The two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interface exhibits gate tunable superconductivity with a domelike shape of $T_{\rm{C}}$ as a function of electron concentration. Here, we propose that the experimentally observed behavior can be explained as a direct effect of the dominant $extended$ $s$-$wave$ symmetry of the superconducting gap. Our results agree very well with the experimental data. As shown, neither the correlation effects nor the spin-orbit coupling influence significantly the physical picture of the paired state steaming out from our analysis.
We demonstrate top-gate tunable Josephson junction like behavior in the two dimensional electron gas at the LaAlO$_3$-SrTiO$_3$ interface. A combination of global back-gating and local top-gating is used to define the junctions, providing an efficient way for much finer spatial control over the properties of the interface, as compared to back-gating alone. The variation of critical currents and zero bias resistances with temperature shows that the junctions behave like short, overdamped weak links. This technique could be an important tool to illuminate the nature of superconductivity in the L…
We describe the transport properties of mesoscopic devices based on the two dimensional electron gas (2DEG) present at the LaAlO$_3$/SrTiO$_3$ interface. Bridges with lateral dimensions down to 500~nm were realized using electron beam lithography. Their detailed characterization shows that processing and confinement do not alter the transport parameters of the 2DEG. The devices exhibit superconducting behavior tunable by electric field effect. In the normal state, we measured universal conductance fluctuations, signature of phase-coherent transport in small structures. The achievement of relia…
We examine superconductivity in LaAlO$_3$/SrTiO$_3$ channels in which the channel width transitions from the 1D to 2D regime. The superconducting critical current is independent of the channel width and increases approximately linearly with the number of parallel channels. Signatures of electron pairing outside of the superconducting phase are also independent of channel width. Collectively, these results indicate that electron pairing and superconductivity exist at the boundary of these channels and are absent within the interior region of the channels. The intrinsic 1D nature of superconduct…
The interface between two band insulators LaAlO$_3$ and SrTiO$_3$ exhibits low-temperature superconductivity coexisting with an in-plane ferromagnetic order. We show that topological superconductivity hosting Majorana bound states can be induced at the interface by applying a magnetic field perpendicular to the interface. We find that the dephasing effect of the in-plane magnetization on the topological superconducting state can be overcomed by tuning a gate-voltage. We analyze the vortex-core excitations showing the zero-energy Majorana bound states and the effect of non-magnetic disorder on …
The LaAlO3/SrTiO3 interface provides a unique platform for controlling the electronic properties of the superconducting semiconductor SrTiO3. Prior investigations have shown that two-dimensional superconductivity can be produced at the LaAlO3/SrTiO3 interface and tuned electrostatically. The recently demonstrated reversible control of the metal-insulator transition at the same interface using conductive atomic force microscopy (c-AFM) raises the question of whether this room-temperature technique can produce structures that exhibit superconducting, normal metallic and insulating phases at sub-…
Diverse phenomena emerge at the interface between band insulators LaAlO3 and SrTiO3, such as superconductivity and ferromagnetism, showing an opportunity for potential applications as well as bringing fundamental research interests. Particularly, the two-dimensional electron gas formed at LaAlO3/SrTiO3 interface offers an appealing platform for quantum phase transition from a superconductor to a weakly localized metal. Here we report the superconductor-metal transition in superconducting two-dimensional electron gas formed at LaAlO3/SrTiO3(110) interface driven by a perpendicular magnetic fiel…
We report the electrical top-gating of a 2-dimensional electron gas (2DEG) formed at the LaAlO3/SrTiO3 interface, using electron-beam evaporated Au gate electrodes. In these structures, epitaxial LaAlO3 films grown by pulsed laser deposition induce the 2DEGs at the interface to the SrTiO3 substrate and simultaneously act as the gate dielectric. The structured top-gates enable a local tuning and complete on/off switching of the interface (super)-conductivity, while maintaining the usual, intrinsic characteristics for these LaAlO3/SrTiO3 interfaces when no gate voltage is applied.
