On July 10, 1908, helium was liquefied for the first time by Kamerlingh Onnes at the University of Leiden, a feat that earned him a Nobel Prize in Physics. Three years later, Onnes made another landmark discovery. After immersing mercury wire in liquid helium, Onnes observed that at temperatures below 4.2 K (–268.95°C), electrical resistance was “practically zero.”1 In his sample, a temperature increase of less than 0.01 K had been accompanied by an increase in resistance from essentially zero to 0.1 ohms.2 Onnes had discovered superconductivity.
At the time of its discovery, superconductivity was a truly startling phenomenon. For physicists, it was also an effect that was entirely unexplainable. Their bewilderment was further compounded in 1914 when Onnes demonstrated a persistent current flowing indefinitely in a loop of superconducting material. In 1932, a member of Onnes’s team, Gerrit Flim, created a sensation at the Royal Institution. Flim arrived in London with a “portable dewar containing a lead ring immersed in liquid helium and carrying a persistent current of 200 A.”3 The presence of a magnetic field created by the circulating current was confirmed using a compass, proving that the persistent current had not dissipated en route.
Despite these dramatic demonstrations, it was not until 46 years later that a satisfactory microscopic theory explaining the phenomenon of superconductivity was formulated by John Bardeen, Leon Cooper, and John Robert Schrieffer.4 The central concept of the Bardeen–Cooper–Schrieffer (BCS) theory was due to Cooper. Electrons, he suggested, pair up to become an effective boson. The spins of the electrons form a spin-singlet—a spin-zero object that is antisymmetric in its spin space. At first glance, this might seem counterintuitive. How is it possible for two electrons to become bound together? According to BCS theory, the electrons, known as a Cooper pair, are only bound together rather loosely and should not be considered an atom-like object. The electrons, it should be noted, move around against a net-positive electrically charged background arising from the structural material. The vibrations of this lattice of positive atoms serve to mediate the effective attractive electron–electron interaction. In effect, the positively charged background responds to a passing electron, causing another nearby electron to be drawn toward a locally positive region. Phonon-mediated interaction between the electrons then binds them together in a pairing mechanism. The collection of effective bosons forms a superfluid with a wave function that can be described in quantum-mechanical terms.
The BCS theory allows for characteristic effects associated with superconductivity to be checked experimentally and explained in quantitative terms using relatively few parameters. The theory has been successfully applied to explain the ability of a superconductor to expel a magnetic field, known as the Meissner effect; the amount of energy needed to break apart a Cooper pair of electrons; and how the critical temperature of normal metal–superconductor phase transitions is dependent on the mass of the ions. Bardeen, Cooper, and Schrieffer were jointly awarded the 1972 Nobel Prize in Physics for their contribution.
In 1986, J. Georg Bednorz and K. Alex Müller discovered that a class of ceramic materials known as cuprates exhibited superconductivity at much higher temperatures than had been previously observed.5 The importance of this discovery was immediately apparent, and the pair were subsequently awarded Nobel Prizes. The exotic new superconductors discovered by Bednorz and Müller were quite unlike simple, elemental substances such as lead, mercury, or aluminum. The term cuprate is a reference to copper-oxygen planar structures formed in the lattice of complex materials such as YBaCu3O4 or La2–xSrxCuO4. It seems that these two-dimensional planes play a crucial role in high Tc superconductivity, where Tc denotes the transition temperature. Cuprates become superconductive at around 138 K (–135°C), meaning that liquid nitrogen can be used for cooling rather than liquid helium.
The discovery of this property in cuprates is tantalizing, hinting at the possibility that superconductivity may be possible at still higher temperatures. Appropriately structured materials may even prove to be superconductive at room temperature, forming the basis for a range of new technologies such as lossless power transmission and magnetically levitated trains. Despite the best efforts of condensed matter theorists, cuprate superconductors have thus far resisted all attempts at explaining their physics. A survey of condensed matter textbooks is illustrative of the problem. The phenomenology of the effect is discussed, albeit sparingly, but there is little, if anything, beyond guesses as to the cause and underlying pairing mechanism. The BCS theory has proven inadequate to fully explain cuprate superconductivity and it seems that a satisfactory microscopic explanation will require an entirely different set of ideas.
