Non-unitary quantum electronics: Novel functions from the edge of the quantum world

Novel categories of electronic devices and quantum materials are obtained by pipelining the unitary evolution of electron quantum states as described by Schrödinger’s equation with non-unitary processes that interrupt the coherent propagation of electrons. These devices and materials reside in the fascinating transition regime between quantum mechanics and classical physics. The devices are designed such that a nonreciprocal unitary state evolution, achieved by means of a broken inversion symmetry, is interrupted by individual inelastic scattering events caused by defects coupled to an environment. Two-terminal non-unitary quantum devices, for example, feature nonreciprocal conductance in linear response. Thus, they are exemptions to Onsager’s reciprocal relation, and they challenge the second law of thermodynamics. Furthermore, materials and metamaterials featuring such functionalities may be realized by embedding such nanostructures into their unit cells.

The oxidation kinetics of thin nickel films between 250 and 500 °C

The oxidation kinetics of thin polycrystalline Ni films is of fundamental interest as well as being relevant for potential applications. It was investigated between 250 and 500 °C for 10-150 nm thick films. Even for the thinnest films, oxidation was found to be diffusion controlled. The high density of grain boundaries in the formed NiO layer leads to a tracer diffusion coefficient that is higher than reported in the literature, indicating accelerated Ni diffusion along the grain boundaries. Cr segregation to the bottom interface in doped-NiO films hindered the acceleration of the oxidation of thin films.

Electrical transport measurements of thin film samples under high hydrostatic pressure

We present a method to perform electrical measurements of epitaxial films and heterostructures a few nanometers thick under high hydrostatic pressures in a diamond anvil cell (DAC). Hydrostatic pressure offers the possibility to tune the rich landscape of properties shown by epitaxial heterostructures, systems in which the combination of different materials, performed with atomic precision, can give rise to properties not present in their individual constituents. Measuring electrical conductivity under hydrostatic pressure in these systems requires a robust method that can address all the challenges: the preparation of the sample with side length and thickness that fits in the DAC setup, a contacting method compatible with liquid media, a gasket insulation that resists high forces, as well as an accurate procedure to place the sample in the pressure chamber. We prove the robustness of the method described by measuring the resistance of a two dimensional electron system buried at the interface between two insulating oxides under hydrostatic conditions up to ∼5 GPa. The setup remains intact until ∼10 GPa, where large pressure gradients affect the two dimensional conductivity.

Artificial atoms based on correlated materials

Low-dimensional electron systems fabricated from quantum matter have in recent years become available and are being explored with great intensity. This article gives an overview of the fundamental properties of such systems and summarizes the state of the field. We furthermore present and consider the concept of artificial atoms fabricated from quantum materials, anticipating remarkable scientific advances and possibly important applications of this new field of research. The surprising properties of these artificial atoms and of molecules or even of solids assembled from them are presented and discussed.

Direct k-space mapping of the electronic structure in an oxide-oxide interface

The interface between LaAlO(3) and SrTiO(3) hosts a two-dimensional electron system of itinerant carriers, although both oxides are band insulators. Interface ferromagnetism coexisting with superconductivity has been found and attributed to local moments. Experimentally, it has been established that Ti 3d electrons are confined to the interface. Using soft x-ray angle-resolved resonant photoelectron spectroscopy we have directly mapped the interface states in k space. Our data demonstrate a charge dichotomy. A mobile fraction contributes to Fermi surface sheets, whereas a localized portion at higher binding energies is tentatively attributed to electrons trapped by O vacancies in the SrTiO(3). While photovoltage effects in the polar LaAlO(3) layers cannot be excluded, the apparent absence of surface-related Fermi surface sheets could also be fully reconciled in a recently proposed electronic reconstruction picture where the built-in potential in the LaAlO(3) is compensated by surface O vacancies serving also as a charge reservoir.

Electric-field-induced polar order and localization of the confined electrons in LaAlO3/SrTiO3 heterostructures

With ellipsometry, x-ray diffraction, and resistance measurements we investigated the electric-field effect on the confined electrons at the LaAlO3/SrTiO3 interface. We obtained evidence that the localization of the electrons at negative gate voltage is induced, or at least enhanced, by a polar phase transition in SrTiO3 which strongly reduces the lattice polarizability and the subsequent screening. In particular, we show that the charge localization and the polar order of SrTiO3 both develop below ∼50  K and exhibit similar, unipolar hysteresis loops as a function of the gate voltage.

