Two-dimensional superconducting phase in LaTiO3/SrTiO3 heterostructures induced by high-mobility carrier doping

Tuning of the magnetotransport properties of a spin-polarized 2D electron system using visible light

We report on the effects of visible light on the low temperature electronic properties of the spin-polarized two dimensional electron system (2DES) formed at the interfaces between LaAlO[Formula: see text], EuTiO[Formula: see text] and (001) SrTiO[Formula: see text]. A strong, persistent modulation of both longitudinal and transverse conductivity was obtained using light emitting diodes (LEDs) with emissions at different wavelengths in the visible spectrum range. In particular, Hall effect data show that visible light induces a non-volatile electron filling of bands with mainly 3d[Formula: see text] character, and at the same time an enhancement of the anomalous Hall effect associated to the magnetic properties of the system. Accordingly, a suppression of the weak-anti localization corrections to the magneto-conductance is found, which correlates with an enhancement of the spin-polarization and of the ferromagnetic character of 2DES. The results establish the LED-induced photo-doping as a viable route for the control of the ground state properties of artificial spin-polarized oxide 2DES.

Spontaneous rotational symmetry breaking in KTaO3 heterointerface superconductors

Broken symmetries play a fundamental role in superconductivity and influence many of its properties in a profound way. Understanding these symmetry breaking states is essential to elucidate the various exotic quantum behaviors in non-trivial superconductors. Here, we report an experimental observation of spontaneous rotational symmetry breaking of superconductivity at the heterointerface of amorphous (a)-YAlO₃/KTaO₃(111) with a superconducting transition temperature of 1.86 K. Both the magnetoresistance and superconducting critical field in an in-plane field manifest striking twofold symmetric oscillations deep inside the superconducting state, whereas the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute this behavior to the mixed-parity superconducting state, which is an admixture of s-wave and p-wave pairing components induced by strong spin-orbit coupling inherent to inversion symmetry breaking at the heterointerface of a-YAlO₃/KTaO₃. Our work suggests an unconventional nature of the underlying pairing interaction in the KTaO₃ heterointerface superconductors, and brings a new broad of perspective on understanding non-trivial superconducting properties at the artificial heterointerfaces.

Two-Dimensional Superconductivity at the Titanium Sesquioxide Heterointerface

The study of exotic superconductivity in two dimensions has been a central theme in the solid state and materials research communities. Experimentally exploring and identifying exotic, fascinating interface superconductors with a high transition temperature (T_c) are challenging. Here, we report an experimental observation of intriguing two-dimensional superconductivity with a T_c of up to 3.8 K at the interface between a Mott insulator Ti₂O₃ and polar semiconductor GaN. At the verge of superconductivity, we also observe a striking quantum metallic-like state, demonstrating that it is a precursor to the two-dimensional superconductivity as the temperature is decreased. Our work shows an exciting opportunity to exploit the underlying, emergent quantum phenomena at the heterointerfaces via heterostructure engineering.

Superfluid stiffness of a KTaO3-based two-dimensional electron gas

After almost twenty years of intense work on the celebrated LaAlO₃/SrTiO₃system, the recent discovery of a superconducting two-dimensional electron gas (2-DEG) in (111)-oriented KTaO₃-based heterostructures injects new momentum to the field of oxides interface. However, while both interfaces share common properties, experiments also suggest important differences between the two systems. Here, we report gate tunable superconductivity in 2-DEGs generated at the surface of a (111)-oriented KTaO₃ crystal by the simple sputtering of a thin Al layer. We extract the superfluid stiffness of the 2-DEGs and show that its temperature dependence is consistent with a node-less superconducting order parameter having a gap value larger than expected within a simple BCS weak-coupling limit model. The superconducting transition follows the Berezinskii-Kosterlitz-Thouless scenario, which was not reported on SrTiO₃-based interfaces. Our finding offers innovative perspectives for fundamental science but also for device applications in a variety of fields such as spin-orbitronics and topological electronics.

