposition (PLD) chamber, we use O^{2−} vacancy doping to achieve the high n_{2D} values necessary for this project. To this end, we synthesise LaAlO_{3}/SrTiO_{3} heterostructures at an intermediate O_{2} pressure (10^{−3} mbar), without any postannealing procedure (further growth and characterisation details may be found in the Methods and Supplementary Material). The lack of annealing guarantees a high O^{2−} vacancy concentration and hence a large n_{2D}, while the intermediate growth pressure ensures that these vacancies do not penetrate far into the SrTiO_{3} substrate. Low pressure growth (10^{−6} mbar) without annealing^{16,17} has previously been shown to result in macroscopic substrate conduction, with n_{2D} ≥ 5 × 10^{15} cm^{−2}; in contrast, our method of synthesis consistently yields heterostructures with asgrown Hall carrier densities in the 10^{14}–10^{15} cm^{−2} range, which we will refer to as “series B”. For comparative purposes, we have also annealed certain heterostructures (“series A”) at high O_{2} pressures, yielding n_{2D} ~ 10^{13} cm^{−2}. Atype interfaces are comparable to the majority of those previously studied in the literature^{3,5,6}, in which carrier injection is dominated by the polar catastrophe. Both series exhibit coexistent superconductivity (SC) and ferromagnetism (FM), a comprehensive analysis of which may be found in ref. 20. For quantitative continuity in the present work, we focus on two specific samples A and B, with asgrown n_{2D} = 2.3 × 10^{13} cm^{−2}, 6.9 × 10^{14} cm^{−2} at T = 0.1 K and SC channel thicknesses d = 18 ± 1 nm, 9 ± 1 nm respectively. Sample B has a back gate beneath the SrTiO_{3}: n_{2D} increases to 2.4 × 10^{15} cm^{−2} (d = 19 ± 2 nm) at gate voltage V_{g} = 350 V. The heterostructure withstands V_{g} = 500 V with no discernible leakage current and the substrate capacitance ~ 1 nF is comparable to values measured in annealed LaAlO_{3}/SrTiO_{3} heterostructures with lower n_{2D}^{5,6} (see Supplementary section 1). Such conditions can only be achieved if the bulk of the SrTiO_{3} substrate is insulating: this confirms that O^{2−} vacancies have not penetrated deep into the SrTiO_{3} and are restricted to the neighbourhood of the interface.
We probe the electronic structure and FS geometry using SdH oscillations in the magnetoresistance (MR) R_{xx}(H) (Fig. 1a). Two magnetic field orientations are principally considered: H ⊥ (001) (H_{⊥}) and H//[110] (H_{//}), where the [100] directions correspond to the crystallographic axes of the SrTiO_{3} substrate and [001] points outofplane. Sample A does not display any SdH effect for either orientation. In contrast, sample B exhibits strong oscillations for H_{//} as low as 2.5 T, with faint oscillations also emerging for H_{⊥} > 6 T. However, data acquired with an inplane field H//[010] do not show any oscillations up to 4 T. Symmetry dictates that the plane of a 2D FS in LaAlO_{3}/SrTiO_{3} must lie parallel to the interface; any such FS will therefore lack states with outofplane momenta and cannot exhibit any SdH effect for inplane fields. It is therefore immediately clear that the oscillations which we observe with H//[110] must originate from an anisotropic 3D FS.
For H//[110], the SdH oscillations in sample B are sufficiently pronounced for us to extract the effective mass m* and the Dingle temperature T_{D} (a measure of the scattering) from their temperaturedependent amplitude (Fig. 1b). The magnitude of the oscillatory resistance is given by:
where R_{bg} is the background resistance. Fitting this equation to the oscillation amplitude (Fig. 1c) yields m* = 1.24 ± 0.1 m_{e} and T_{D} = 1.4 ± 0.4 K. m* is similar to values previously reported for the LaAlO_{3}/SrTiO_{3} 2DEG^{7,8}, although our T_{D} is lower which implies a higher carrier mobility in our heterostructures. To estimate this mobility, we initially calculate the Hall mobility μ_{H} = 1/n_{2D}eR_{xx}, where R_{xx}(V_{g} = 0) = 0.28 Ω/□ and we assume singleband transport. This yields an exceptionally high Hall mobility μ_{H} = 32000 cm^{2}V^{−1}s^{−1}, setting a new record for pure LaAlO_{3}/SrTiO_{3} and rivalling the best epitaxial SrTiO_{3} films^{21}.