Very large capacitance enhancement in a two-dimensional electron system

Increases in the gate capacitance of field-effect transistor structures allow the production of lower-power devices that are compatible with higher clock rates, driving the race for developing high-κ dielectrics. However, many-body effects in an electronic system can also enhance capacitance. Onto the electron system that forms at the LaAlO(3)/SrTiO(3) interface, we fabricated top-gate electrodes that can fully deplete the interface of all mobile electrons. Near depletion, we found a greater than 40% enhancement of the gate capacitance. Using an electric-field penetration measurement method, we show that this capacitance originates from a negative compressibility of the interface electron system. Capacitance enhancement exists at room temperature and arises at low electron densities, in which disorder is strong and the in-plane conductance is much smaller than the quantum conductance.

Evolution of the interfacial structure of LaAlO3 on SrTiO3

The evolution of the atomic structure of LaAlO_{3} grown on SrTiO_{3} was investigated using surface x-ray diffraction in conjunction with model-independent, phase-retrieval algorithms between two and five monolayers film thickness. A depolarizing buckling is observed between cation and oxygen positions in response to the electric field of polar LaAlO_{3}, which decreases with increasing film thickness. We explain this in terms of competition between elastic strain energy, electrostatic energy, and electronic reconstructions. Based on these structures, the threshold for formation of a two-dimensional electron system at a film thickness of 4 monolayers is quantitatively explained. The findings are also qualitatively reproduced by density-functional-theory calculations.

Is there an intrinsic limit to the charge-carrier-induced increase of the Curie temperature of EuO?

Rare earth doping is the key strategy to increase the Curie temperature (T(C)) of the ferromagnetic semiconductor EuO. The interplay between doping and charge carrier density (n), and the limit of the T(C) increase, however, are yet to be understood. We report measurements of n and T(C) of Gd-doped EuO over a wide range of doping levels. The results show a direct correlation between n and T(C), with both exhibiting a maximum at high doping. On average, less than 35% of the dopants act as donors, raising the question about the limit to increasing T(C).

Dynamical response and confinement of the electrons at the LaAlO3/SrTiO3 interface

With infrared ellipsometry and transport measurements we investigated the electrons at the interface between LaAlO3 and SrTiO3. We obtained a sheet carrier concentration of N(s) approximately = 5-9x10(13) cm(-2), an effective mass of m*=3.2+/-0.4m(e), and a strongly frequency dependent mobility. The latter are similar as in bulk SrTi(1-x)Nb(x)O3 and therefore suggestive of polaronic correlations. We also determined the vertical concentration 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.

Profiling the interface electron gas of LaAlO3/SrTiO3 heterostructures with hard x-ray photoelectron spectroscopy

The conducting interface of LaAlO3/SrTiO3 heterostructures has been studied by hard x-ray photoelectron spectroscopy. From the Ti 2p signal and its angle dependence we derive that the thickness of the electron gas is much smaller than the probing depth of 4 nm and that the carrier densities vary with increasing number of LaAlO3 overlayers. Our results point to an electronic reconstruction in the LaAlO3 overlayer as the driving mechanism for the conducting interface and corroborate the recent interpretation of the superconducting ground state as being of the Berezinskii-Kosterlitz-Thouless type.

Orbital reconstruction and the two-dimensional electron gas at the LaAlO3/SrTiO3 interface

In 2004, Ohtomo and Hwang discovered that an electron gas is created at the interface between insulating LaAlO3 and SrTiO3 compounds. Here we show that the generation of a conducting electron gas is related to an orbital reconstruction occurring at the LaAlO3/SrTiO3 interface. Our results are based on extensive investigations of the electronic properties and of the orbital structure of the interface using x-ray absorption spectroscopy. In particular, we find that the degeneracy of the Ti 3d states is fully removed and that the Ti 3d xy levels become the first available states for conducting electrons.

Electron scattering at dislocations in LaAlO3/SrTiO3 interfaces

We report experimental investigations of the effects of microstructural defects and of disorder on the properties of 2D electron gases at oxide interfaces. The cross section for scattering of electrons at dislocations in LaAlO(3)/SrTiO(3) interfaces has been measured and found to equal approximately 5 nm. Our experiments reveal that the transport properties of these electron gases are strongly influenced by scattering at dislocation cores.

