scispace - formally typeset
Search or ask a question

Showing papers on "High-temperature superconductivity published in 2000"


Journal ArticleDOI
TL;DR: Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed in this paper, with particular emphasis on critical properties at the quantum phase transitions.
Abstract: Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-Tc cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of pa...

332 citations


Journal ArticleDOI
TL;DR: In this article, high trapped fields were found in zinc-doped, bulk melt-textured YBa2Cu3O7−x (YBCO) material showing a pronounced peak effect in the field dependence of the critical current density.
Abstract: High trapped fields were found in zinc-doped, bulk melt-textured YBa2Cu3O7−x (YBCO) material showing a pronounced peak effect in the field dependence of the critical current density Trapped fields up to 11 T were found at 77 K at the surface of a YBCO disk (diameter 26 mm, height 12 mm) Very high trapped fields up to 1435 T were achieved at 225 K for a YBCO disk pair (diameter 26 mm, height 24 mm) by the addition of silver and using a bandage made of stainless steel The pinning forces and trapped fields obtained in bulk YBCO material are compared with results reported for melt-processed NdBa2Cu3O7−x and SmBa2Cu3O7−x

143 citations


Journal ArticleDOI
TL;DR: In this article, the authors report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the YBCO{6+x} high temperature superconductor.
Abstract: We report a comprehensive polarized and unpolarized neutron scattering study of the evolution of the dynamical spin susceptibility with temperature and doping in three underdoped single crystals of the \YBCO{6+x} high temperature superconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85} (T_c = 87 K). Theoretical implications of these data are discussed, and a critique of recent attempts to relate the spin excitations to the thermodynamics of high temperature superconductors is given.

136 citations


Journal ArticleDOI
TL;DR: In this paper, angular-resolved photoemission experiments on high-temperature superconductors are consistent with a phenomenological description of the normal state of these materials as marginal Fermi liquids.
Abstract: Recent angular-resolved photoemission experiments on high-temperature superconductors are consistent with a phenomenological description of the normal state of these materials as marginal Fermi liquids. The experiments also provide constraints on microscopic theories.

99 citations


Journal ArticleDOI
TL;DR: In this paper, the relation between the incommensurability observed in neutron scattering experiments in bilayer cuprate superconductors and the electronic structure is investigated, and it is found that the observed pattern, as well as its dependence on energy, can be well reproduced by electronic dispersions motivated by angle-resolved photoemission data.
Abstract: The relation between the incommensurability observed in neutron scattering experiments in bilayer cuprate superconductors and the electronic structure is investigated. It is found that the observed incommensurability pattern, as well as its dependence on energy, can be well reproduced by electronic dispersions motivated by angle-resolved photoemission data. The commensurate resonance and its contribution to the superconducting condensation energy are discussed in the context of these calculations. (c) 2000 The American Physical Society.

98 citations


Journal ArticleDOI
TL;DR: In this article, the results of studies of crystal chemistry and phase equilibria are presented to give materials scientists a comprehensive insight into the phase equilibrium and crystal chemistry of these challenging materials.
Abstract: Ten years after the discovery of high-Tc superconductivity in the system Bi-Sr-Ca-Cu-O, the superconducting compounds have been identified, and their structures, crystal chemistry, phase equilibria, and properties have been extensively investigated. In this review, the results of studies of crystal chemistry and phase equilibria are presented to give materials scientists a comprehensive insight into the phase equilibria and crystal chemistry of these challenging materials.

84 citations


Journal ArticleDOI
TL;DR: In this paper, a superconducting permanent magnet system was constructed for the first time in the world by c-axis oriented Sm-Ba-Cu-O bulk superconductors fabricated through the melt processing as trapped field magnets.
Abstract: Superconducting permanent magnet systems generating magnetic fields of 2–5 T have been constructed for the first time in the world by c -axis oriented Sm–Ba–Cu–O bulk superconductors fabricated through the melt processing as trapped field magnets. The trapped magnetic fields of 3.8 and 6.7 T have been produced on the bulk surface at 30 K by the pulsed field magnetization (PFM) and field cooling (FC) methods, respectively. The magnetic field in the open space outside the vacuum vessel exceeds 2.0 and 3.2 T when magnetized by the PFM and FC modes, respectively. It was found that the iteratively magnetizing pulsed-field operation with reducing amplitudes (IMRA method) is very effective in magnetizing high J c bulk superconductors. This implies the superconducting permanent magnets can be used as high magnetic field generators in various practical applications.