In order to justify such a high mobility, we evaluate the Drude scattering time τ_{dr} ≡ m*μ_{H}/e = 23 ps, which is more than an order of magnitude greater than the Dingle scattering time ps. An alternative estimate of the scattering time in sample B may be extracted from the field at which a SdH effect first appears, using the quantum oscillation emergence condition ω_{c}τ_{SDH} ~ 1 (where ω_{c} ≡ Be/m* is the cyclotron frequency and B the magnetic field strength). For H//[110], oscillations are visible above 2.5 T: this corresponds to τ_{SDH} = 2.8 ps, which is also shorter than τ_{dr} suggested by our high μ_{H}. It is likely that four factors contribute to this disparity: firstly, all scattering events suppress quantum oscillations and contribute to τ_{D}, while only backscattering influences τ_{dr} and the Drude conductivity. Similar variance between τ_{D} and τ_{dr} can be seen in other LaAlO_{3}/SrTiO_{3} heterostructures^{7}. Secondly, the finite thickness of the conducting channel in our heterostructures may postpone the emergence of any SdH effect, until the applied field is sufficiently large for the diameter of the cyclotron orbits to fall below this thickness. Thirdly, superconducting fluctuations at fields below ~2.5 T effectively “shortcircuit” our heterostructures, reducing our ability to probe transport from carriers deeper below the interface. Finally, our singleband estimate for μ_{H} is an oversimplification, since multiband transport is expected for carrier densities above the Lifshitz transition in LaAlO_{3}/SrTiO_{3}^{12,22}. A threeband approximation to the fielddependent Hall coefficient (see Supplementary section 2) suggests a minority contribution from a highmobility band with μ_{H} ≈ 8000 cm^{2}V^{−1}s^{−1}. The total number of conduction bands in our heterostructures and their fielddependent mobilities remain unknown, so we cannot obtain a more precise value for the mobility of these quantumoscillating carriers. However, it is clear that our SdH effect, resistivity and Hall data all indicate the presence of a highmobility band with an anisotropic FS and μ_{H} ~ 10^{4} cm^{2}V^{−1}s^{−1}.
The fact that our measured T_{D} is lower than than those reported for the LaAlO_{3}/SrTiO_{3} 2DEG^{7,8} also suggests that the band whose FS generates the inplane oscillations lies within an extremely clean region of our heterostructures, far from the cation defects and magnetic scattering expected at oxygendeficient PLDgrown LaAlO_{3}/SrTiO_{3} interfaces. To determine the location of these highmobility carriers more precisely, we examine the evolution of the SdH oscillation frequencies with fieldeffect doping, obtained from the peaks in fast Fourier transforms (FFTs) of R_{xx}(H_{//,⊥}) (Fig. 2a,b). The Onsager relation links the peak frequency F with the extremal area S of the FS normal to the applied field via : since the size of the FS should be proportional to the carrier density, it is useful to compare F(V_{g}) with our experimentallydetermined total n_{2D} as well as the superconducting critical temperature T_{c} (which varies strongly with the local threedimensional carrier density n_{3D}^{23,24}). Once the interfacial carrier density exceeds n_{3D} ~ 10^{20} cm^{−3}, we expect a gradual suppression of SC leading to a dome in T_{c}(V_{g})^{5,6}; this is indeed observed (Fig. 2c). However, the inplane oscillation frequency F_{//} is independent of V_{g}, implying that the FS area S ⊥ [110] responsible for these oscillations remains roughly constant upon fieldeffect doping. Furthermore, F_{//}(V_{g}) displays no correlation with T_{c}(V_{g}) or n_{2D}(V_{g}): the FS (and hence the density of states) of the SC band(s) is being influenced by fieldeffect doping, but the FS of the highmobility band is not. Fieldeffect doping should have a similar effect on all occupied bands within the same spatial region. Therefore, the only possible explanation for this decoupling between T_{c}(V_{g}) and F_{//}(V_{g}) is that the SdHoscillating electron gas must be spatially separated from superconductivity, i.e. the highmobility carriers lie below the SC channel.
