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Interlayer space in graphite is impermeable to ions and molecules, including protons. Its controlled expansion would find several applications in desalination, gas purification, high-density batteries, etc. In the past, metal intercalation has been used to modify graphitic interlayer spaces; however, resultant intercalation compounds are unstable in water. Here, we successfully expanded graphite interlayer spaces by intercalating aqueous KCl ions electrochemically. Our spectroscopy studies provide clear evidence for cation-π interactions explaining the stability of the devices, though weak anion-π interactions were also detectable. The water conductivity shows several orders of enhancement when compared to unintercalated graphite. Water evaporation experiments further confirm the high permeation rate. There is weak ion permeation through interlayer spaces, up to the highest chloride concentration of 1 M, an indication of sterically limited transport. In these very few transported ions, we observe hydration energy-dependent selectivity between salt ions. These strongly suggest a soft ball model of steric exclusion, which is rarely reported. These findings improve our understanding of molecular and ionic transport at the atomic scale.

Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one angstrom even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures(1-5). Here, we show that van der Waals gaps between atomic planes of layered crystals provide angstrom-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher barrier than deuterons when entering van der Waals gaps in hexagonal boron nitride and molybdenum disulfide. This is attributed to the difference in the de Broglie wavelengths of the isotopes. Once inside the crystals, transport of both isotopes can be described by classical diffusion, albeit with unexpectedly fast rates comparable to that of protons in water. The demonstrated angstrom-size channels can be exploited for further studies of atomistic quantum confinement and, if the technology can be scaled up, for sieving hydrogen isotopes.

Defect-free monolayers of graphene and hexagonal boron nitride are surprisingly permeable to thermal protons, despite being completely impenetrable to all gases. It remains untested whether small ions can permeate through the two-dimensional crystals. Here we show that mechanically exfoliated graphene and hexagonal boron nitride exhibit perfect Nernst selectivity such that only protons can permeate through, with no detectable flow of counterions. In the experiments, we use suspended monolayers that have few, if any, atomic-scale defects, as shown by gas permeation tests, and place them to separate reservoirs filled with hydrochloric acid solutions. Protons account for all the electrical current and chloride ions are blocked. This result corroborates the previous conclusion that thermal protons can pierce defect-free two-dimensional crystals. Besides the importance for theoretical developments, our results are also of interest for research on various separation technologies based on two-dimensional materials., Defect-free monolayers of graphene and hexagonal boron nitride are highly permeable to thermal protons, but are impenetrable to gases. Here the authors show that mechanically exfoliated crystals exhibit perfect proton selectivity, corroborating proton transport through the bulk without atomic-scale defects.

Nanometre-scale graphitic capillaries with atomically flat walls are engineered and studied, revealing unexpectedly fast transport of liquid water through channels that accommodate only a few layers of water. Artificial nanometre-sized capillaries have enabled new research and led to the emergence of nanofluidics, but surface roughness in particular makes it very challenging to exactly control their dimensions. Andre Geim and colleagues now show that van der Waals assembly can produce narrow and smooth capillaries that have atomically flat top and bottom graphite sheets, separated by spacers made from a precisely controlled number of graphene layers. Water transport through the channels, which range in height from a single atomic plane to dozens of them, is unexpectedly fast and speeds up further in channels that accommodate only a few layers of water. The fabrication method is expected to give access to a wide range of capillaries with atomically precise sizes, and with permeation properties that are tunable by the choice of two-dimensional material used for creating the channel walls. Nanometre-scale pores and capillaries have long been studied because of their importance in many natural phenomena and their use in numerous applications1. A more recent development is the ability to fabricate artificial capillaries with nanometre dimensions, which has enabled new research on molecular transport and led to the emergence of nanofluidics2,3,4. But surface roughness in particular makes it challenging to produce capillaries with precisely controlled dimensions at this spatial scale. Here we report the fabrication of narrow and smooth capillaries through van der Waals assembly5, with atomically flat sheets at the top and bottom separated by spacers made of two-dimensional crystals6 with a precisely controlled number of layers. We use graphene and its multilayers as archetypal two-dimensional materials to demonstrate this technology, which produces structures that can be viewed as if individual atomic planes had been removed from a bulk crystal to leave behind flat voids of a height chosen with atomic-scale precision. Water transport through the channels, ranging in height from one to several dozen atomic planes, is characterized by unexpectedly fast flow (up to 1 metre per second) that we attribute to high capillary pressures (about 1,000 bar) and large slip lengths. For channels that accommodate only a few layers of water, the flow exhibits a marked enhancement that we associate with an increased structural order in nanoconfined water. Our work opens up an avenue to making capillaries and cavities with sizes tunable to angstrom precision, and with permeation properties further controlled through a wide choice of atomically flat materials available for channel walls.