64 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used angle-resolved photoemission (ARPES) data to investigate the relationship between the normal and superconducting states and their spectral properties.
Abstract: If high-temperature cuprate superconductivity is due to electronic correlations, then the energy difference between the normal and superconducting states can be expressed in terms of the occupied part of the single-particle spectral function. The latter can, in principle, be determined from angle-resolved photoemission (ARPES) data. As a consequence, the energy gain driving the development of the superconducting state is intimately related to the dramatic changes in the photoemission line shape when going below T{sub c}. These points are illustrated in the context of the ''mode'' model used to fit ARPES data in the normal and superconducting states, where the question of kinetic-energy versus potential-energy-driven superconductivity is explored in detail. We use our findings to comment on the relation of ARPES data to the condensation energy and to various other experimental data. In particular, our results suggest that the nature of the superconducting transition is strongly related to how anomalous (non-Fermi-liquid-like) the normal-state spectral function is and, as such, is dependent upon the doping level. (c) 2000 The American Physical Society.

60 citations


Journal ArticleDOI
TL;DR: In this article, the magnetic properties of superconductor/ferromagnet (SC/FM) heterostructures were analyzed relative to a pure superconducting YBa2Cu3O7(SC) and BaFe12O19(FM) samples.
Abstract: Pinning of vortices in a high-temperature superconductor by the magnetic domain structure of a highly anisotropic ferromagnet is investigated by means of magnetic measurements in nanoscale period superconductor/ferromagnet (SC/FM) heterostructures. Two different samples consisting of highly epitaxial films of YBa2Cu3O7(SC) and BaFe12O19(FM) are analyzed relative to a pure superconducting YBa2Cu3O7 film. The irreversibility line obtained in the magnetic-field-reduced-temperature phase diagram for each heterostructure is found to shift upwards when compared to the line corresponding to the pure superconducting sample. This effect is interpreted as an evidence for the enhancement of pinning of vortices in the SC layer by the magnetic domain structure in the FM layer.

58 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigated the mechanical stress caused by flux pinning in a cylindrical superconductor with a concentric hole and derived exact expressions for the radial and hoop stress using the critical-state model.
Abstract: The mechanical stress caused by flux pinning in a cylindrical superconductor with a concentric hole is investigated theoretically. Exact expressions for the radial and hoop stress are derived using the critical-state model. Stress profiles during a magnetization process often used to activate high-Tc superconductors as strong trapped-field magnets are presented and analyzed in detail. It is shown that due to the hole the tensile hoop stress is enhanced by a factor of 2 or more, depending on the hole diameter. The dramatic increase in cracking probability is emphasized.

58 citations


Journal ArticleDOI
TL;DR: In this article, two types of 211 particles are formed; large NEG-211 and submicron-sized particles containing mostly Gd in the rare earth site are formed which can act as effective flux pinning sites.
Abstract: (Nd0.33Eu0.33Gd0.33)2BaCuO5 (NEG-211) particles are added to ternary (Nd0.33Eu0.33Gd0.33)Ba2Cu3Oy (NEG) bulk, melt-processed superconductors. By means of transmission electron and polarized light microscopy, we found that two types of 211 particles are formed; large NEG-211 and submicron-sized particles containing mostly Gd in the rare earth site are formed which can act as effective flux pinning sites. The critical current density at zero field increases monotonously as a function of the NEG-211 concentration, but the secondary peak vanishes above 40 mol % 211 addition. As a result, a critical current density of 68 000 A cm−2 at 77 K and 2.5 T applied field is achieved with at 40 mol % 211 additions.