SrTiO$_3$ is a superconducting semiconductor with a pairing mechanism that is not well understood. SrTiO$_3$ undergoes a ferroelastic transition at $T=$ 105 K, leading to the formation of domains with boundaries that can couple to electronic properties. At two-dimensional SrTiO$_3$ interfaces, the orientation of these ferroelastic domains is known to couple to the electron density, leading to electron-rich regions that favor out-of-plane distortions and electron-poor regions that favor in-plane distortion. Here we show that ferroelastic domain walls support low energy excitations that are anal…
The tetragonal domain structure in SrTiO$_{3}$ (STO) is known to modulate the normal-state carrier density in LaAlO$_{3}$/SrTiO$_{3}$ (LAO/STO) heterostructures, among other electronic properties, but the effect of STO domains on the superconductivity in LAO/STO has not been fully explored. Using a scanning SQUID susceptometer microscope to map the superconducting response as a function of temperature in LAO/STO, we find that the superconducting transition temperature is spatially inhomogeneous and modulated in a pattern that is characteristic of structural domains in the STO.
We propose a kinetically driven mechanism based on the breaking of the spatial reflection symmetry to describe the magnetic moment and the torque observed by Lu-Li et al. (Ref. 1) for the $LaAlO_3/SrTiO_3$ system. We find that the itinerant electrons are in a zero helicity state and predict the existence of charge inhomogeneities that cross the interface at constant rate. There is mass and thickness anisotropies between the two sides of the interface.
The effect of spatial inhomogeneity on the properties of a two-dimensional non-centrosymmetric superconductor in an in-plane magnetic field is investigated, as it can be realized in LaAlO_3-SrTiO_3 interfaces. We demonstrate that the spatial variation of Rashba spin-orbit coupling (RSOC) yields a local magnetic flux pattern due to the field-induced inhomogeneous helical phase. For sufficiently strong fields, vortices can nucleate at inhomogeneities of the RSOC.
In strontium titanate, the Froehlich electron - LO-phonon interaction dominates the electron response and can also provide superconductivity. Because of high LO-phonon frequencies in SrTiO3, the superconducting system is non-adiabatic. We demonstrate that the dielectric function approach is an adequate theoretical method for superconductivity in SrTiO3 and on the SrTiO3-LaAlO3 interface. The critical temperatures are calculated using realistic material parameters. The obtained critical temperatures are in line with experimental data both for bulk and interface superconductivity. The present me…
Although discovered many decades ago, superconductivity in doped SrTiO$_{3}$ remains a topic of intense research. Recent experiments revealed that, upon increasing the carrier concentration, multiple bands cross the Fermi level, signaling the onset of Lifshitz transitions. Interestingly, $T_{c}$ was observed to be suppressed across the Lifshitz transition of oxygen-deficient SrTiO$_{3}$; a similar behavior was also observed in gated LaAlO$_{3}$/SrTiO$_{3}$ interfaces. Such a behavior is difficult to explain in the clean theory of two-band superconductivity, as the additional electronic states …
Resistance as a function of temperature down to 20mK and magnetic fields up to 18T for various carrier concentrations is measured for nanowires made from the SrTiO3/LaAlO3 interface using a hard mask shadow deposition technique. The narrow width of the wires (of the order of 50nm) allows us to separate out the magnetic effects from the dominant superconducting ones at low magnetic fields. At this regime hysteresis loops are observed along with the superconducting transition. From our data analysis we find that the magnetic order probed by the giant magnetoresistance (GMR) effect vanishes at TC…
The 2DEG at the LaAlO3/SrTiO3 interface promises to add a new dimension to emerging electronic devices due to its high tunability. Defects in the form of Oxygen vacancies in titanate surfaces and interfaces, on the other hand, play a key role in the emergence of novel phases. Based on an effective model, we study the influence of Oxygen vacancies on superconductivity and ferromagnetism at LaAlO3/SrTiO3 interface. Using the Bogoliubov-de Gennes formulation in conjunction with Monte-Carlo simulation, we find a clustering of the Oxygen vacancies at the interface that favours formation of coexisti…
We investigate the superconductivity in two-dimensional electron systems formed in SrTiO3 nanostructures. Our the- oretical analysis is based on the three-orbital model, which takes into account t2g orbitals of Ti ions. Because of the interfacial breaking of mirror symmetry, a Rashba-type antisymmetric spin-orbit coupling arises from the cooperation of intersite and interorbital hybridyzation and atomic LS coupling. This model shows a characteristic spin texture and carrier density dependence of Rashba spin-orbit coupling through the orbital degree of freedom. Superconductivity is mainly cause…
