IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

Domains in ferroelectrics were considered to be well understood by the middle of the last century: They were generally rectilinear, and their walls were Ising-like. Their simplicity stood in stark contrast to the more complex Bloch walls or N\'eel walls in magnets. Only within the past decade and with the introduction of atomic-resolution studies via transmission electron microscopy, electron holography, and atomic force microscopy with polarization sensitivity has their real complexity been revealed. Additional phenomena appear in recent studies, especially of magnetoelectric materials, where functional properties inside domain walls are being directly measured. In this paper these studies are reviewed, focusing attention on ferroelectrics and multiferroics but making comparisons where possible with magnetic domains and domain walls. An important part of this review will concern device applications, with the spotlight on a new paradigm of ferroic devices where the domain walls, rather than the domains, are the active element. Here magnetic wall microelectronics is already in full swing, owing largely to the work of Cowburn and of Parkin and their colleagues. These devices exploit the high domain wall mobilities in magnets and their resulting high velocities, which can be supersonic, as shown by Kreines' and co-workers 30 years ago. By comparison, nanoelectronic devices employing ferroelectric domain walls often have slower domain wall speeds, but may exploit their smaller size as well as their different functional properties. These include domain wall conductivity (metallic or even superconducting in bulk insulating or semiconducting oxides) and the fact that domain walls can be ferromagnetic while the surrounding domains are not.

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Domain wall nanoelectronics

Maxwell's equations successfully describe the statistical properties of fluorescence from an ensemble of atoms or semiconductors in one or more dimensions But quantization of the radiation field is required to explain the correlations of light generated by a single two-level quantum emitter, such as an atom, ion or single molecule The observation of photon antibunching in resonance fluorescence from a single atom unequivocally demonstrated the non-classical nature of radiation Here we report the experimental observation of photon antibunching from an artificial system--a single cadmium selenide quantum dot at room temperature Apart from providing direct evidence for a solid-state non-classical light source, this result proves that a single quantum dot acts like an artificial atom, with a discrete anharmonic spectrum In contrast, we find the photon-emission events from a cluster of several dots to be uncorrelated

Quantum correlation among photons from a single quantum dot at room temperature

Tunneling spectroscopy has played a central role in the experimental verification of the microscopic theory of superconductivity in classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy and spectroscopy (STM and STS) on these compounds allowed the main difficulties to be overcome. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. The crucial efforts to gain control over the technique and to obtain reproducible results are first recalled. Then a discussion on how the STM and STS techniques have contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors is presented: the unusually large gap values and the absence of scaling with the critical temperature, the pseudogap and its relation to superconductivity, the unprecedented small size of the vortex cores and its influence on vortex matter, the unexpected electronic properties of the vortex cores, and the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states and in the vortex cores.

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Scanning tunneling spectroscopy of high-temperature superconductors

We demonstrated short segments of a superconducting wire that meets or exceeds performance requirements for many large-scale applications of high-temperature superconducting materials, especially those requiring a high supercurrent and/or a high engineering critical current density in applied magnetic fields. The performance requirements for these varied applications were met in 3-micrometer-thick YBa 2 Cu 3 O 7-δ films epitaxially grown via pulsed laser ablation on rolling assisted biaxially textured substrates. Enhancements of the critical current in self-field as well as excellent retention of this current in high applied magnetic fields were achieved in the thick films via incorporation of a periodic array of extended columnar defects, composed of self-aligned nanodots of nonsuperconducting material extending through the entire thickness of the film. These columnar defects are highly effective in pinning the superconducting vortices or flux lines, thereby resulting in the substantially enhanced performance of this wire.

https://science.sciencemag.org/content/sci/311/5769/1911.full.pdf

High-performance high-TC superconducting wires.

Interest in vortex matter has risen considerably since the discovery of the high-temperature superconductors, which exhibit magnetic vortex states that are especially rich and complex1. The global behaviour of magnetic vortices in nearly perfect crystals—such as melting of the vortex lattice2,3,4,5—has been much studied, but of more technological relevance is the influence on the vortex states of the various structural defects present in most practical superconductors. An important example of such a defect is the twin boundary present in twinned orthorhombic crystals of YBa2Cu3O7−δ (YBCO). Studies of such samples using magnetic-field-sensitive probes6,7,8,9 have suggested that the twin boundary plays an important role in pinning the vortices and so enhancing the currents that YBCO can support while remaining superconducting. But the low spatial resolution of these techniques does not permit these effects to be studied at the scale of the vortices or boundaries themselves. Scanning tunnelling spectroscopy offers a means of circumventing these problems of resolution10,11,12, as it directly probes the superconducting order parameter at nanometre length scales. Here we use this technique to investigate the importance of twin boundaries in YBCO. In particular, we observe an unexpectedly large pinning strength for perpendicular vortex flux across the boundary, which implies that the critical current that can be supported along the boundary approaches the theoretical ‘depairing’ limit.