Journal ArticleDOI
Jan Zaanen1
13 Apr 2000-Nature
TL;DR: Two studies add further credibility to an emerging picture of electrons in solids known as 'dynamical stripes' and challenge the universal validity of the conventional theories of metals and superconductors.
Abstract: Two studies add further credibility to an emerging picture of electrons in solids known as 'dynamical stripes'. At the same time they challenge the universal validity of the conventional theories of metals and superconductors.

Journal ArticleDOI
TL;DR: In this article, X-ray diffraction experiments reveal that compressive strain exists in the a-b plane for YBa2Cu3O7−δ (YBCO) thin films on LaAlO3 and SrTiO3 (STO) substrates, while tensile strain occurs for films on STO.
Abstract: Ultrathin YBa2Cu3O7−δ (YBCO) films down to two unit cells thick have been prepared on LaAlO3 (LAO) and SrTiO3 (STO) substrates for the study of substrate-induced strain effects on critical transition temperature (Tc). The YBCO on LAO has a higher Tc than that on STO for very thin films, and this Tc difference increases with reduction of film thickness. X-ray diffraction experiments reveal that compressive strain exists in the a–b plane for YBCO thin films on LAO, while tensile strain occurs for films on STO. The different stresses in these films account for the Tc difference.


Journal ArticleDOI
TL;DR: In this paper, the surface resistance of YBa2Cu3Ox thin films at frequencies between 0.087 and 2 THz and temperatures between 50 and 120 K by time-domain terahertz-transmission spectroscopy (TDTTS) and resonant microwave spectrograms was investigated.
Abstract: We report on measurements of the surface resistance of YBa2Cu3Ox thin films at frequencies between 0.087 and 2 THz and temperatures between 50 and 120 K by time-domain terahertz-transmission spectroscopy (TDTTS) and resonant microwave spectroscopy. The determination of the surface resistance of superconducting thin films by TDTTS is extended to higher frequencies and thicker films than previously by numerically solving the complex transmission coefficient. The numerical solution also provides the dielectric function of the YBa2Cu3Ox thin films. The temperature and frequency dependence of the surface resistance of YBa2Cu3Ox thin films in the THz range is successfully explained by a weak coupling model of d-wave superconductivity which incorporates inelastic and elastic scattering. The surface resistance of YBa2Cu3Ox thin films at THz frequencies is compared to the surface resistance of gold and niobium. The advantages of YBa2Cu3Ox thin films for superconducting THz electronic devices are discussed.

Journal ArticleDOI
TL;DR: In this paper, the authors report on measurements of the ac losses of YBa2Cu3O7−x conductors on technical substrates, which are taken from conductors 1 m long produced with an ion beam assisted deposition step in the manufacturing process.
Abstract: We report on measurements of the ac losses of YBa2Cu3O7−x conductors on technical substrates. The samples are taken from conductors 1 m long produced with an ion beam assisted deposition step in the manufacturing process yielding 1 cm wide conductors with critical currents approaching 100 A at 77.4 K. The losses due to combinations of ac transport currents and ac magnetic fields were measured calorimetrically and the results compared to theoretical estimates. While the results of our measurements are similar to the theoretical estimates, there are some important differences in the qualitative behavior.

Journal ArticleDOI
TL;DR: In this article, the field dependence of flux-flow resistivity of the Josephson vortex lattice in a layered superconductor taking into account both the interplane and in-plane dissipation channels is investigated.
Abstract: We calculate the flux-flow resistivity of the Josephson vortex lattice in a layered superconductor taking into account both the interplane and in-plane dissipation channels. We consider the limiting cases of small fields (isolated vortices) and high fields (overlapping vortices). In the case of the dominating in-plane dissipation, typical for high-temperature superconductors, the field dependence of flux-flow resistivity is characterized by three distinct regions. As usual, at low fields the flux-flow resistivity grows linearly with field. When the Josephson vortices start to overlap the flux-flow resistivity crosses over to the regime of quadratic field dependence. Finally, at very high fields the flux-flow resistivity saturates at the c-axis quasiparticle resistivity. The intermediate quadratic regime indicates the dominant role of the in-plane dissipation mechanism. The shape of the field dependence of the flux-flow resistivity can be used to extract both components of the quasiparticle conductivity.