Nanoscale control of an interfacial metal-insulator transition at room temperature

Experimental and theoretical investigations have demonstrated that a quasi-two-dimensional electron gas (q-2DEG) can form at the interface between two insulators: non-polar SrTiO3 and polar LaTiO3 (ref. 2), LaAlO3 (refs 3-5), KTaO3 (ref. 7) or LaVO3 (ref. 6). Electronically, the situation is analogous to the q-2DEGs formed in semiconductor heterostructures by modulation doping. LaAlO3/SrTiO3 heterostructures have recently been shown to exhibit a hysteretic electric-field-induced metal-insulator quantum phase transition for LaAlO3 thicknesses of 3 unit cells. Here, we report the creation and erasure of nanoscale conducting regions at the interface between two insulating oxides, LaAlO3 and SrTiO3. Using voltages applied by a conducting atomic force microscope (AFM) probe, the buried LaAlO3/SrTiO3 interface is locally and reversibly switched between insulating and conducting states. Persistent field effects are observed using the AFM probe as a gate. Patterning of conducting lines with widths of approximately 3 nm, as well as arrays of conducting islands with densities >10(14) inch(-2), is demonstrated. The patterned structures are stable for >24 h at room temperature.

Superconducting Interfaces Between Insulating Oxides

At interfaces between complex oxides, electronic systems with unusual electronic properties can be generated. We report on superconductivity in the electron gas formed at the interface between two insulating dielectric perovskite oxides, LaAlO3 and SrTiO3. The behavior of the electron gas is that of a two-dimensional superconductor, confined to a thin sheet at the interface. The superconducting transition temperature of congruent with 200 millikelvin provides a strict upper limit to the thickness of the superconducting layer of congruent with 10 nanometers.

Subtleties in ADF imaging and spatially resolved EELS: A case study of low-angle twist boundaries in SrTiO3

A screw dislocation network at the low-angle SrTiO3/Nb:SrTiO3 twist grain boundary has been analyzed by annular dark field (ADF) imaging and spatially resolved electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM). The cores of one set of dislocations running parallel to the beam direction appear dark in the ADF STEM images. EELS on the dislocation core reveals a reduced Sr/Ti ratio compared to the bulk suggesting Sr-deficient cores. The second set of dislocations, orthogonal to the latter, is imaged by its strain field using low-angle annular dark field (LAADF) imaging. Multislice image simulations suggest channeling of the electron probe on the atomic columns for small tilts, theta < 1 degree, where the Sr columns act as beam guides. Only for larger tilts is the channeling effect strongly reduced and the fringe contrast approaches the value predicted by a purely incoherent imaging model. Ti-L(2,3) EELS across the dislocation core shows an asymmetry between the EELS and the ADF signal which cannot be explained by the geometry or beam broadening. This asymmetry might be explained by an effective nonlocal potential representing inelastic scattering in EELS.

Tunable Quasi-Two-Dimensional Electron Gases in Oxide Heterostructures

We report on a large electric-field response of quasi-two-dimensional electron gases generated at interfaces in epitaxial heterostructures grown from insulating oxides. These device structures are characterized by doping layers that are spatially separated from high-mobility quasi-two-dimensional electron gases and therefore present an oxide analog to semiconducting high-electron mobility transistors. By applying a gate voltage, the conductivity of the electron gases can be modulated through a quantum phase transition from an insulating to a metallic state.

Local spectroscopy and atomic imaging of tunneling current, forces, and dissipation on graphite

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be similar to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM and STM images differ substantially depending on the distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift, and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.

Robust dx2-y2 pairing symmetry in hole-doped cuprate superconductors

Although initially quite controversial, it is now widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wave function symmetry, and the controversy has now shifted to whether the pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y(0.7)Ca(0.3)Ba(2)Cu(3)O(7-delta) (Ca-doped Y-123), La2-xSrxCuO4 (La-214), and Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212), with doping levels covering the underdoped, optimal, and overdoped regions. Our work implies that predominantly d x2-y2 pairing symmetry is robust over a large variation in doping.

Electron transport through YBa2Cu3O7-delta grain boundary interfaces between 4.2 and 300 K

The current-induced dissipation in YBa(2)Cu(3)O(7-delta) grain boundary tunnel junctions has been measured between 4.2 and 300 K. It is found that the resistance of 45 degrees (100)/(110) junctions decreases linearly by a factor of 4 when their temperature is increased from 100 to 300 K. At the superconducting transition temperature T(c) the grain boundary resistance of the normal state and of the superconducting state extrapolates to the same value.