Two-dimensional superconductivity at the surfaces of KTaO3 gated with ionic liquid

The recent discovery of superconductivity at the interfaces between KTaO₃ and EuO (or LaAlO₃) gives birth to the second generation of oxide interface superconductors. This superconductivity exhibits a strong dependence on the surface plane of KTaO₃, in contrast to the seminal LaAlO₃/SrTiO₃ interface, and the superconducting transition temperature T_c is enhanced by one order of magnitude. For understanding its nature, a crucial issue arises: Is the formation of oxide interfaces indispensable for the occurrence of superconductivity? Exploiting ionic liquid (IL) gating, we are successful in achieving superconductivity at KTaO₃(111) and KTaO₃(110) surfaces with T_c up to 2.0 and 1.0 K, respectively. This oxide-IL interface superconductivity provides a clear evidence that the essential physics of KTaO₃ interface superconductivity lies in the KTaO₃ surfaces doped with electrons. Moreover, the controllability with IL technique paves the way for studying the intrinsic superconductivity in KTaO₃.

Hysteretic temperature dependence of resistance controlled by gate voltage in LaAlO3/SrTiO3 heterointerface electron system

For two-dimensional electron gas device applications, it is important to understand how electrical-transport properties are controlled by gate voltage. Here, we report gate voltage-controllable hysteresis in the resistance–temperature characteristics of two-dimensional electron gas at LaAlO₃/SrTiO₃ heterointerface. Electron channels made of the LaAlO₃/SrTiO₃ heterointerface showed hysteretic resistance–temperature behavior: the measured resistance was significantly higher during upward temperature sweeps in thermal cycling tests. Such hysteretic behavior was observed only after application of positive back-gate voltages below 50 K in the thermal cycle, and the magnitude of hysteresis increased with the applied back-gate voltage. To explain this gate-controlled resistance hysteresis, we propose a mechanism based on electron trapping at impurity sites, in conjunction with the strong temperature-dependent dielectric constant of the SrTiO₃ substrate. Our model explains well the observed gate-controlled hysteresis of the resistance–temperature characteristics, and the mechanism should be also applicable to other SrTiO₃-based oxide systems, paving the way to applications of oxide heterostructures to electronic devices.

On the Superconducting Critical Temperature of Heavily Disordered Interfaces Hosting Multi-Gap Superconductivity

LaAlO3/SrTiO3 interfaces are a nice example of a two-dimensional electron gas, whose carrier density can be varied by top- and back-gating techniques. Due to the electron confinement near the interface, the two-dimensional band structure is split into sub-bands, and more than one sub-band can be filled when the carrier density increases. These interfaces also host superconductivity, and the interplay of two-dimensionality, multi-band character, with the possible occurrence of multi-gap superconductivity and disorder calls for a better understanding of finite-bandwidth effects on the superconducting critical temperature of heavily disordered multi-gap superconductors.

Controlling transport properties at LaFeO3/SrTiO3interfaces by defect engineering

The formation of conductive LaFeO₃/SrTiO₃interfaces is first time reported by pulsed laser deposition via controlling the defects of SrTiO₃, which are closely related to the surface of substrate. It is found that the interfaces grown on SrTiO₃substrates without terraces exhibit the two dimensional electron gas. Moreover, the conductive interfaces show a resistance upturn at low temperatures which is strongly diminished by light irradiation. These interfaces favor the persistent photoconductivity, and the enormous value of relative change in resistance, about 60 185.8%, is also obtained at 20 K. The experimental results provide fundamental insights into controlling the defects at conductive interfaces of oxides and paving a way for complex-oxides based optoelectronic devices.

Chemistry in Superconductors

Superconductors with exotic physical properties are critical to current and future technology. In this review, we highlight several important superconducting families and focus on their crystal structure, chemical bonding, and superconductivity correlations. We connect superconducting materials with chemical bonding interactions based on their structure-property relationships, elucidating our empirically chemical approaches and other methods used in the discovery of new superconductors. Furthermore, we provide some technical strategies to synthesize superconductors and basic but important characterization for chemists needed when reporting new superconductors. In the end, we share our thoughts on how to make new superconductors and where chemists can work on in the superconductivity field. This review is written using chemical terms, with a focus on providing some chemically intuitive thoughts on superconducting materials design.

Inhomogeneous superconductivity and quasilinear magnetoresistance at amorphous LaTiO3/SrTiO3 interfaces

We have studied the transport properties of LaTiO3/SrTiO3 (LTO/STO) heterostructures. In spite of 2D growth observed in reflection high energy electron diffraction, transmission electron microscopy images revealed that the samples tend to amorphize. Still, we observe that the structures are conducting, and some of them exhibit high conductance and/or superconductivity. We established that conductivity arises mainly on the STO side of the interface, and shows all the signs of the two-dimensional electron gas usually observed at interfaces between STO and LTO or LaAlO3, including the presence of two electron bands and tunability with a gate voltage. Analysis of magnetoresistance (MR) and superconductivity indicates the presence of spatial fluctuations of the electronic properties in our samples. That can explain the observed quasilinear out-of-plane MR, as well as various features of the in-plane MR and the observed superconductivity.

