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Fragile superconductivity at high magnetic fields

Ever since the discovery of superconductivity by Kamerlingh Onnes’ group in 1911, this phenomenon has continued to intrigue successive generations of scientists. One of the most spectacular discoveries since 1911 was that of high-temperature superconductivity in a copper oxide (1). Tens of thousands of papers have been written on these cuprate materials, yet 35 years later, they continue to surprise us. In PNAS, Hsu et al. (2) demonstrate that a fragile form of superconductivity persists in a cuprate up to the highest magnetic field they can muster. The original superconductor discovered by Onnes’ group is of a class now known as type I superconductors. These superconductors expel a magnetic field, with superconductivity surviving up to a critical field where the energy gain due to superconductivity equals that associated with the magnetic field. However, in 1957, Abrikosov (3) proposed another class of superconductors, now known as type II superconductors. In these superconductors (as illustrated in Fig. 1, Left), above a lower critical field, superconductivity survives in the form of a unique state of matter where the magnetic field penetrates as an array of quantized magnetic flux lines. Once the cores of these socalled vortices overlap, then superconductivity disappears at a higher field known as the upper critical field. Since superconductivity survives to much higher magnetic fields, most practical applications involve type II superconductors. This requires that the vortices be pinned, as their motion leads to dissipation and thus a finite resistance. Now, when high-temperature superconductivity was discovered in 1986, there was a realization that they differ in fundamental ways from conventional type II superconductors. In particular, these materials are highly two-dimensional in nature, and therefore the vortex lattice is more fragile (Fig. 1, Right). At low temperatures, it takes the form of a glassy state (4). Thermal fluctuations lead to depinning of the vortices, with the glassy state melting to form a liquid of vortices that leads to dissipation. As such, this vortex liquid is separated from the normal state by just a crossover line. Most theories (4, 5) focus on lower magnetic fields, where one can think in terms of thermal fluctuations, with the vortex lattice melting much like a solid melts to form a liquid. However, in the high-field, low-temperature regime, quantum effects come into play, making theoretical treatments more difficult, but in turn opening up the possibility for more surprises. To proceed, we should mention that cuprates have a somewhat complicated phase diagram (6). The parent phase is a magnetic insulator. Upon introduction of carriers (typically by chemical doping), magnetism is suppressed and superconductivity emerges. This superconductivity as a function of temperature and doping takes the form of a dome. The maximum of this dome separates the lower doped region (known as underdoped) from the higher doped region (known as overdoped). The underdoped side is the more intriguing of the two, as it is characterized by a M ag ne tic F ie ld