The gate evolution of R_{xx}(H_{⊥}) is very different from R_{xx}(H_{//}), with two V_{g}dependent peaks appearing in the FFTs (Fig. 2b). One of these (F_{1⊥}, grey arrows) lies below 20 T and is suppressed for large V_{g}: although this frequency seems too low to originate from the d_{xy} interfacial bands (which form a larger FS at much lower n_{2D}^{7,8}), spinorbit splitting may create a series of small FS for high n_{2D} at the interface. The other peak (F_{2⊥}, red arrows) mirrors n_{2D}(V_{g}) as V_{g} increases, saturating and broadening at ~40 T for large V_{g}. This implies that F_{2⊥} also cannot arise from a d_{xy} 2DEG at the interface, since for backgate doping at the interfacial d_{xy} occupancy should not change significantly: instead, carriers move deeper into the SrTiO_{3}. It is therefore tempting to link this peak with the 40 T mode from de Haasvan Alphen experiments^{25} on δdoped bulk SrTiO_{3}; however the light 3D band whose spherical FS was shown to be responsible for the 40 T oscillation^{15} is only occupied for n_{3D} > 6.7 × 10^{17} cm^{−3}, by when SrTiO_{3} already shows SC^{24}. Since d ≤ 20 nm for sample B^{20}, n_{3D} ≤ 5.5 × 10^{17} cm^{−3} below the SC channel, ruling out any occupancy of this light band. We therefore attribute F_{2⊥} to the gradual population of the 3D FS from the first occupied band in bulk doped SrTiO_{3}, which is formed by degenerate Ti 3d_{xy,xz,yz} orbitals and remains approximately isotropic for such low .
It is clear that the inplane SdH effect F_{//} in our data is unrelated not only to F_{2⊥}, but also to any previously reported 2D^{7,8} or 3D^{16} quantum oscillations in LaAlO_{3}/SrTiO_{3}. Instead, our oscillations originate from a highly anisotropic FS (since there is no SdH effect for H_{⊥} < 6 T), which occupies a clean intermediate region between the interface and the bulk. We estimate the minimum thickness of this region using the cyclotron radius : since a depth of at least 2r_{g} is necessary to establish SdH oscillations for H//(001), we use (where Φ_{0} is the magnetic flux quantum and we assume a spherical FS for simplicity), obtaining 2r_{g} ~ 140 nm at 2.5 T.
To understand the origin of these inplane SdH oscillations, we calculate the evolution of the subinterfacial orbital occupancy (which determines the FS symmetry) with increasing n_{2D}. The majority of electronic structure calculations for LaAlO_{3}/SrTiO_{3} to date have only considered the first few layers below the interface for n_{2D} ≤ 10^{14} cm^{−2} and are of limited use in our heterostructures. We have therefore performed firstprinciples calculations of the depthdependent band structure in LaAlO_{3}/SrTiO_{3} for n_{2D} = 3 × 10^{13}, 3 × 10^{14} and 8 × 10^{14} cm^{−2}, specifically chosen to approach our experimental n_{2D} in samples A, B (V_{g} ~ 0) and B (V_{g} > 0) respectively. Our calculated orbital occupancies are plotted in Fig. 3a and can also be seen in Fig. 4a–c: although computational power limits us to considering the first 10 unit cells below the interface, this is already sufficient to reveal the FS anisotropy responsible for our inplane SdH effect.
The central result from these calculations is a crossover from d_{xy} to d_{xz,yz} occupancy as we move away from the interface. Close to the interface and for small n_{2D}, d_{xy} states dominate due to quantum confinement, as expected^{10,12}. The absence of a clear SdH signal from the 2D d_{xy} interfacial FS in sample A is due to scattering from local moments^{10} and the large Rashba spinorbit coupling; we note that there are no reports of a 2D SdH effect in FM LaAlO_{3}/SrTiO_{3} in the literature. The important new result from our calculations is the creation of a conducting “tail” deeper below the interface for large n_{2D}, with a disproportionate occupation of d_{xz}_{,yz} orbitals. For example, the d_{xz}_{,yz}:d_{xy} ratio in layer 9 for n_{2D} = 8 × 10^{14} cm^{−2} is 2.8:1, significantly greater than the 2:1 expected in bulk SrTiO_{3}. A recent study of topgated SrTiO_{3} also hints at a low density “tail” of carriers persisting over at least 50 TiO_{2} layers, independently of the total n_{2D}^{13}. While the majority of carriers occupy tightlybound bands close to the interface, the backgate field in our sample B should reduce the quantum confinement and expand the “tail” still further into the SrTiO_{3}: this competition between confinement and decompression is responsible for the weak variation of F_{//}(V_{g}) (Fig. 2c). We therefore identify a d_{xz}_{,yz}dominated FS as the source of our inplane SdH effect.