Large Switchable Photoconduction within 2D Potential Well of a Layered Ferroelectric Heterostructure

The coexistence of large conductivity and robust ferroelectricity is promising for high-performance ferroelectric devices based on polarization-controllable highly efficient carrier transport. Distinct from traditional perovskite ferroelectrics, Bi₂ WO₆ with a layered structure shows a great potential to preserve its ferroelectricity under substantial electron doping. Herein, by artificial design of photosensitive heterostructures with desired band alignment, three orders of magnitude enhancement of the short-circuit photocurrent is achieved in Bi₂ WO₆ /SrTiO₃ at room temperature. The microscopic mechanism of this large photocurrent originates from separated transport of electrons and holes in [WO₄ ]^-2 and [Bi₂ O₂ ]⁺² layers respectively with a large in-plane conductivity, which is understood by a combination of ab initio calculations and spectroscopic measurements. The layered electronic structure and appropriately designed band alignment in this layered ferroelectric heterostructure provide an opportunity to achieve high-performance and nonvolatile switchable electronic devices.

Electron Trapping Mechanism in LaAlO_{3}/SrTiO_{3} Heterostructures

In LaAlO_{3}/SrTiO_{3} heterostructures, a still poorly understood phenomenon is that of electron trapping in back-gating experiments. Here, by combining magnetotransport measurements and self-consistent Schrödinger-Poisson calculations, we obtain an empirical relation between the amount of trapped electrons and the gate voltage. The amount of trapped electrons decays exponentially away from the interface. However, contrary to earlier observations, we find that the Fermi level remains well within the quantum well. The enhanced trapping of electrons induced by the gate voltage can therefore not be explained by a thermal escape mechanism. Further gate sweeping experiments strengthen that conclusion. We propose a new mechanism which involves the electromigration and clustering of oxygen vacancies in SrTiO_{3} and argue that such electron trapping is a universal phenomenon in SrTiO_{3}-based two-dimensional electron systems.

Gap suppression at a Lifshitz transition in a multi-condensate superconductor

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO₃/SrTiO₃ interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen-Cooper-Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

Erasable and recreatable two-dimensional electron gas at the heterointerface of SrTiO3 and a water-dissolvable overlayer

While benefiting greatly from electronics, our society also faces a major problem of electronic waste, which has already caused environmental pollution and adverse human health effects. Therefore, recyclability becomes a must-have feature in future electronics. Here, we demonstrate an erasable and recreatable two-dimensional electron gas (2DEG), which can be easily created and patterned by depositing a water-dissolvable overlayer of amorphous Sr₃Al₂O₆ (a-SAO) on SrTiO₃ (STO) at room temperature. The 2DEG can be repeatedly erased or recreated by depositing the a-SAO or dissolving in water, respectively. Photoluminescence results show that the 2DEG arises from the a-SAO-induced oxygen vacancy. Furthermore, by gradually depleting the 2DEG, a transition of nonlinear to linear Hall effect is observed, demonstrating an unexpected interfacial band structure. The convenience and repeatability in the creation of the water-dissolvable 2DEG with rich physics could potentially contribute to the exploration of next generation electronics, such as environment-friendly or water-soluble electronics.

How heteroepitaxy occurs on strontium titanate

In traditional models of heteroepitaxy, the substrate serves mainly as a crystalline template for the thin-film lattice, dictating the initial roughness of the film and the degree of coherent strain. Here, performing in situ surface x-ray diffraction during the heteroepitaxial growth of LaTiO₃ on SrTiO₃ (001), we find that a TiO₂ adlayer composed of the ( 13 × 13 ) R33.7° and ( 2 × 2 ) R45.0° reconstructions is a highly active participant in the growth process, continually diffusing to the surface throughout deposition. The effects of the TiO₂ adlayer on layer-by-layer growth are investigated using different deposition sequences and anomalous x-ray scattering, both of which permit detailed insight into the dynamic layer rearrangements that take place. Our work challenges commonly held assumptions regarding growth on TiO₂-terminated SrTiO₃ (001) and demonstrates the critical role of excess TiO₂ surface stoichiometry on the initial stages of heteroepitaxial growth on this important perovskite oxide substrate material.