Journal ArticleDOI
TL;DR: In this article, the properties of existing superconductors with ejectron spectrum instabilities, namely charge-density waves (CDWs) and spin-density wave (SDWs), are reviewed.
Abstract: The properties of existing superconductors with ejectron spectrum instabilities, namely charge-density waves (CDWs) and spin-density waves (SDWs), are reviewed. In such substances the superconducting gap exists over the whole Fermi surface, whereas the dielectric gap emerges only on its nested sections. In particular, CDW superconductors include layered dichalcogenides, NbSe3, compounds with the A15 and C15 structures, etc. There is a lot of evidence that high-Tc oxides also belong to this group of materials. SDW superconductors include, e.g., URu2Si2 and related heavy-fermion compounds, Cr–Re alloys and organic superconductors. The theoretical description given in this review is based mostly on the Bilbro-McMillan model of the partially dielectrized metal. Various thermodynamic and electrodynamic properties are calculated in the framework of this model. The main subject of the review is the nonstationary Josephson effect in tunnel junctions involving CDW or SDW superconductors. A new effect of symmetry breaking in symmetrical tunnel junctions is predicted by the authors. A comparison with experiment is given.

Journal ArticleDOI
TL;DR: In this article, the photo-induced effects of high temperature superconductors are investigated and the experimental data and theoretical models related to these photoinduced effects are reviewed, and the authors propose theoretical models to probe and modify the properties of grain boundaries in grain boundary Josephson junctions.
Abstract: Persistent photoconductivity is an interesting and unusual property of high temperature superconductors. Illumination of these compounds can lead to a change in doping that is persistent at low temperature and relaxes back to its initial value at elevated temperatures. This photodoping can give rise to an improvement of superconducting properties, which is contrary to the illumination effects in conventional superconductors. Furthermore, these photo-induced effects can also be used to probe and modify the properties of grain boundaries in grain boundary Josephson junctions. This paper reviews the experimental data and proposed theoretical models related to these photoinduced effects.

Journal ArticleDOI
TL;DR: In this paper, the melting curve of vortex matter, now detected in the specific heat of Dy-123, Eu-123 and Y-123 up to very high fields, is described by a critical exponent.
Abstract: Thermal fluctuations are observed in the specific heat of high-temperature superconductors (HTS) near Tc. This is seen both in the shape of the zero-field anomaly, characterized by critical exponents and amplitude ratios, and in the broadening of the transition versus the magnetic field, which obeys scaling laws. 3D-XY fluctuations are found for YBa2Cu3Ox (Y-123) near optimal doping, whereas systematic deviations occur away from this point. The large deviations found for the most anisotropic HTS may be attributed to both reduced dimensionality and a crossover between BCS and Bose condensations. Low-temperature data are discussed in this context. The melting curve of vortex matter, now detected in the specific heat of Dy-123, Eu-123 and Y-123 up to very high fields, is described by a critical exponent.

Journal ArticleDOI
TL;DR: The discovery of high-temperature superconductivity (HTS) in 1986-1988 rekindled interest in superconducting power transmission cables and many projects are underway around the world to study the use of HTS power transmission cable.
Abstract: The discovery of high-temperature superconductivity (HTS) in 1986-1988 rekindled interest in superconducting power transmission cables. Many projects are underway around the world to study the use of HTS power transmission cables. The siting and environmental issues facing the expansion of transmission capacity have become increasingly more difficult with time. The HTS power cable may be able to address some of these issues, especially in urban areas, where HTS retrofits of existing conventional cables can increase capacity substantially without increasing the footprint of the cable right of way. Several of the cable projects employing HTS are discussed in this article.