The strong asymmetry in our observed SdH effect (i.e. the absence of oscillations for small H_{⊥}) may be explained by considering the FS geometry. In Fig. 3b,c, we plot the calculated (001) and (110) extremal crosssections of the interfacial FS at n_{2D} = 3 × 10^{14} and 8 × 10^{14} cm^{−2}. The elliptical crosssection of the d_{xz}_{,yz} FS implies that our previouslycalculated r_{g} will be scaled by k_{F}_{[001]}/k_{F}_{[110]} = 0.73, reducing the minimum thickness over which the electronic structure deviates from that of bulk SrTiO_{3} to ~100 nm. Furthermore, the variation in k_{F} across the FS drives a corresponding modulation in the effective band mass , shown for the (001) and (110) planes in Fig. 3d. Electrons in the (001) plane are significantly heavier and hence more easily scattered: therefore, SdH oscillations will only emerge for . Our measured F_{//} ~ 25 T is clearly too small to originate from the large interfacial FS projections in Fig. 3c: instead, our inplane oscillations are generated by a similarlyshaped smaller FS deeper below the interface, where n_{3D} is lower. The overall symmetry of the d_{xz}_{,yz} FS does not vary significantly with depth and hence our effective mass argument justifying the suppression of oscillations for H_{⊥} remains valid. In the (110) plane, the average band mass of the carriers is , which only allows for a small electronphonon coupling λ ~ 0.8 when compared with our measured m* = 1.24 m_{e} (since . However, we note that SdH experiments on both LaAlO_{3}/SrTiO_{3} and ntype SrTiO_{3} heterostructures have persistently yielded small effective masses^{7,8,26}.
Identifying the role of in determining the emergence of SdH oscillations allows us to make a profound statement regarding the shape of the inplane oscillating FS. In Fig. 3d, we sketch the approximate dependence in the (110) plane expected for a degenerate (bulklike) d_{xy}_{,xz,yz} FS. Here, the variation is similar to that in the (001) plane, though with a 180° rather than 90° period. We attribute the absence of oscillations for small H_{⊥} to the presence of heavy carriers in the (001) plane: therefore, the emergence of oscillations at small H_{//} implies that cannot rise significantly at 0°. Consequentially, the FS within this subinterfacial region must be flattened along the [001] direction in comparison with the bulk, i.e. the d_{xy}_{,xz,yz} degeneracy is lifted and the d_{xz}_{,yz} orbitals are shifted to lower energy. To illustrate this point further, in Fig. 3e,f we sketch d_{xy}_{,xz,yz} and d_{xz}_{,yz}dominated Fermi surfaces, comparing the shapes of their extremal orbits perpendicular to [001], [010] and [110]. The lowfrequency SdH oscillations which we observe with H//[110] must originate from a FS whose extremal orbits are composed exclusively of light carriers (i.e. the FS crosssectional area must be small): it is clear that this condition is only satisfied for the d_{xz}_{,yz}dominated FS.
Discussion
What is the physical origin of this change in the FS? We note that the shape of our d_{xz}_{,yz} FS is similar to that calculated by Mattheiss^{27} using a crystalfield parameter D which was subsequently shown to be too large^{15}. Since D is related to the tetragonal structure of SrTiO_{3}, our renormalised electronic structure may result from strain effects at the interface  such as the compression from the LaAlO_{3} layer  which are known to influence the 2DEG^{28}. Studies of the 2D–3D crossover in δdoped SrTiO_{3} films^{26} (in which strain should be absent) have not revealed the d_{xz}_{,yz}dominated intermediate FS which we observe; nevertheless it remains unclear whether a longrange interfaceinduced change in D or the spinorbit coupling is responsible for our results. Finally, our determination of the FS orbital character assumes the SrTiO_{3} tetragonal caxis lies parallel to [001]: since orthogonal tetragonal domains are expected for T < 105 K, this may not initially seem plausible. However, an offset surface potential exists between domains with c//[001] and c//[100] in LaAlO_{3}/SrTiO_{3}, requiring substantial charge transfer to equalise the chemical potential^{29}. This increases the carrier density in domains with c//[001], so transport predominantly occurs within these regions. Previous transport studies of Ladoped SrTiO_{3} have also indicated a prevalence of [001]oriented domains^{30}.