Diluted Oxide Interfaces with Tunable Ground States

The metallic interface between two oxide insulators, such as LaAlO₃ /SrTiO₃ (LAO/STO), provides new opportunities for electronics and spintronics. However, due to the presence of multiple orbital populations, tailoring the interfacial properties such as the ground state and metal-insulator transitions remains challenging. Here, an unforeseen tunability of the phase diagram of LAO/STO is reported by alloying LAO with a ferromagnetic LaMnO₃ insulator without forming lattice disorder and at the same time without changing the polarity of the system. By increasing the Mn-doping level, x, of LaAl_{1- x} Mn_x O₃ /STO (0 ≤ x ≤ 1), the interface undergoes a Lifshitz transition at x = 0.225 across a critical carrier density of n_c = 2.8 × 10¹³ cm^-2 , where a peak T_SC ≈255 mK of superconducting transition temperature is observed. Moreover, the LaAl_{1- x} Mn_x O₃ turns ferromagnetic at x ≥ 0.25. Remarkably, at x = 0.3, where the metallic interface is populated by only d_xy electrons and just before it becomes insulating, a same device with both signatures of superconductivity and clear anomalous Hall effect (7.6 × 10¹² cm^-2 < n_s ≤ 1.1 × 10¹³ cm^-2 ) is achieved reproducibly. This provides a unique and effective way to tailor oxide interfaces for designing on-demand electronic and spintronic devices.

Majorana Fermions in One-Dimensional Structures at LaAlO3/SrTiO3 Oxide Interfaces

We study one-dimensional structures that may be formed at the LaAlO 3 /SrTiO 3 oxide interface by suitable top gating. These structures are modeled via a single-band model with Rashba spin-orbit coupling, superconductivity and a magnetic field along the one-dimensional chain. We first discuss the conditions for the occurrence of a topological superconducting phase and the related formation of Majorana fermions at the chain endpoints, highlighting a close similarity between this model and the Kitaev model, which also reflects in a similar condition the formation of a topological phase. Solving the model in real space, we also study the spatial extension of the wave function of the Majorana fermions and how this increases with approaching the limit condition for the topological state. Using a scattering matrix formalism, we investigate the stability of the Majorana fermions in the presence of disorder and discuss the evolution of the topological phase with increasing disorder.

A possible superconductor-like state at elevated temperatures near metal electrodes in an LaAlO3/SrTiO3 interface

We experimentally investigated the transport properties near metal electrodes installed on a conducting channel in a LaAlO3/SrTiO3 interface. The local region around the Ti and Al electrodes has a higher electrical conductance than that of other regions, where the upper limits of the temperature and magnetic field can be well defined. Beyond these limits, the conductance abruptly decreases, as in the case of a superconductor. The samples with the Ti- or Al-electrode have an upper-limit temperature of approximately 4 K, which is 10 times higher than the conventional superconducting critical temperature of LaAlO3/SrTiO3 interfaces and delta-doped SrTiO3. This phenomenon is explained by the mechanism of electron transfer between the metal electrodes and electronic d-orbitals in the LaAlO3/SrTiO3 interface. The transferred electrons trigger a phase transition to a superconductor-like state. Our results contribute to the deep understanding of the superconductivity in the LaAlO3/SrTiO3 interface and will be helpful for the development of high-temperature interface superconductors.

Tailoring Materials for Mottronics: Excess Oxygen Doping of a Prototypical Mott Insulator

The Mott transistor is a paradigm for a new class of electronic devices-often referred to by the term Mottronics-which are based on charge correlations between the electrons. Since correlation-induced insulating phases of most oxide compounds are usually very robust, new methods have to be developed to push such materials right to the boundary to the metallic phase in order to enable the metal-insulator transition to be switched by electric gating. Here, it is demonstrated that thin films of the prototypical Mott insulator LaTiO₃ grown by pulsed laser deposition under oxygen atmosphere are readily tuned by excess oxygen doping across the line of the band-filling controlled Mott transition in the electronic phase diagram. The detected insulator to metal transition is characterized by a strong change in resistivity of several orders of magnitude. The use of suitable substrates and capping layers to inhibit oxygen diffusion facilitates full control of the oxygen content and renders the films stable against exposure to ambient conditions. These achievements represent a significant advancement in control and tuning of the electronic properties of LaTiO_3+x thin films making it a promising channel material in future Mottronic devices.