Electric field effect in correlated oxide systems

Semiconducting field-effect transistors are the workhorses of the modern electronics era. Recently, application of the field-effect approach to compounds other than semiconductors has created opportunities to electrostatically modulate types of correlated electron behaviour--including high-temperature superconductivity and colossal magnetoresistance--and potentially tune the phase transitions in such systems. Here we provide an overview of the achievements in this field and discuss the opportunities brought by the field-effect approach.

Extremely small energy gap in the quasi-one-dimensional conducting chain compound SrNbO3.41

Resistivity, optical, and angle-resolved photoemission experiments reveal unusual one-dimensional electronic properties of highly anisotropic SrNbO3.41. Along the conducting chain direction, we find an extremely small energy gap of only a few meV at the Fermi level. A discussion in terms of typical 1D instabilities (Peierls, Mott-Hubbard) shows that neither seems to provide a satisfactory explanation for the unique properties of SrNbO3.41.

Observation of splintered Josephson vortices at grain boundaries in YBa(2)Cu(3)O(7-delta)

We have directly observed well-separated Josephson vortex splinters with unquantized magnetic flux at asymmetric 45 degrees grain boundaries in YBa(2)Cu(3)O(7-delta) films by imaging magnetic flux with scanning SQUID microscopy. The existence of these splinter vortices has been predicted and is well described by a model based on dx(2)(-y(2)) pairing symmetry and facetting of the grain boundary on a length scale shorter than the Josephson penetration depth.

d-wave induced zero-field resonances in dc pi-superconducting quantum interference devices

A dc pi SQUID consists of a superconducting ring interrupted by two Josephson junctions, one of which carries in equilibrium a pi phase difference, caused, for example, by the d-wave pairing symmetry of the high- T(c) cuprates. If this phase shift is maintained in the voltage state, anomalous resonance currents are expected in the SQUIDs transport characteristics. Here we report the observation of such resonances for high- T(c) dc pi SQUIDs, providing evidence for the influence of the d-wave symmetry on the voltage state of a Josephson junction for frequencies of several tens of GHz.

Evidence of doping-dependent pairing symmetry in cuprate superconductors

Scanning tunneling spectroscopy studies reveal long-range spatial homogeneity and predominantly d(x(2)-y(2))-pairing spectral characteristics in under- and optimally doped YBa2Cu 3O (7-delta) superconductors, whereas STS on YBa2(Cu 0.9934Zn 0.0026Mg (0.004))3O (6.9) exhibits microscopic spatial modulations and strong scattering near the Zn or Mg impurity sites, together with global suppression of the pairing potential. In contrast, in overdoped (Y 0.7Ca (0.3))Ba 2Cu 3O (7-delta), (d(x(2)-y(2))+s)-pairing symmetry is found, suggesting significant changes in the superconducting ground state at a critical doping value.

Subatomic Features on the Silicon (111)-(7x7) Surface Observed by Atomic Force Microscopy

The atomic force microscope images surfaces by sensing the forces between a sharp tip and a sample. If the tip-sample interaction is dominated by short-range forces due to the formation of covalent bonds, the image of an individual atom should reflect the angular symmetry of the interaction. Here, we report on a distinct substructure in the images of individual adatoms on silicon (111)-(7x7), two crescents with a spherical envelope. The crescents are interpreted as images of two atomic orbitals of the front atom of the tip. Key for the observation of these subatomic features is a force-detection scheme with superior noise performance and enhanced sensitivity to short-range forces.

Spatially Resolved Observation of Supercurrents Across Grain Boundaries in YBaCuO Films

Spatially resolved resistivity measurements of current transport across individual grain boundaries have been made on superconducting YBa(2)Cu(3)O(7). These experiments were done by low-temperature scanning electron microscopy with a resolution of 1 to 2 micrometers, and they show directly the limitation of the critical current density caused by grain boundaries in YBa(2)Cu(3)O(7). Furthermore, complex spatial patterns of the current transport across grain boundaries were observed. These patterns reflect self-excited resonances of the grain boundaries and are closely correlated to the unexplained "sub-gap structure" in the current-voltage characteristics of polycrystalline YBa(2)Cu(3)O(7).