Journal ArticleDOI
TL;DR: In this paper, an open-flat coil (OFC) was used for high resolution measurements of magnetic field penetration depth into thin films or plate-like high-Tc superconductors by replacing a solenoid testing coil by an OFC driven by a tunnel diode oscillator of low power and a highly stable frequency.
Abstract: The “LC resonator” method was greatly improved for high resolution measurements of magnetic-field penetration depth, λ, of radio frequency into thin films or plate-like high-Tc superconductors by replacing a solenoid testing coil by an open-flat coil (OFC) driven by a tunnel diode oscillator of a low power and a highly stable frequency The assembled OFC magnetometer showed new technical advantages such as simplicity, convenience, and high resolution of Δλ∼1–3 A (Δλ/λ∼10−6), ability of reliable operation in wide ranges of temperature (42–300 K) and magnetic field (up to 12 T), etc This enables us to use it for studying peculiarities of the vortex dynamics with weak signal in small sample volume high-Tc cuprates As a first test of the assembled 23 MHz measuring setup, the temperature dependence of the upper critical field, HC2(T), is determined from the magnetic transition curves at different temperatures for Y1Ba2Cu3O7−δ thin-film ring The HC2(T) data obey the formula: [1−(T/Tc)2]β with β=122±003 at

Journal ArticleDOI
TL;DR: In this paper, the transport critical current density (J c ) has been measured at various applied magnetic fields and temperatures up to liquid nitrogen for Y 1 Ba 2 Cu 3 O x (YBCO)-coated conductors by metal-organic chemical vapor deposition (MOCVD) process.
Abstract: Recent progress achieved at Intermagnetics General Corporation (IGC) is presented on high-temperature superconductors. The transport critical current density ( J c ) has been measured at various applied magnetic fields and temperatures up to liquid nitrogen for Y 1 Ba 2 Cu 3 O x (YBCO)-coated conductors by metal–organic chemical vapor deposition (MOCVD) process. J c >1.4 MA/cm 2 in self-field at 77 K have been achieved in the YBCO samples. In addition, good progress has been achieved in the multifilament BiSrCaCuO powder-in-tube wires and tapes. Development of strengthened sheath designs and improvement in filament uniformity in production lengths up to 300 m is reported. The transport J c of 348,786 A/cm 2 in self-field at 4.2 K is obtained for round multifilament Bi 2 Sr 2 Ca 1 Cu 3 O x (BSCCO-2212) wires.

Journal ArticleDOI
TL;DR: The thermal stability limit of the 3D solid is found, and the free energy to a 2D liquid is compared to determine the first-order melting transition and its jump in entropy.
Abstract: We calculate the melting line of the pancake-vortex system in a layered superconductor, interpolating between two-dimensional (2D) melting at high fields and the zero-field limit of single-stack evaporation. Long-range interactions between pancake vortices in different layers permit a mean-field approach, the "substrate model, " where each 2D crystal fluctuates in a substrate potential due to the vortices in other layers. We find the thermal stability limit of the 3D solid, and compare the free energy to a 2D liquid to determine the first-order melting transition and its jump in entropy.

BookDOI
01 Jan 2000
TL;DR: In this article, Komarek et al. discuss the application of high temperature superconductors in magnetic bearingings and flywheels, as well as their application in superconducting composite tape.
Abstract: Preface. Acknowledgments. 1. Low- and High-Tc SQUIDs and Some Applications J. Clarke. 2. Multichannel SQUID Biomagnetic Systems J. Vrba. 3. Applications of SQUID Magnetometers to Biomagnetism and Nondestructive Evaluation J.P. Wikswo. 4. Applications of Josephson Electronics in Digital Systems J.X. Przybysz, Sr. 5. Superconductors Devices For Ultrafast Computing K.K. Likharev. 6. Microwave Applications of High Temperature Superconductors H.J. Chaloupka. 7. MRI Magnets F.J. Davies. 8. Power Quality, Micro Superconducting Magnetic Energy Storage System and Fault Current Limiters M. Parizh, E. Leung. 9. High Current Application of Superconductivity. Part I: Applications in Research and Industrial Areas P. Komarek. 10. High Current Application of Superconductivity. Part II: Superconducting Magnets for Fusion P. Komarek. 11. The Mechanical Deformation Processing of High-Temperature Superconducting Composite Tape T. Freltoft, Z. Han. 12. Applications of High Temperature Superconductors in Magnetic Bearings and Flywheels K.B. Ma. 13. Cryogenic Systems for Superconducting Devices H.J.M. ter Brake. 14. Superconductor Measurement Techniques and Cryostat Design J. Ekin. 15. Superconductivity R&D at Istec and Elsewhere in Japan G. Pindoria.

