Controlling Complexity in Cuprates for New Quantum Devices
Author: Antonio Bianconi
Affiliation: Department of Physics, Sapienza University of Rome, Italy
The quantum state of matter made of a macroscopic quantum condensate that is able to resist the decoherence attacks of high temperature was discovered by Alex Muller and Georg Bednoz -- specifically in ceramic conductors. Today we know many different high temperature superconducting materials from ceramics to diborides, from iron pnictides to chalcogenides that share a common material spatial architecture. As shown in Figure 1, they are heterostructures at atomic limit made of superconducting atomic layers (11) intercalated by different spacer layers (12).
Figure 1: schematic picture of a generic high temperature superconductor made of superconducting layers (11) intercalated by spacer layers (12). The dopants are inserted in the spacer layers (12) to control the critical temperature.
The high-temperature superconductivity (HTS) emerges in these lamellar materials when defects called dopants, atomic substitutions or extra (interstitial) or missing (vacancy) oxygen atoms, are injected in spacer layers (12). The dopants roam around in the spacer layers of the material at high temperature, and they freeze in ordered or random patterns when the samples are cooled.
The high temperature superconducting properties of these ceramic and intermetallic materials depend on the complex interplay of multiple electronic components that -- below the critical temperature -- form multigap superconductors made of a mixture of quantum condensates coupled by shape resonances (also known as Feshbach or Fano resonances). These complex electronic phases occur on a “low energy scale” of tens of hundreds of milli-electronvolts, i.e. at the low energy scale of the thermal energy at room temperature (KBT =25 milli-electron volts).
It remained a puzzle for so many years that at such a fine energy scale the distribution of dopants is expected to modify the electronic structure. Therefore learning how to control dopant distribution will open the new field in material science “superconductors by design”, since it will allow us to manipulate the multiple superconducting gaps and the critical temperature.
For many years most scientists assumed a homogeneous distribution of dopants in spite of indications of complexity emerged in the early nineties in the works of Jorgensen -- who observed the increase of Tc waiting for mobile oxygen ions to get self organized in the time scale of months. This was supported by observation of photo-induced superconductivity i.e. the increase of Tc by shining a laser light on the sample, and by our findings in 1994 that lattice fluctuations in the spacer layers are related to structural nano-scale phase separation of distorted stripes and undistorted stripes in the superconducting CuO2 plane modulating the superconductor electronic structure.
Ceramics have been around as long as human civilizations have been around for many thousands years. Our ancestors knew how to fire pots, and different civilizations are characterized by innovations in this technology. We have started to think that the imaging and control of the spatial organization of the dopants will allow us the manipulate these new ceramics at the nanoscale to get new functional materials. In the latest issue of 'Nature Materials' Poccia et al  show that actually these superconducting ceramics can be manipulated on a nanoscale with X-rays to get complex materials by design.
Last year we used  a new microscopy method developed thanks to the advances in focusing to nanoscale the X-ray beam emitted by synchrotron radiation facilities. This has allowed us to unveil the sample complexity by recording thousands of x-ray diffraction patterns for each crystal. This novel technique provided a complex real space map of the order in the k-space of oxygen interstitials in a cuprate where the oxygen interstitials are mobile. The fractal structure that emerged was typical complex systems ranging from social networks as "Facebook", and opinion dynamics to networks of protein interactions in living matter that show the complex world of "no scale" statistical distributions. We discovered that the best superconductivity was obtained when the microstructure was most ‘connected’ (see Figure 2), meaning that it is possible to trace a path with the same nanostructure (exhibited by oxygen atoms) over a large distance. If we zoom in on the material’s structure at increasing levels of magnification, its appearance would remain the same.
Figure 2: A fractal network of connected channels of ordered oxygen defects in a ceramic copper oxide promotes superconductivity. The green and red spheres represent the paired electrons responsible for superconductivity.
The physics of these materials was therefore expected to show fluctuations over states in complex rough potential landscape like in some soft materials with time evolution over multiple time scales. It has taken years for us to learn how to change the internal structure of a copper oxide superconductor via simple heat treatments – an approach employed by ceramicists over millennia to modify oxide materials.
To see whether the fractal pattern was important, we interfered with it by heating and then quickly cooling the superconductor. Crystals with stronger fractal patterns performed better as a superconductor at higher temperatures than those with weaker fractal patterns.
Ordering takes place on a time scale of months, and little was known about the details of this process.
We discovered that illuminating with X-rays causes a small scale re-arrangement of the oxygen atoms in the material, resulting in high temperature superconductivity. We have been attracted by this "beautiful example of a non-equilibrium, disordered system finding equilibrium". Here in these ceramics X-rays bring the oxygen interstitials into equilibrium, while they usually would cause radiation damage.
Illuminating a disordered sample by with x-rays fast-forward the ordering dynamics, and x-ray diffraction (XRD) was used to monitor the evolution of order, both parallel (a and b axes) and perpendicular (c axis) to the CuO2 layers. The XRD data reveal that the initial sample has small almost isotropic ordered islands, which act as nuclei. They initially combine, then grow predominantly in the a-b plane, and finally along the c axis. The unveiled details of the out-off- equilibrium domain growth process shed light on the previously unknown statistical physics features of these complex systems.
Figure 3: The illumination of the ceramic materials by x-ray beams of synchrotron radiation in the upper part of the figure is shown to allow to write superconducting planar circuits, such as those depicted in the lower image showing a magnification of the sample area. Here, solid lines indicate electrical connections while semicircles denote superconducting junctions, whose states are indicated by red arrows. (Credit: UCL Press Office).
At this point we learned how to manipulate the order of oxygen interstitials on a nano scale with X-rays. The X-ray beam is used like a pen to draw shapes (dots and lines) in two dimensions. Using this new approach the feasibility to write superconductors with dimensions down to nanometers and to erase those structures by applying heat treatments is shown. This new tool allows us to write and erase new superconducting circuits with high precision using just a few simple steps and without the chemicals ordinarily used in device fabrication. This ability to re-arrange the underlying structure of a material has wider applications in similar compounds containing metal atoms and oxygen, ranging from fuel cells to catalysts.
Our validation of a one-step, chemical-free technique to generate superconductors opens up exciting new possibilities for electronic devices, particularly in re-writing superconducting logic circuits. Of profound importance is the key to solving many of the world's great computational challenges. We want to create computers on demand to solve this problem, with applications from genetics to logistics. A discovery like this  means that a paradigm shift in computing technology is advanced one step closer.
 Nicola Poccia, Michela Fratini, Alessandro Ricci, Gaetano Campi, Luisa Barba, Alessandra Vittorini-Orgeas, Ginestra Bianconi, Gabriel Aeppli, Antonio Bianconi. "Evolution and control of oxygen order in a cuprate superconductor". Nature Materials, DOI: 10.1038/nmat3088 (Published online August 21, 2011). Abstract.
 Michela Fratini, Nicola Poccia, Alessandro Ricci, Gaetano Campi, Manfred Burghammer, Gabriel Aeppli, Antonio Bianconi. "Scale-free structural organization of oxygen interstitials in La2CuO4+y. Nature 466, 841–844 (2010) doi:10.1038/nature09260. Abstract.
[More information about this work can be obtained at Superstripes Press]