Nonzero Berry phase in quantum oscillations from giant Rashba-type spin splitting in LaTiO3/SrTiO3 heterostructures

The manipulation of the spin degrees of freedom in a solid has been of fundamental and technological interest recently for developing high-speed, low-power computational devices. There has been much work focused on developing highly spin-polarized materials and understanding their behavior when incorporated into so-called spintronic devices. These devices usually require spin splitting with magnetic fields. However, there is another promising strategy to achieve spin splitting using spatial symmetry breaking without the use of a magnetic field, known as Rashba-type splitting. Here we report evidence for a giant Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃. Analysis of the magnetotransport reveals anisotropic magnetoresistance, weak anti-localization and quantum oscillation behavior consistent with a large Rashba-type splitting. It is surprising to find a large Rashba-type splitting in 3d transition metal oxide-based systems such as the LaTiO₃/SrTiO₃ interface, but it is promising for the development of a new kind of oxide-based spintronics.

Rashba-type splitting is an effective way to manipulate the spin degrees of freedom in a solid without external magnetic field. Here, the authors demonstrate a strong Rashba-type splitting at the interface of LaTiO₃ and SrTiO₃ which is promising for the development of oxide-based spintronics.

Competition between electron pairing and phase coherence in superconducting interfaces

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin-orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high-energy dxz/dyz bands in the quantum well, more apt to host superconductivity.

Influence of In-Gap States on the Formation of Two-Dimensional Election Gas at ABO3/SrTiO3 Interfaces

We explored in-gap states (IGSs) in perovskite oxide heterojunction films. We report that IGSs in these films play a crucial role in determining the formation and properties of interfacial two-dimensional electron gas (2DEG). We report that electron trapping by IGSs opposes charge transfer from the film to the interface. The IGS in films yielded insulating interfaces with polar discontinuity and explained low interface carrier density of conducting interfaces. An ion trapping model was proposed to explain the physics of the IGSs and some experimental findings, such as the unexpected formation of 2DEG at the initially insulating LaCrO₃/SrTiO₃ interface and the influence of substitution layers on 2DEG.

Link between the Superconducting Dome and Spin-Orbit Interaction in the (111) LaAlO_{3}/SrTiO_{3} Interface

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 superconductivity and spin-orbit interaction as well as the enhancement of the parallel upper critical field, well beyond the Chandrasekhar-Clogston limit, suggest that superconductivity and the spin-orbit interaction are linked in a nontrivial fashion. We propose possible scenarios to explain this unconventional behavior.

Inducing and Manipulating Heteroelectronic States in a Single MoS_{2} Thin Flake

By dual gating a few-layer MoS_{2} flake, we induce spatially separated electronic states showing superconductivity and Shubnikov-de Haas (SdH) oscillations. While the highly confined superconductivity forms at the K/K^{'} valleys of the topmost layer, the SdH oscillations are contributed by the electrons residing in the Q/Q^{'} valleys of the rest of the bottom layers, which is confirmed by the extracted Landau level degeneracy of 3, electron effective mass of 0.6m_{e}, and carrier density of 5×10^{12}  cm^{-2}. Mimicking conventional heterostructures, the interaction between the heteroelectronic states can be electrically manipulated, which enables "bipolarlike" superconducting transistor operation. The off-on-off switching pattern can be continuously accessed at low temperatures by a field effect depletion of carriers with a negative back gate bias and the proximity effect between the top superconducting layer and the bottom metallic layers that quenches the superconductivity at a positive back gate bias.

Dielectric collapse at the LaAlO3/SrTiO3 (001) heterointerface under applied electric field

The fascinating interfacial transport properties at the LaAlO₃/SrTiO₃ heterointerface have led to intense investigations of this oxide system. Exploiting the large dielectric constant of SrTiO₃ at low temperatures, tunability in the interfacial conductivity over a wide range has been demonstrated using a back-gate device geometry. In order to understand the effect of back-gating, it is crucial to assess the interface band structure and its evolution with external bias. In this study, we report measurements of the gate-bias dependent interface band alignment, especially the confining potential profile, at the conducting LaAlO₃/SrTiO₃ (001) heterointerface using soft and hard x-ray photoemission spectroscopy in conjunction with detailed model simulations. Depth-profiling analysis incorporating the electric field dependent dielectric constant in SrTiO₃ reveals that a significant potential drop on the SrTiO₃ side of the interface occurs within ~2 nm of the interface under negative gate-bias. These results demonstrate gate control of the collapse of the dielectric permittivity at the interface, and explain the dramatic loss of electron mobility with back-gate depletion.