Electric field effect in electronic double layer transistor (EDLT) configuration with ionic liquids as the dielectric materials is a powerful means of exploring various properties in different materials. Here we demonstrate the modulation of electrical transport properties and extremely high mobility of two-dimensional electron gas at LaAlO$_3$/SrTiO$_3$ (LAO/STO) interface through ionic liquid-assisted electric field effect. By changing the gate voltages, the depletion of charge carrier and the resultant enhancement of electron mobility up to 19380 cm$^2$/Vs are realized, leading to quantum oscillations of the conductivity at the LAO/STO interface. The present results suggest that high-mobility oxide interfaces which exhibit quantum phenomena could be obtained by ionic liquid-assisted field effect., 22 pages, 4 figures, ACS Nano, March 09, 2016

Only the water may pass Removing objects by size to keep only the smallest ones is simple in theory, but it requires a sieve, membrane, or filter with holes small enough to allow only the smallest objects to pass. Gopinadhan et al. engineered two-dimensional water channels by removing an atomic plane of atoms from a sandwich made from bulk crystal with a graphene spacer. Water flowed through the channels without resistance, but the channels excluded all ions except for protons because the ion hydration shells could not squeeze through the channels. Science , this issue p. 145

In this manuscript, we demonstrate a method based on atomic force microscopy which enables local probing of surface wettability. The maximum pull-off force, obtained from force spectroscopy shows a remarkable correlation with the macroscopically observed water contact angle, measured over a wide variety of surfaces starting from hydrophilic, all the way through to hydrophobic ones. This relationship, consequently, facilitates the establishment of a universal behaviour. The adhesion forces scale with the polar component of surface energy. However, no such relation could be established with the dispersive component. Hence, we postulate that the force(s) which enable us to correlate the force spectroscopy data measured on the nanoscale to the macroscopic contact angle are primarily arising from electrostatic-dipole-dipole interactions at the solid-liquid interface. London forces play less of a role. This effect in is line with density functional theory (DFT) calculations suggesting a higher degree of hydroxylation of hydrophilic surfaces. This result shows that molecular simulations and measurements on an atomic scale can be extrapolated to macroscopic surface wetting problems.

The two-dimensional electron gas in SrTiO3 created by an overlayer of amorphous LaAlO3 is compared with those at the TiO2-terminated surfaces of rutile and anatase. Differences in conductivity are explained in terms of the limiting Ti–O–Ti bond angles (orbital corrugation), band dispersion, and polaron formation. At 300 K, the sheet conductivity and mobility of anatase exceed those for SrTiO3 or rutile by one or two orders of magnitude, respectively. The electrons in rutile become localized below 25 K.

Squeezing through a hole Transport of an ion is usually directly related to its hydrated radius and assumed to be nonflexible. Either a hydrated ion fits through an aperture or it does not, and shape should play a dominant role rather than charge. Esfandiar et al. created nanofluidic devices by stacking structured bulk materials, including graphite, boron nitride, and molybdenum disulfide. They investigated the transport of ions in aqueous solutions through the nanochannels in the devices. Unexpectedly, they observed different behavior for ions of similar hydrated size but opposite charge. Science , this issue p. 511

We report the angular dependence of magnetoresistance in the two-dimensional electron gas at the ${\mathrm{LaAlO}}_{3}$/${\mathrm{SrTiO}}_{3}$ interface. We find that this interfacial magnetoresistance exhibits a similar angular dependence to the spin Hall magnetoresistance observed in ferromagnet/heavy metal bilayers, which has been so far discussed in the framework of the bulk spin Hall effect of the heavy metal layer. The observed magnetoresistance is in qualitative agreement with a theoretical model calculation including both Rashba spin-orbit coupling and an exchange interaction. Our result suggests that magnetic interfaces subject to spin-orbit coupling can generate a non-negligible contribution to the spin Hall magnetoresistance, and the interfacial spin-orbit coupling effect is therefore key to the understanding of various spin-orbit-coupling-related phenomena in magnetic/nonmagnetic bilayers.

Understanding magnetoresistance, the change in electrical resistance upon an external magnetic field, at the atomic level is of great interest both fundamentally and technologically.