We summarise the evolution of the LaAlO_{3}/SrTiO_{3} interface with n_{2D} in Fig. 4, where we schematically represent the spatial distribution of SC together with the approximate n_{3D} variation and our calculated depthdependent d_{xy} and d_{xz}_{,yz} orbital occupancies (Fig. 4a–c). At low carrier densities (Fig. 4a), d_{xy} orbitals dominate and the charge is concentrated within a few unit cells of the interface. Electrons in the top TiO_{2} layer tend to localise^{10,31}, creating an inhomogeneous patchwork of FM zones above a narrow (≤20 nm) SC channel^{20}.
As n_{2D} increases (Fig. 4b), FM and SC both remain present at the interface. However, a highmobility d_{xz}_{,yz} “tail” of minimum thickness 100 nm develops below the interface, generating an anisotropic 3D FS which exhibits SdH oscillations for small inplane fields. Together, the appearance of this SdH effect, its independence from n_{2D}(V_{g}) and T_{c}(V_{g}) and its absence in small perpendicular fields indicate that d_{xz}_{,yz} orbital occupancy is favoured over d_{xy} to a depth of at least 120 nm below the interface. Unfortunately, it is not possible to accurately determine the maximum depth reached by this “tail”, since the carrier density very close to the interface (where we expect the majority of the carriers to reside) is unknown. However, our data do enable us to comment on the O^{2−} vacancy penetration depth, which we already believe to be small since the capacitance of our Btype samples is comparable to values seen in annealed heterostructures. The high electron mobility within the “tail” region is primarily a consequence of the low carrier density (which leads to a small FS and low effective mass), but a lack of crystal defects (e.g. O^{2−} vacancies) below the interface may also play an important role. Recently, ultrahigh mobility carriers (μ_{H} ~ 50,000 cm^{2}V^{−1}s^{−1}) have been observed in SrCuO_{2}capped LaAlO_{3}/SrTiO_{3} heterostructures, in which O^{2−} vacancy formation is suppressed^{32}. This suggests that although the carriers in our Btype heterostructures originate from O^{2−} vacancies, these vacancies may be confined close to the interface (or in the LaAlO_{3} layer) while the electrons which they donate are redistributed deeper within the SrTiO_{3}. This concept is supported by the absence of any parasitic SrTiO_{3} surface conduction in our heterostructures (whose presence would be expected in the case of deep O^{2−} vacancy penetration), as well as theoretical work which indicates that O^{2−} vacancies preferentially inhabit the LaAlO_{3} surface rather than the interface^{33}. Ideally, future theoretical work should examine the evolution of the electronic structure in the “tail” as a function of O^{2−} vacancy density and location. It also remains to be determined whether the absence of superconductivity from the “tail” region is merely due to a subcritical carrier density, or if the d_{xz}_{,yz} orbital character also plays some role.
At the maximum n_{2D} which we are able to simulate (Fig. 4c), only the top TiO_{2} monolayer at the interface still has a d_{xy} character, with d_{xz}_{,yz} states dominating below. We illustrate the effects of a backgate electric field in Fig. 4d: as V_{g} increases, the carrier density in the superconducting channel rises and a shift to the overdoped side of the superconducting dome occurs (as seen in Fig. 2c). In parallel, electrons in the “tail” decompress away from the interface due to bandbending from the electric field, migrating hundreds of nanometres into the bulk. This migration creates the 3D FS responsible for the SdH oscillations which we observe with H⊥(001), whose frequency scales with the total carrier density. Between the interface and the bulk, the carrier density of the d_{xz}_{,yz}dominated region remains roughly constant: electrons which it “loses” to deeperlying bulk states are replaced by electrons from the interface. The presence of a large carrier population below the interface results in a screening of the electric field, thus explaining the relatively small increase of d to 19 nm at V_{g} = 350 V compared to d > 40 nm reported at much smaller backgate fields in the literature^{34}. Finally, Figs. 4e,f display exaggerated sketches illustrating the evolution of the FS as we move deeper into the SrTiO_{3}, from d_{xz}_{,yz} domination (Fig. 4e) to a gradual recovery of d_{xy}_{,xz,yz} degeneracy (Fig. 4f) over a lengthscale ≥ 120 nm. While the microscopic origins of this longdistance evolution are still unclear, our work shows that functional oxide devices can reliably hope to profit from a renormalised electronic structure tens of nanometres away from a symmetrybreaking interface.