Journal ArticleDOI
TL;DR: In this article, a parity-breaking first order phase transition in high-temperature superconductors was shown to be possible in a (2+1)-dimensional P-even massive Gross-Neveu model.
Abstract: In the framework of a (2+1)-dimensional P-even massive Gross-Neveu model, an external magnetic field is shown to induce a parity breaking first order phase transition. Possibility of applying the results obtained to description of magnetic phase transitions in high-temperature superconductors is discussed.

Journal ArticleDOI
TL;DR: In this paper, the spin-dependent transport in a ferromagnet-superconductor-ferromagnetic double barrier tunnel junction was theoretically studied, and the effect of asymmetry in the double tunnel junction, where the barrier height of the tunnel junction and the spin polarization of the ferromagnets are different, on spin injection was discussed.
Abstract: We theoretically study the spin-dependent transport in a ferromagnet–superconductor–ferromagnet double barrier tunnel junction. The spin-polarized tunneling currents give rise to spin imbalance in the superconductor. The resulting nonequilibrium spin density suppresses the superconductivity with increase of the tunneling currents. We focus on the effect of asymmetry in the double tunnel junction, where the barrier height of the tunnel junction and the spin polarization of the ferromagnets are different, on spin injection, and discuss how the superconductivity is suppressed in the asymmetric junction. Our results explain recent experimental results on the critical current suppression in high-Tc superconductors by spin injection.

23 Sep 2000
TL;DR: In this article, a large effort has been made by the scientific community to investigate this field towards a possible application of the new oxide superconductors to different devices like SMES, magnetic bearings, flywheels energy storage, magnetic shielding, transmission cables, fault current limiters, etc.
Abstract: Since the discovery of high temperature superconductivity, a large effort has been made by the scientific community to investigate this field towards a possible application of the new oxide superconductors to different devices like SMES, magnetic bearings, flywheels energy storage, magnetic shielding, transmission cables, fault current limiters, etc. However, all present day large scale applications using superconductivity in accelerator technology are based on conventional materials operating at liquid helium temperatures. Poor mechanical properties, low critical current density and sensitivity to the magnetic field at high temperature are the key parameters whose improvement is essential for a large scale application of high temperature superconductors to such devices. Current leads, used for transferring currents from the power converters, working at room temperature, into the liquid helium environment, where the magnets are operating, represent an immediate application of the emerging technology of high temperature superconductivity. The LHC, currently under construction at CERN, will transfer more than 3 million amperes of current through leads having high temperature superconducting sections, thus providing a unique opportunity to incorporate these materials into large scale systems. The status of this project and the cost-benefit consequence of its application will be reported.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the c-axis tunneling matrix of high-T-c superconductors depend strongly on the in-plane momentum of electrons and vanish along the four nodal lines of the d(x2-y2)-wave energy gap.
Abstract: The c-axis tunneling matrix of high-T-c superconductors is shown to depend strongly on the in-plane momentum of electrons and vanish along the four nodal lines of the d(x2-y2)-wave energy gap. This anisotropic tunneling matrix suppresses completely the contribution of the most extended quasiparticles in the vortex core to the c-axis tunneling current and leads to a spectrum similar to that of a nodeless superconductor. Our results give a natural explanation of the absence of the zero-bias peak as well. as other features observed in the vortex tunneling spectra of high-T-c cuprates.

Journal ArticleDOI
TL;DR: In this paper, the leakage current and ferroelectricity properties of Pb(Zr, Ti)O3(PZT)/YBa2Cu3Ox heterostructure were investigated using a modified atomic force microscopy.
Abstract: In this letter we present an investigation on probing leakage current and ferroelectricity of Pb(Zr, Ti)O3(PZT)/YBa2Cu3Ox heterostructure using a modified atomic force microscopy. Inhomogeneities of leakage current and ferroelectric properties were concurrently mapped and quantitatively studied on a nanometer scale. It shows that microscopically the leakage current can be described by a model based on space-charge-limited current.