Ion permeation and selectivity of graphene oxide membranes with sub-nm channels dramatically alters with the change in interlayer distance due to dehydration effects whereas permeation of water molecules remains largely unaffected. Graphene oxide membranes show exceptional molecular permeation properties, with promise for many applications1,2,3,4,5. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of ∼9 A (ref. 4), which is larger than the diameters of hydrated ions of common salts4,6. The cutoff is determined by the interlayer spacing (d) of ∼13.5 A, typical for graphene oxide laminates that swell in water2,4. Achieving smaller d for the laminates immersed in water has proved to be a challenge. Here, we describe how to control d by physical confinement and achieve accurate and tunable ion sieving. Membranes with d from ∼9.8 A to 6.4 A are demonstrated, providing a sieve size smaller than the diameters of hydrated ions. In this regime, ion permeation is found to be thermally activated with energy barriers of ∼10–100 kJ mol–1 depending on d. Importantly, permeation rates decrease exponentially with decreasing sieve size but water transport is weakly affected (by a factor of

Wetting behaviour of surfaces is believed to be affected by van der Waals (vdW) forces, however, there is no clear demonstration of this. With the isolation of two-dimensional vdW layered materials it is possible to test this hypothesis. In this paper, we report the wetting behaviour of vdW heterostructures which include, chemical vapor deposition (CVD) grown graphene, molybdenum disulfide (MoS2) and tungsten disulfide (WS2) on few layers of hexagon boron nitride (h-BN) and SiO2/Si. Our study clearly shows that while this class of two-dimensional materials are not wetting transparent, there seems to be a significant amount of influence on their wetting properties by the underlying substrate due to dominant vdW forces. Contact angle measurements indicate that graphene and graphene-like layered transitional metal dichalcogenides invariably have intrinsically dispersive surfaces with a dominating London-vdW force-mediated wettability. Electric field controlled wetting studies of MoS2/WS2/SiO2/Si heterostructures were performed and no notable changes to the water contact angle was seen with applied voltage although two orders of magnitude change in resistance was observed. We postulate that the highly dispersive nature of these surfaces arising from the predominant London-vdW forces could be the reason for such observation.

We demonstrate a new contact technology for realizing a near band edge contact Schottky barrier height (FB) in black phosphorus (BP) p- channel transistors. This is achieved via the use of high work function nickel (Ni) and thermal anneal to produce a novel nickelphosphide (Ni2P) alloy which enables a record low hole FB of 12 meV. The formation of reactive Ni2P/ BP contact was found to further improve the transmission probability as compared to the Ni/ BP contact. Moreover, the penetration of Ni2P in the source and drain regions could additionally reduce the parasitic series resistance, leading to drive current improvement.

Black phosphorus (BP) is a new class of 2D material which holds promise for next generation transistor applications owing to its intrinsically superior carrier mobility properties. Among other issues, achieving good ohmic contacts with low source-drain parasitic resistance in BP field-effect transistors (FET) remains a challenge. For the first time, we report a new contact technology that employs the use of high work function nickel (Ni) and thermal anneal to produce a metal alloy that effectively reduces the contact Schottky barrier height (ΦB) in a BP FET. When annealed at 300 °C, the Ni electrode was found to react with the underlying BP crystal and resulted in the formation of nickel-phosphide (Ni2P) alloy. This serves to de-pin the metal Fermi level close to the valence band edge and realizes a record low hole ΦB of merely ~12 meV. The ΦB at the valence band has also been shown to be thickness-dependent, wherein increasing BP multi-layers results in a smaller ΦB due to bandgap energy shrinkage. The integration of hafnium-dioxide high-k gate dielectric additionally enables a significantly improved subthreshold swing (SS ~ 200 mV/dec), surpassing previously reported BP FETs with conventional SiO2 gate dielectric (SS > 1 V/dec).