Methods
Two series of LaAlO_{3}/SrTiO_{3} heterostructures, “A” and “B”, were grown using a standard pulsed laser deposition system manufactured by Twente Solid State Technology B.V., equipped with a reflection highenergy electron diffraction (RHEED) facility. We use 0.5 mm thick commercial 5 × 5 mm SrTiO_{3} (001) “STEP” substrates from Shinkosha: these are HFtreated for TiO_{2} termination and cleaned by the manufacturer, then vacuumpacked for shipping. We do not perform any additional surface cleaning or annealing prior to deposition: the substrates are loaded directly into our PLD chamber, which is subsequently evacuated to base pressure prior to backfilling with 10^{−3} mbar O_{2}. The substrate is then heated to growth temperature (800°C). Series A and B both feature 10 unit cells of LaAlO_{3}, deposited using a total incident laser energy of 9 mJ focussed onto a 6 mm^{2} rectangular spot. The O_{2} pressure and substrate temperature were maintained at 10^{−3} mbar and 800°C respectively for both sample series throughout the deposition process. Subsequently, Atype samples underwent an annealing stage: after cooling to 500°C at 10^{−3} mbar, the O_{2} pressure was increased to 0.1 bar. The temperature was held at 500°C for 30 minutes before natural cooling to 20°C in 0.1 bar O_{2}. In contrast, Btype samples were cooled naturally to 20°C in 10^{−3} mbar O_{2}.
To fabricate Hall bars on these LaAlO_{3}/SrTiO_{3} films, we first defined contact pad areas using photolithography with AZ5214 photoresist. 2 nm Ti followed by 8 nm Au were evaporated directly onto the LaAlO_{3} surface; the remaining photoresist was removed by soaking in acetone for 30 minutes, then rinsed in IPA. Sample B also had an AuTi back gate deposited across the entire base of the SrTiO_{3} substrate prior to fabrication. The Hall bars were defined using a similar photolithography process and the Hall bar mesas etched using a dry Ar ion technique (at a slow rate of 1 Å s^{−1} to avoid any substrate heating). The Hall bar width was 80 μm and the voltage contact separation 660 μm. Multiple Hall bars were fabricated on each 5 × 5 mm substrate: tests showed that the Hall bars were electrically isolated from each other (thus ruling out any parasitic conduction from the SrTiO_{3} surface) and displayed similar transport properties (indicating that our heterostructures are homogeneous). Prior to measurement, the Hall bars were mounted in thermallyconductive chipcarriers, with electrical contacts made using 10 μm Au wires ballbonded to the AuTi contact pads.
Transport data were acquired in a cryogenfree dilution refrigerator, using an AC technique with two digital lockin amplifiers and a current source outputting 500 nA at 19 Hz. This value was chosen to maximise the signaltonoise ratio whilst minimising sample heating below 0.1 K. Our noise threshold is approximately 1 nV. The substrate capacitance was measured with femtoFarad sensitivity for gate voltages up to 500 V using a General Radio 1621 manual capacitance bridge. All results presented in this work were qualitatively reproducible over a 6month period comprising numerous cooldowns of both samples. A total of 6 “Atype” and 4 “Btype” heterostructures were fabricated in our laboratory using identical “recipes” to those detailed above: all samples displayed similar behaviour to those discussed in the present work.
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Acknowledgements
The authors gratefully acknowledge discussions with H. Hilgenkamp, A. Fujimori and I. Martin. This work was supported by the National Research Foundation, Singapore, through Grant NRFCRP4200804. The research at the University of NebraskaLincoln (UNL) was supported by the National Science Foundation through the Materials Research Science and Engineering Center (Grant No. DMR0820521) and the Designing Materials to Revolutionize and Engineer our Future (DMREF) Program (Grant No. DMR1234096). Computations were performed at the UNL Holland Computing Center and the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy.
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A.P.P. and C.P. conceived the project. A.D. and T.W. grew the heterostructures. K.L., S.H. and C.B. fabricated and tested the Hall bars. A.P.P. and A.P. set up and performed the experiments. T.P. and E.T. contributed the band structure and Fermi surface calculations. A.P.P. and C.P. wrote the paper. C.P. supervised the entire study. All authors discussed the results and manuscript.
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Longrange electronic reconstruction to a d_{xz,yz}dominated Fermi surface below the LaAlO_{3}/SrTiO_{3} interface: Supplementary Material
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Petrović, A., Paré, A., Paudel, T. et al. Longrange electronic reconstruction to a d_{xz,yz}dominated Fermi surface below the LaAlO_{3}/SrTiO_{3} interface. Sci Rep 4, 5338 (2014). https://doi.org/10.1038/srep05338
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DOI: https://doi.org/10.1038/srep05338
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