Gate-Tunable Band Structure of the LaAlO_{3}-SrTiO_{3} Interface

The two-dimensional electron system at the interface between LaAlO_{3} and SrTiO_{3} has several unique properties that can be tuned by an externally applied gate voltage. In this work, we show that this gate tunability extends to the effective band structure of the system. We combine a magnetotransport study on top-gated Hall bars with self-consistent Schrödinger-Poisson calculations and observe a Lifshitz transition at a density of 2.9×10^{13}cm^{-2}. Above the transition, the carrier density of one of the conducting bands decreases with increasing gate voltage. This surprising decrease is accurately reproduced in the calculations if electronic correlations are included. These results provide a clear, intuitive picture of the physics governing the electronic structure at complex-oxide interfaces.

Reversible Formation of 2D Electron Gas at the LaFeO3 /SrTiO3 Interface via Control of Oxygen Vacancies

A conducting 2D electron gas (2DEG) is formed at the interface between epitaxial LaFeO₃ layers >3 unit cells thick and the surface of SrTiO₃ single crystals. The 2DEG is exquisitely sensitive to cation intermixing and oxygen nonstoichiometry. It is shown that the latter thus allows the controllable formation of the 2DEG via ionic liquid gating, thereby forming a nonvolatile switch.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: a review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

Dissipative phases across the superconductor-to-insulator transition

Competing phenomena in low dimensional systems can generate exotic electronic phases, either through symmetry breaking or a non-trivial topology. In two-dimensional (2D) systems, the interplay between superfluidity, disorder and repulsive interactions is especially fruitful in this respect although both the exact nature of the phases and the microscopic processes at play are still open questions. In particular, in 2D, once superconductivity is destroyed by disorder, an insulating ground state is expected to emerge, as a result of a direct superconductor-to-insulator quantum phase transition. In such systems, no metallic state is theoretically expected to survive to the slightest disorder. Here we map out the phase diagram of amorphous NbSi thin films as functions of disorder and film thickness, with two metallic phases in between the superconducting and insulating ones. These two dissipative states, defined by a resistance which extrapolates to a finite value in the zero temperature limit, each bear a specific dependence on disorder. We argue that they originate from an inhomogeneous destruction of superconductivity, even if the system is morphologically homogeneous. Our results suggest that superconducting fluctuations can favor metallic states that would not otherwise exist.

Dual-Gate Modulation of Carrier Density and Disorder in an Oxide Two-Dimensional Electron System

Carrier density and disorder are two crucial parameters that control the properties of correlated two-dimensional electron systems. In order to disentangle their individual contributions to quantum phenomena, independent tuning of these two parameters is required. Here, by utilizing a hybrid liquid/solid electric dual-gate geometry acting on the conducting LaAlO₃/SrTiO₃ heterointerface, we obtain an additional degree of freedom to strongly modify the electron confinement profile and thus the strength of interfacial scattering, independent from the carrier density. A dual-gate controlled nonlinear Hall effect is a direct manifestation of this profile, which can be quantitatively understood by a Poisson-Schrödinger sub-band model. In particular, the large nonlinear dielectric response of SrTiO₃ enables a very wide range of tunable density and disorder, far beyond that for conventional semiconductors. Our study provides a broad framework for understanding various reported phenomena at the LaAlO₃/SrTiO₃ interface.

Predictive Control over Charge Density in the Two-Dimensional Electron Gas at the Polar-Nonpolar NdTiO_{3}/SrTiO_{3} Interface

Through systematic control of the Nd concentration, we show that the carrier density of the two-dimensional electron gas (2DEG) in SrTiO_{3}/NdTiO_{3}/SrTiO_{3}(001) can be modulated over a wide range. We also demonstrate that the NdTiO_{3} in heterojunctions without a SrTiO_{3} cap is degraded by oxygen absorption from air, resulting in the immobilization of donor electrons that could otherwise contribute to the 2DEG. This system is, thus, an ideal model to understand and control the insulator-to-metal transition in a 2DEG based on both environmental conditions and film-growth processing parameters.