Magnetic interactions in solids are normally mediated by short-range exchange or weak dipole fields. Here we report a magnetic interaction that can propagate over long distances (∼10 nm) across a polar insulating oxide spacer. Evidence includes oscillations of magnetization, coercivity and field-cooled loop shift with the thickness of LaAlO3 in La0.67Sr0.33MnO3/LaAlO3/SrTiO3 heterostructures. Similar modifications of the hysteresis loop appear when two coupled films of La0.67Sr0.33MnO3 are separated by LaAlO3, or another polar insulator, but they are absent when the oxide spacer layer is nonpolar. The loop shift is attributed to strong spin–orbit coupling and Dzyaloshinskii–Moriya interaction at the interfaces. There is evidence from inelastic light scattering that the polar spacer mediates long-range transmission of orbital magnetization. This coupling mechanism is expected to apply for any conducting ferromagnetic oxide with mixed valence; in view of electron hopping frequency involved, it raises the prospect of terahertz tunability of magnetic coupling., Magnetic interactions in solids are usually short-range or else they involve itinerant electrons. Here, the authors evidence a long-range magnetic coupling mediated by orbital moments in a polar spacer layer of nonmagnetic insulating oxide, with a sign which oscillates with spacer thickness.

The two-dimensional electron gas in SrTiO3 created by an overlayer of amorphous LaAlO3 is compared with those at the TiO2-terminated surfaces of rutile and anatase. Differences in conductivity are explained in terms of the limiting Ti-O-Ti bond angles (orbital corrugation), band dispersion, and polaron formation. At 300 K, the sheet conductivity and mobility of anatase exceed those for SrTiO3 or rutile by one or two orders of magnitude, respectively. The electrons in rutile become localized below 25 K.

We use ionic liquid-assisted electric field effect to tune the carrier density in an electron-doped cuprate ultrathin film and cause a two-dimensional superconductor-insulator transition (SIT). The low upper critical field in this system allows us to perform magnetic field (B)-induced SIT in the liquid-gated superconducting film. Finite-size scaling analysis indicates that SITs induced both by electric and magnetic field are quantum phase transitions and the transitions are governed by percolation effects - quantum mechanical in the former and classical in the latter case. Compared to the hole-doped cuprates, the SITs in electron-doped system occur at critical sheet resistances (Rc) much lower than the pair quantum resistance RQ=h/(2e)2=6.45 k{\Omega}, suggesting the possible existence of fermionic excitations at finite temperature at the insulating phase near SITs., Comment: Manuscript including supplementary materials

Understanding magnetoresistance, the change in electrical resistance under an external magnetic field, at the atomic level is of great interest both fundamentally and technologically. Graphene and other two-dimensional layered materials provide an unprecedented opportunity to explore magnetoresistance at its nascent stage of structural formation. Here we report an extremely large local magnetoresistance of∼2,000% at 400 K and a non-local magnetoresistance of >90,000% in an applied magnetic field of 9 T at 300 K in few-layer graphene/boron–nitride heterostructures. The local magnetoresistance is understood to arise from large differential transport parameters, such as the carrier mobility, across various layers of few-layer graphene upon a normal magnetic field, whereas the non-local magnetoresistance is due to the magnetic field induced Ettingshausen–Nernst effect. Non-local magnetoresistance suggests the possibility of a graphene-based gate tunable thermal switch. In addition, our results demonstrate that graphene heterostructures may be promising for magnetic field sensing applications., Magnetoresistance, the change in electrical resistance of a material with its magnetic state, is an important phenomenon utilized in technological applications. Here, the authors report large local and non-local magnetoresistance effects in few-layer graphene/boron–nitride heterostructures at room temperature.

Ta and Nb substituted TiO2 are important transparent conducting oxides that have potential for applications in photovoltaics, photocatalysis, and water splitting/CO2 sequestration. In addition to donating electrons, what are the effects of Nb and Ta substitution? Here we observe strong experimental evidence that Ta and Nb substitution induces large and small polarons in anatase TiO2 epitaxial thin films. The degenerate donor electrons (from both Nb and Ta) show a high temperature T3 dependence on electrical resistivity, which confirms the presence of large polarons, along with room temperature metallic transport. This is further confirmed by the enhancement in the electron effective mass, which was estimated from thermopower measurements. Femtosecond transient absorption (fs-TA) reveals the life time of the Ti-t2g and eg levels and the separation of these levels are consistent with the X-ray absorption spectroscopy (XAS) measurement. In addition, fs-TA reveals the presence of small polarons with a life time substantially >1 ns, which arises from defect levels and is a consequence of Ta and Nb substitution. X-ray photoelectron spectroscopy (XPS) provides evidence of Ti3+, which may be identified as the defects responsible for the small polarons. These long-lived small polarons may provide a way to minimize recombination dynamics in TiO2-based electrodes for photo-excited devices.