It has been suggested that a quantum critical point (QCP) might form the basis for high Tc superconductivity. A QCP occurs at absolute zero and is associated with a change of order in the quantum ground state as a parameter of the system is changed. Although it is associated with a diverging susceptibility at absolute zero, the influence of this QCP can also be felt at high temperatures. A more commonly encountered critical point occurs in thermodynamic systems where the boundary between phases ceases to exist and large fluctuations can be observed. When water is heated to 374°C and pressurized to 218 atm, any distinction between liquid and steam disappears. When materials reach a critical point, large fluctuations in density can result in critical opalescence: light can no longer penetrate the wildly fluctuating material, and a transparent substance can become increasingly cloudy.6 In the quantum context, these zero-point fluctuations are associated with Heisenberg’s uncertainty relation.
The existence of a QCP might help explain the interconnected phenomena associated with high Tc superconductors. These become evident as the doping fraction of the material is varied. The mixture of impurities during the creation of the materials can add conduction electrons, or holes arising from the absence of an electron. This results in changes to the thermodynamic phases that can occur, such as pseudogap metals, antiferromagnetic insulators, strange metals, and charge density waves. The superconducting phase can be found in the midst of these other phases. The key feature of the QCP is the change of ground state order as one passes through it. It was theorized that this critical point should occur at a doping level around p = 0.2, where p denotes the amount of hole doping per Cu atom.7 If a change in order is indeed taking place, it will be evident from observing carrier density,8 which can be measured using the Hall effect. If a perpendicular magnetic field is applied to a rectangular sample and a voltage is also applied across the conductor causing a current to flow, another voltage will appear in the transverse direction. A new resistance, known as the Hall resistance, is defined by the ratio of the transverse voltage to the current. This new resistance is useful because even the simplest treatment of free charge carriers yields a nice result. The inverse of the Hall resistance is proportional to the carrier density and can be easily calibrated and measured. With this in mind, testing the QCP might seem straightforward.
For the experiment described by Sven Badoux and his colleagues to work, electrons need to behave as individual electrons. Superconductivity masks that behavior. The approach adopted by Badoux et al. was conceptually simple, but extremely difficult in technical terms: eliminate any superconductivity.9 This can be achieved by heating the system, by applying a voltage or current sufficient to drive to the normal metal, or by applying a magnetic field large enough to break up the Cooper pairs. In the context of the work undertaken by Badoux et al., the first method will not work because the QCP is near absolute zero. The second method is also unsuitable because sensitive electrical measurements need to be made using the sample. In conventional superconductors such as aluminum, only a few milliteslas (a measure of magnetic fields) are needed to drive the system to a normal state. For cuprate superconductors, the mechanism for superconductivity is much stronger, which is why it persists at such high temperatures. For this reason, the magnetic fields involved in the third method also need to be much stronger. These experiments required fields of around 90 teslas, which can only be generated by a magnetic field pulse that attains such a large value for a hundredth of a second. Once the superconductivity had been momentarily shattered, the hidden critical point was revealed. As predicted, a jump in carrier density was observed as the doping changed from sample to sample.
Although the experiment by Badoux et al. did indeed reveal the existence of a QCP, many questions remain. What kind of order is present in the low doping regime? It is clearly a kind of strongly correlated behavior among the electrons. Some theorists have suggested that it is an antiferromagnetic order—electron spins change direction in space at every other site.10 No direct evidence has been forthcoming to support this idea. Other, more exotic proposals involving fractionalized electron spin and charge have also been put forward. These ideas are the subject of ongoing research, but definite conclusions have not yet been reached.
Understanding the microscopic mechanisms that give rise to cuprate superconductivity is an essential step in the quest to fabricate materials that exhibit superconductivity at room temperature. The eminent theoretical condensed matter physicist Markus Büttiker once remarked to me that it took almost 50 years for the BCS theory to appear after superconductivity was first discovered, so we should not expect a satisfactory theory of high Tc superconductivity until at least 50 years after its discovery. According to Büttiker’s estimate, we still have another 15 years to wait.