Gate dependence of upper critical field in superconducting (110) LaAlO3/SrTiO3 interface

The fundamental parameters of the superconducting state such as coherence length and pairing strength are essential for understanding the nature of superconductivity. These parameters can be estimated by measuring critical parameters such as upper critical field, H_c2. In this work, H_c2 of a superconducting (110) LaAlO₃/SrTiO₃ interface is determined through magnetoresistive measurements as a function of the gate voltage, V_G. When V_G increases, the critical temperature has a dome-like shape, while H_c2 monotonically decreases. This relationship of independence between the variation of T_c and of H_c2 suggests that the Cooper pairing potential is stronger in the underdoped region and the coherence length increases with the increase of V_G. The result is as for high temperature superconducting cuprates and it is different than for conventional low temperature superconductors.

Unconventional dc Transport in Rashba Electron Gases

We discuss the transport properties of a disordered two-dimensional electron gas with strong Rashba spin-orbit coupling. We show that in the high-density regime where the Fermi energy overcomes the energy associated with spin-orbit coupling, dc transport is accurately described by a standard Drude's law, due to a nontrivial compensation between the suppression of backscattering and the relativistic correction to the quasiparticle velocity. On the contrary, when the system enters the opposite dominant spin-orbit regime, Drude's paradigm breaks down and the dc conductivity becomes strongly sensitive to the spin-orbit coupling strength, providing a suitable tool to test the entanglement between spin and charge degrees of freedom in these systems.

Phase Separation from Electron Confinement at Oxide Interfaces

Oxide heterostructures are of great interest for both fundamental and applicative reasons. In particular, the two-dimensional electron gas at the LaAlO_{3}/SrTiO_{3} or LaTiO_{3}/SrTiO_{3} interfaces displays many different properties and functionalities. However, there are clear experimental indications that the interface electronic state is strongly inhomogeneous and therefore it is crucial to investigate possible intrinsic mechanisms underlying this inhomogeneity. Here, the electrostatic potential confining the electron gas at the interface is calculated self-consistently, finding that such confinement may induce phase separation, to avoid a thermodynamically unstable state with a negative compressibility. This provides a robust mechanism for the inhomogeneous character of these interfaces.

Interplay between density and superconducting quantum critical fluctuations

We consider the case of a density-driven metal-superconductor transition in the proximity of an electronic phase separation. In particular, we investigate the interplay between superconducting fluctuations and density fluctuations, which become quantum critical when the electronic phase separation vanishes at zero temperature into a quantum critical point. In this situation, the critical dynamical density fluctuations strongly affect the dynamics of the Cooper-pair fluctuations, which acquire a more singular character with a z  =  3 dynamical critical index. This gives rise to a scenario that possibly rules the disappearance of superconductivity when the electron density is reduced by electrostatic gating at the LaAlO3/SrTiO3 interface.

Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO3/SrTiO3 devices

The recent development in the fabrication of artificial oxide heterostructures opens new avenues in the field of quantum materials by enabling the manipulation of the charge, spin and orbital degrees of freedom. In this context, the discovery of two-dimensional electron gases (2-DEGs) at LaAlO₃/SrTiO₃ interfaces, which exhibit both superconductivity and strong Rashba spin-orbit coupling (SOC), represents a major breakthrough. Here, we report on the realisation of a field-effect LaAlO₃/SrTiO₃ device, whose physical properties, including superconductivity and SOC, can be tuned over a wide range by a top-gate voltage. We derive a phase diagram, which emphasises a field-effect-induced superconductor-to-insulator quantum phase transition. Magneto-transport measurements show that the Rashba coupling constant increases linearly with the interfacial electric field. Our results pave the way for the realisation of mesoscopic devices, where these two properties can be manipulated on a local scale by means of top-gates.

Enhanced spin-orbit coupling and charge carrier density suppression in LaAl1-xCrxO3/SrTiO3 hetero-interfaces

We report a gradual suppression of the two-dimensional electron gas (2DEG) at the LaAlO(3)/SrTiO(3) interface on substitution of chromium at the Al sites. The sheet carrier density at the interface (n□) drops monotonically from ∼2.2 × 10(14) cm(-2) to ∼2.5 × 10(13) cm(-2) on replacing ≈60% of the Al sites by Cr and the sheet resistance (R□) exceeds the quantum limit for localization (h/2e(2)) in the concentrating range 40-60% of Cr. The samples with Cr ⩽40% show a distinct minimum (T(m)) in metallic R□(T) whose position shifts to higher temperatures on increasing the substitution. Distinct signatures of Rashba spin-orbit interaction (SOI) induced magnetoresistance (MR) are seen in R□ measured in out of plane field (H⊥) geometry at T ⩽ 8 K. Analysis of these data in the framework of Maekawa-Fukuyama theory allows extraction of the SOI critical field (H(SO)) and time scale (τ(SO)) whose evolution with Cr concentration is similar as with the increasing negative gate voltage in LAO/STO interface. The MR in the temperature range 8 K ⩽ T ⩽ T(m) is quadratic in the field with a +ve sign for H⊥ and -ve sign for H∥. The behaviour of H∥ MR is consistent with Kondo theory which in the present case is renormalized by the strong Rashba SOI at T < 8 K.