We report the observation of spatially separated Kondo scattering and ferromagnetism in anatase Ta0.06Ti0.94O2 thin films as a function of thickness (10–200 nm). The Kondo behavior observed in thicker films is suppressed on decreasing thickness and vanishes below ~25 nm. In 200 nm film, transport data could be fitted to a renormalization group theory for Kondo scattering though the carrier density in this system is lower by two orders of magnitude, the magnetic entity concentration is larger by a similar magnitude and there is strong electronic correlation compared to a conventional system such as Cu with magnetic impurities. However, ferromagnetism is observed at all thicknesses with magnetic moment per unit thickness decreasing beyond 10 nm film thickness. The simultaneous presence of Kondo and ferromagnetism is explained by the spatial variation of defects from the interface to surface which results in a dominantly ferromagnetic region closer to substrate-film interface while the Kondo scattering is dominant near the surface and decreasing towards the interface. This material system enables us to study the effect of neighboring presence of two competing magnetic phenomena and the possibility for tuning them.

A clear gate voltage tunable weak antilocalization and a giant magnetoresistance of 400 percent are observed at 1.9 K in single layer graphene with an out-of-plane field. A large magnetoresistance value of 275 percent is obtained even at room temperature implying potential applications of graphene in magnetic sensors. Both the weak antilocalization and giant magnetoresistance persists far away from the charge neutrality point in contrast to previous reports, and both effects are originated from charged impurities. Interestingly, the signatures of Shubnikov-de Haas oscillations and the quantum Hall effect are also observed for the same sample., Phys. Rev. B (2013)

The confinement of the two-dimensional electron gas (2DEG), preferential occupancy of the Ti 3$d$ orbital, and strong spin-orbit coupling at the LaAlO${}_{3}$/SrTiO${}_{3}$ interface play a significant role in its emerging properties. Here we report a fourfold oscillation in the anisotropic magnetoresistance (AMR) and planar Hall effect (PHE) at the LaAlO${}_{3}$/SrTiO${}_{3}$ heterointerface. We evaluate the carrier confinement effects on the AMR and find that the fourfold oscillation appears only for the case of 2DEG systems while it is twofold for the three-dimensional system. The AMR behavior is further found to be sensitive to applied electric field, emphasizing the significance of spin-orbit coupling at the interface. These confinement effects suggest that the magnetic interactions are predominant at the interface, and the gate electric field modulation of AMR shows the tunability of magnetic interactions. As the fourfold oscillation fits well to the phenomenological model for a cubic symmetry system, this suggests that the origin of the oscillation may be linked to the anisotropy in magnetic scattering arising from the interaction of electrons with the localized magnetic moments coupled to the crystal symmetry. The observed large PHE further indicates the in-plane nature of magnetic ordering that arises from the in-plane Ti 3${d}_{xy}$ orbitals.

The observation of a high-mobility two-dimensional electron gas between two insulating complex oxides, especially LaAlO3/SrTiO3, has enhanced the potential of oxides for electronics. The occurrence of this conductivity is believed to be driven by polarization discontinuity, leading to an electronic reconstruction. In this scenario, the crystal orientation has an important role and no conductivity would be expected, for example, for the interface between LaAlO3 and (110)-oriented SrTiO3, which should not have a polarization discontinuity. Here we report the observation of unexpected conductivity at the LaAlO3/SrTiO3 interface prepared on (110)-oriented SrTiO3, with a LaAlO3-layer thickness-dependent metal-insulator transition. Density functional theory calculation reveals that electronic reconstruction, and thus conductivity, is still possible at this (110) interface by considering the energetically favourable (110) interface structure, that is, buckled TiO2/LaO, in which the polarization discontinuity is still present. The conductivity was further found to be strongly anisotropic along the different crystallographic directions with potential for anisotropic superconductivity and magnetism, leading to possible new physics and applications., Although LaAlO3 and SrTiO3 are both insulators, when they are brought together at a (100) interface, a highly conducting two-dimensional electron gas forms between them. Annandi et al. show that this also happens at a (110) interface, counter to expectations that it should not.

We report the temperature dependent electrical transport properties of gated bilayer graphene devices. We see a clear evidence of insulating behavior due to electron-hole charge puddles. The electrical resistivity increases while the mobility decreases with decreasing temperature, a characteristic due to carrier inhomogeneity in graphene. The theoretical fittings using an empirical formula of single electron tunneling indicate that electrical resistivity follows a universal curve with a scaling parameter. The scaling parameter is determined to be a measure of the fluctuations in the electron-hole puddle distribution.