Critical currents approaching the depairing limit at a twin boundary in YBa 2 Cu 3 O 7−δ

We consider the experimental trends in a database of specific heat measurements near T c in high magnetic fields for type-II superconductors with a large value of κ = λ/ξ, including mostly high-temperature superconductors. Whereas the BCS limiting case is well established in low-T c superconductors, the exact 3D-XY behavior illustrated by the λ-transition of 4 He applies only in the particular case of optimally doped YBa 2 Cu 3 O x . Otherwise, transitions are intermediate either between the BCS and the 3D-XY models (e.g., YBa 2 Cu 3 O 7.00 ), or between the 3D-XY model and the Bose-Einstein condensation (BEC) (e.g., Bi 2 Sr 2 CaCu 2 O 8 ). The key parameter in ordering this sequence appears to be the product k F ξ of the Fermi wave number by the coherence length, as evaluated from tunneling spectra in the vortex cores. Such a trend, which is consistent with theoretical descriptions of the strong coupling limit, is visible in the thermodynamics of the phase transition. Implications on the effective mass, the density of pairs just above T c , the pseudo-gap behavior, etc., are discussed.

Specific heat of high temperature superconductors in high fields at Tc: from BCS to the Bose–Einstein condensation

The discovery of the high temperature superconductors in 1986 radically changed the situation in the field of superconductivity. Not only did the critical temperature increase drastically, but it becomes more and more clear that the nature of the superconducting state in the high temperature superconductors is radically different from the one found in the well known low temperature superconductors. In spite of a considerable world wide effort to study these new superconductors we still do not know the origin and the nature of the pairing interaction. It remains one of the central challenges of solid state physics today to elucidate this mechanism. One essential ingredient in the quest for an understanding of the superconducting state is the quasiparticle density of states or in other words the density of single particle excitations above the superconducting ground state. In 1960 Ivar Giaever 2 demonstrated that tunneling between a superconductor and a normal metal allowed a direct measurement of the quasiparticle density of states in the superconductor. After this path breaking work, tunneling became a main tool for investigating the various low temperature superconducting materials known at the time. In particular the inversion scheme developed by Rowell and McMillan to extract the electron phonon coupling from the tunneling spectra made a quantitative verification of the BCS model for these low temperature materials possible. Since the discovery of the high temperature superconductors, numerous investigations have been carried out with the hope that such tunneling studies will finally allow to unravel the mechanisms leading to high

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Scanning tunneling spectroscopy on high temperature superconductors

We report STM spectroscopy measurements of in-situ cleaved Bi2Sr2CaCu2O8 single crystals at 4.8 Kelvin, where we achieved strong evidences for true vacuum tunneling. These careful experiments result in very reproducible spectroscopy as a function of position on the surface, and as a function of tip/sample spacing. The characteristic features of the tunneling spectra are a significant filling of the gap region, a large density of states at the gap edges and a weak dip about 70 meV below the Fermi level. Such IV characteristics are not compatible with a single gap BCS-like s-wave theory. Furthermore, we report spatially resolved spectroscopy where we observe regions with two distinct gap values. A double gap structure appears in the tunneling spectra acquired in the vicinity of the boundary between these regions. We believe the double gap structure we observe in this case does not reflect an intrinsic gap anisotropy, but seems rather related to crystalline inhomogeneities. This demonstrates the potential of the STM's spatial resolution to shed some light on the controversy among the tunneling spectroscopy of high temperature superconductors published so far.

Vacuum tunneling spectroscopy of superconducting Bi 2 Sr 2 CaCu 2 O 8 using scanning tunneling microscopy

This paper reviews results obtained from low temperature scanning tunneling spectroscopy investigations on cleaved 2H-Nb1-xTaxSe2 and Bi2Sr2CaCu2O8 single crystals. Our study of the former crystals allowed us to image the vortex lattice, and to study how the peak in the density of states in the centre of the vortices is modified by the transition from the clean to the dirty limit. We have also been able to observe slow vortex motion with this technique. In our study of the Bi2Sr2CaCu2O8 compound, we have been able to obtain reproducible I–V characteristics while scanning. The characteristic features of the differential conductance spectra are sharp peaks at the superconducting gap edge, a weak dip beyond this energy at negative bias, and a finite conductance below the gap. The gap is found to have a value of 31±4 meV, but the experimental density of states shows the presence of states below the gap and cannot easily be fitted to a BCS like s-wave state.

Christophe Renner

Papers

Critical currents approaching the depairing limit at a twin boundary in YBa 2 Cu 3 O 7−δ

Specific heat of high temperature superconductors in high fields at Tc: from BCS to the Bose–Einstein condensation

Scanning tunneling spectroscopy on high temperature superconductors

Vacuum tunneling spectroscopy of superconducting Bi 2 Sr 2 CaCu 2 O 8 using scanning tunneling microscopy

Tunneling Spectroscopy and STM Observation of Flux Lines