Two components for one resistivity in LaVO3/SrTiO3 heterostructure

A series of 100 nm LaVO3 thin films have been synthesized on (0 0 1)-oriented SrTiO3 substrates using the pulsed laser deposition technique, and the effects of growth temperature are analyzed. Transport properties reveal a large electronic mobility and a non-linear Hall effect at low temperature. In addition, a cross-over from a semiconducting state at high-temperature to a metallic state at low-temperature is observed, with a clear enhancement of the metallic character as the growth temperature increases. Optical absorption measurements combined with the two-bands analysis of the Hall effect show that the metallicity is induced by the diffusion of oxygen vacancies in the SrTiO3 substrate. These results allow us to understand that the film/substrate heterostructure behaves as an original semiconducting-metallic parallel resistor, and electronic transport properties are consistently explained.

Engineering two-dimensional superconductivity and Rashba spin-orbit coupling in LaAlO₃/SrTiO₃ quantum wells by selective orbital occupancy

The discovery of two-dimensional electron gases (2DEGs) at oxide interfaces-involving electrons in narrow d-bands-has broken new ground, enabling the access to correlated states that are unreachable in conventional semiconductors based on s- and p- electrons. There is a growing consensus that emerging properties at these novel quantum wells-such as 2D superconductivity and magnetism-are intimately connected to specific orbital symmetries in the 2DEG sub-band structure. Here we show that crystal orientation allows selective orbital occupancy, disclosing unprecedented ways to tailor the 2DEG properties. By carrying out electrostatic gating experiments in LaAlO3/SrTiO3 wells of different crystal orientations, we show that the spatial extension and anisotropy of the 2D superconductivity and the Rashba spin-orbit field can be largely modulated by controlling the 2DEG sub-band filling. Such an orientational tuning expands the possibilities for electronic engineering of 2DEGs at LaAlO3/SrTiO3 interfaces.

Limit of the electrostatic doping in two-dimensional electron gases of LaXO₃(X = Al, Ti)/SrTiO₃

In LaTiO₃/SrTiO₃ and LaAlO₃/SrTiO₃ heterostructures, the bending of the SrTiO₃ conduction band at the interface forms a quantum well that contains a superconducting two-dimensional electron gas (2-DEG). Its carrier density and electronic properties, such as superconductivity and Rashba spin-orbit coupling can be controlled by electrostatic gating. In this article we show that the Fermi energy lies intrinsically near the top of the quantum well. Beyond a filling threshold, electrons added by electrostatic gating escape from the well, hence limiting the possibility to reach a highly-doped regime. This leads to an irreversible doping regime where all the electronic properties of the 2-DEG, such as its resistivity and its superconducting transition temperature, saturate. The escape mechanism can be described by the simple analytical model we propose.

Thermopower enhancement by fractional layer control in 2D oxide superlattices

Precise tuning of the 2D carrier density by using fractional δ-doping of d electrons improves the thermoelectric properties of oxide heterostructures. This promising result can be attributed to the anisotropic band structure in the 2D system, indicating that δ-doped oxide superlattices are good candidates for advanced thermoelectrics.

Multiple quantum criticality in a two-dimensional superconductor

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Intrinsic instability of electronic interfaces with strong Rashba coupling

We consider a model for the two-dimensional electron gas formed at the interface of oxide heterostructures, which includes a Rashba spin-orbit coupling proportional to the electric field perpendicular to the interface. Based on the standard mechanism of polarity catastrophe, we assume that the electric field has a contribution proportional to the electron density. Under these simple and general assumptions, we show that a phase separation instability (signaled by a negative compressibility) occurs for realistic values of the spin-orbit coupling and of the electronic band-structure parameters. This provides an intrinsic mechanism for the inhomogeneous phases observed at the LaAlO(3)/SrTiO(3) or LaTiO(3)/SrTiO(3) interfaces.