The surface termination of (100)-oriented LaAlO3 (LAO) single crystals was examined by atomic force microscopy and optimized to produce a single-terminated atomically flat surface by annealing. Then the atomically flat STO film was achieved on a single-terminated LAO substrate, which is expected to be similar to the n-type interface of two-dimensional electron gas (2DEG), i.e., (LaO)-(TiO2). Particularly, that can serve as a mirror structure for the typical 2DEG heterostructure to further clarify the origin of 2DEG. This newly developed interface was determined to be highly insulating. Additionally, this study demonstrates an approach to achieve atomically flat film growth based on LAO substrates., 4 pages, 3 figures

The interface between the polar LaAlO$_3$ and nonpolar SrTiO$_3$ layers has been shown to exhibit various electronic and magnetic phases such as two dimensional electron gas, superconductivity, magnetism and electronic phase separation. These rich phases are expected due to the strong interplay between charge, spin and orbital degree of freedom at the interface between these complex oxides, leading to the electronic reconstruction in this system. However, until now all of these new properties have been studied extensively based on the interfaces which involve a polar LaAlO$_3$ layer. To investigate the role of the A and B cationic sites of the ABO$_3$ polar layer, here we study various combinations of polar/nonpolar oxide (NdAlO$_3$/SrTiO$_3$, PrAlO$_3$/SrTiO$_3$ and NdGaO$_3$/SrTiO$_3$) interfaces which are similar in nature to LaAlO$_3$/SrTiO$_3$ interface. Our results show that all of these new interfaces can also produce 2DEG at their interfaces, supporting the idea that the electronic reconstruction is the driving mechanism for the creation of the 2DEG at these oxide interfaces. Furthermore, the electrical properties of these interfaces are shown to be strongly governed by the interface strain and strong correlation effects provided by the polar layers. Our observations may provide a novel approach to further tune the properties of the 2DEG at the selected polar/nonpolar oxide interfaces., Comment: 5 pages, 4 figures

The capacitance of MgO based magnetic tunnel junctions (MTJs) has been observed to be magnetic field dependent. We propose an equivalent circuit for the MTJs with a parallel-leaky capacitance (Cl) across the series combination of geometric and interfacial capacitance. The analysis of junctions with different tunneling magnetoresistance (TMR) values suggests higher Cl for low TMR junctions. Using Cole-Cole plots, the capacitive nature of MTJs is manifested. Fitting with Maxwell-Wagner capacitance model validates the RC parallel network model for MTJs and the extracted field dependent parameters match with the experimental values.

We report on the electric-field-induced reversible metal-insulator transition (MIT) of the insulating LaAlO${}_{3}$ thin films observed in metal/LaAlO${}_{3}$/Nb-SrTiO${}_{3}$ heterostructures. The switching voltage depends strongly on the thickness of the LaAlO${}_{3}$ thin film which indicates that a minimum thickness is required for the MIT. A constant opposing voltage is required to deplete the charges from the defect states. Our experimental results exclude the possibility of diffusion of the metal electrodes or oxygen vacancies into the LaAlO${}_{3}$ layer. Instead, the phenomenon is attributed to the formation of a quasi-conduction band (QCB) in the defect states of LaAlO${}_{3}$ that forms a continuum state with the conduction band of the Nb-SrTiO${}_{3}$. Once this continuum (metallic) state is formed, the state remains stable even when the voltage bias is turned off. The thickness dependent reverse switch-on voltage and the constant forward switch-off voltage are consistent with our model. The viewpoint proposed here can provide an alternative mechanism for resistive switching in complex oxides.

We report optical, electrical and magnetotransport properties of oxygen deficient ${\mathrm{SrTiO}}_{3}$ (${\mathrm{SrTiO}}_{3\ensuremath{-}x}$) thin films fabricated by pulsed laser deposition technique. The oxygen vacancies (${\mathrm{O}}_{\mathrm{vac}}$) in the thin film are expected to be uniform. By comparing its electrical properties to those of bulk ${\mathrm{SrTiO}}_{3\ensuremath{-}x}$, it was found that ${\mathrm{O}}_{\mathrm{vac}}$ in bulk ${\mathrm{SrTiO}}_{3\ensuremath{-}x}$ is far from uniform over the whole material. The metal-insulator transition (MIT) observed in the ${\mathrm{SrTiO}}_{3\ensuremath{-}x}$ film was found to be induced by the carrier freeze-out effect. The low temperature frozen state can be reexcited by Joule heating, electric and intriguingly magnetic field.