Superconductivity develops in bulk doped SrTiO$_3$ and at the LaAlO$_3$/SrTiO$_3$ interface with a dome-shaped density dependence of the critical temperature $T_c$, despite different dimensionalities and geometries. We propose that the $T_c$ dome of LaAlO$_3$/SrTiO$_3$ is a shape resonance due to quantum confinement of superconducting bulk SrTiO$_3$. We substantiate this interpretation by comparing the exact solutions of a three-dimensional and quasi-two-dimensional two-band BCS gap equation. This comparison highlights the role of heavy bands for $T_c$ in both geometries. For bulk SrTiO$_3$, w…
The interface superconductivity in LaAlO$_{3}$-SrTiO$_{3}$ heterostructures reveals a non-monotonic behavior of the critical temperature as a function of the two-dimensional density of charge carriers. We develop a theoretical description of interface superconductivity in strongly polar heterostructures, based on the dielectric function formalism. The density dependence of the critical temperature is calculated accounting for all phonon branches including different types of optical (interface and half-space) and acoustic phonons. The LO- and acoustic-phonon-mediated electron-electron interacti…
The resistivity as a function of temperature, magnetic field and its orientation for atomically flat SrTiO3\LaAlO3 interfaces with carrier densities of ~3*10^13 cm^-2 is reported. At low magnetic fields superconductivity is observed below 130mK. The temperature dependence of the high field magnetoresistance and its strong anisotropy suggest possible magnetic ordering below 35K. The origin of this ordering and its possible relation to superconductivity are discussed.
The highly conductive two-dimensional electron gas formed at the interface between insulating SrTiO$_3$ and LaAlO$_3$ shows low-temperature superconductivity coexisting with inhomogeneous ferromagnetism. The Rashba spin-orbit interaction with in-plane Zeeman field of the system favors $p_x \pm i p_y$-wave superconductivity at finite momentum. Owing to the intrinsic disorder at the interface, the role of spatial inhomogeneity on the superconducting and ferromagnetic states becomes important. We find that for strong disorder, the system breaks up into mutually excluded regions of superconductivi…
A rather unique feature of the two-dimensional electron gas (2-DEG) formed at the interface between the two insulators LaAlO3 and SrTiO3 is to host both gate-tunable superconductivity and strong spin-orbit coupling. In the present work, we use the disorder generated by Cr substitution of Al atoms in LaAlO3 as a tool to explore the nature of superconductivity and spin-orbit coupling in these interfaces. A reduction of the superconducting Tc is observed with Cr doping consistent with an increase of electron-electron interaction in presence of disorder. In addition, the evolution of spin-orbit co…
A superconducting phase with an extremely low carrier density of the order of 10^13 cm^-2 is present at LaAlO3-SrTiO3 interfaces. If depleted from charge carriers by means of a gate field, this superconducting phase undergoes a transition into a metallic/insulating state that is still characterized by a gap in the spectral density of states. Measuring and analyzing the critical field of this gap, we provide evidence that macroscopically phase-coherent Cooper pairs are present in the metallic/insulating state. This is characterized by fluctuating vortex-antivortex pairs, and not by individual, …
We report on the discovery and transport study of the superconducting ground state present at the (111)LaAlO$_3$/SrTiO$_3$ interface. The superconducting transition is consistent with a Berezinskii-Kosterlitz-Thouless transition and its 2D nature is further corroborated by the anisotropy of the critical magnetic field, as calculated by Tinkham. The estimated superconducting layer thickness and coherence length are 10 nm and 60 nm, respectively. The results of this work provide a new platform to clarify the microscopic details of superconductivity at LaAlO$_3$/SrTiO$_3$ interfaces, in particula…
The superconducting transition temperature, Tc, of the SrTiO3/LaAlO3 interface was varied by the electric field effect. The anisotropy of the upper critical field and the normal state magneto-transport were studied as a function of gate voltage. The spin-orbit coupling energy is extracted. This tunable energy scale is used to explain the strong gate dependence of the mobility and of the anomalous Hall signal observed. The spin-orbit coupling energy follows Tc for the electric field range under study.
We probe the existence of large correlated non-Gaussian phase fluctuations in the vicinity of the superconducting phase transition in the conducting layer residing at the interface of LaAlO$_3$/SrTiO$_3$ heterostructures. The non-Gaussian fluctuations appear between the Berezinskii-Kosterlitz-Thouless transition temperature $T_{BKT}$ and the mean field transition temperature $T_C$. Subsequent theoretical analysis reveals that non-Gaussianity arises predominantly due to the percolative transition of a Josephson coupled network of superconductors. Our results confirm that the superconductivity i…
We study the symmetry of Cooper pair in a two-dimensional Hubbard model with the Rashba-type spin-orbit interaction as a minimal model of electron gas generated at a heterointerface of SrTiO$_3$/LaAlO$_3$. Solving the Eliashberg equation based on the third-order perturbation theory, we find that the gap function consists of the mixing of the spin-singlet $d_{xy}$-wave component and the spin-triplet $(p_x\pm ip_y)$-wave one due to the broken inversion symmetry originating from the Rashba-type spin-orbit interaction. The ratio of the d-wave and the p-wave component continuously changes with the …
Caviglia et al. [Nature (London) 456, 624 (2008)] have found that the superconducting LaAlO_3 / SrTiO_3 interface can be gate modulated. A central issue is to determine the principal effect of the applied electric field. Using magnetotransport studies of a gated structure, we find that the mobility variation is almost five times as large as the sheet carrier density. Furthermore, superconductivity can be suppressed at both positive and negative gate bias. These results indicate that the relative disorder strength strongly increases across the superconductor-insulator transition.
We measure the gate voltage ($V_g$) dependence of the superconducting properties and the spin-orbit interaction in the (111)-oriented LaAlO$_3$/SrTiO$_3$ interface. Superconductivity is observed in a dome-shaped region in the carrier density-temperature phase diagram with the maxima of superconducting transition temperature $T_c$ and the upper critical fields lying at the same $V_g$. The spin-orbit interaction determined from the superconducting parameters and confirmed by weak-antilocalization measurements follows the same gate voltage dependence as $T_c$. The correlation between the supercon…
A hysteretic in-plane magnetoresistance develops below the superconducting transition of LaAlO$_3$/SrTiO$_3$ interfaces for $\left|H_{/\!/}\right|<$ 0.15 T, independently of the carrier density or oxygen annealing. We show that this hysteresis arises from vortex depinning within a thin superconducting layer, in which the vortices are created by discrete ferromagnetic dipoles located solely above the layer. We find no evidence for finite-momentum pairing or bulk magnetism and hence conclude that ferromagnetism is strictly confined to the interface, where it competes with superconductivity.
Superconductivity at the interface between the insulators LaAlO3 and SrTiO3 has been tuned with the electric field effect. The data provide evidence for a two dimensional quantum superconductor to insulator (2D-QSI) transition. Here we explore the compatibility of this phase transition line with Berezinskii-Kosterlitz-Thouless (BKT) behavior and a 2D-QSI transition. In an intermediate regime, limited by a finite size effect, we uncover remarkable consistency with BKT- criticality, weak localization in the insulating state and non-Drude behavior in the normal state. Our estimates for the critic…
The relative importance of atomic defects and electron transfer in explaining conductivity at the crystalline LaAlO3/SrTiO3 interface has been a topic of debate. Metallic interfaces with similar electronic properties produced by amorphous oxide overlayers on SrTiO3 have called in question the original polarization catastrophe model. We resolve the issue by a comprehensive comparison of (100)-oriented SrTiO3 substrates with crystalline and amorphous overlayers of LaAlO3 of different thicknesses prepared under different oxygen pressures. For both types of overlayers, there is a critical thicknes…
With infrared ellipsometry and transport measurements we investigated the electrons at the interface between LaAlO3 and SrTiO3. We obtained a sheet carrier density of Ns~5-9x 10E13 cm^-2, an effective mass of m*~3m_e, and a strongly frequency dependent mobility. The latter are similar as in bulk SrTi1-xNbxO3 and therefore suggestive of polaronic correlations of the confined carriers. We also determined the vertical density profile which has a strongly asymmetric shape with a rapid initial decay over the first 2 nm and a pronounced tail that extends to about 11 nm.
