Heating up of Superconductors

The Race Begins

When some conductors are cooled to very low temperatures their electrical resistance suddenly drops to zero—a current flows indefinitely through the material with nothing to stop it. In 1911, mercury was the first such “superconducting” material to be discovered, with a transition temperature of 4.1 K—below this temperature the material superconducts, above this temperature the material behaves like a regular conductor with resistance. Scientist have been searching for higher temperature superconductors ever since.

In 1986, Johannes Bednorz and Karl Müller demonstrated superconductivity in a copper-oxide compound at a temperature of 35 K, 12 K above the then previous record, starting an immediate race to find compounds with even higher transition temperatures. Their results were published in Zeitschrift für Physik B. In the two years that followed the duo’s discovery, superconducting transition temperatures of around 40 K, 90 K, and then 120 K were achieved in other copper-oxide compounds known as cuprates. Maw-Kuen Wu and his colleagues were the first to attain a transition temperature higher than the 77 K boiling point of liquid nitrogen, making superconductors more attractive for technological applications. Today the record temperature for superconductivity in a cuprate is around 140 K.

Summary from Physical Review Letters’ Milestone Collection

Nobel Foundation/Kenneth C. Zirkel/Wikimedia

Explaining Superconductivity

The microscopic theory of superconductivity came well before the discovery of the so-called high-temperature superconductors of Bednorz, Müller, and then others. In 1957, John Bardeen, Leon Cooper, and Robert Schrieffer devised a theory to explain how materials, like mercury, can conduct electricity without resistance at low temperatures. This theory has gone on to be one of the most successful in solid-state physics.

Known as “BCS” theory—the trio’s initials—the theory links superconductivity to bound pairs of electrons, known as Cooper pairs. If the quantum-mechanical wave functions of these electron pairs align, the electrons form a collective state where they can’t “see” other electrons, or the lattice, allowing them to move without resistance. While the theory works well for low-temperature superconductors, it fails to completely explain high-temperature superconductors. The binding force of Cooper pairs predicted by BCS theory is very low and shouldn’t survive the larger thermal vibrations present at higher temperatures.

See Physics article: Focus: Landmarks—Superconductivity Explained

High Temperature Superconductivity Needs Holes

In an attempt to gain better understanding of the high-temperature superconductivity observed in the 1986 and 1987 experiments, Victor Emery identified the carriers of cuprates’ “supercurrent”: pairs of oxygen holes located in the same copper-oxide plane. These hole pairs act in the same way as BCS’s Cooper pairs, enabling them to move unhindered. Building on work by Philip Anderson, Fuchun Zhang and Thomas Rice then derived a single-band effective Hamiltonian description of superconductivity in which oxygen holes first form a singlet with a neighboring copper spin ion, and then move through the lattice carrying the supercurrent.

Since the publication of the papers by Emery, Zhang, and Rice, many other high-temperature superconductivity models have been proposed. Most of these models also predict that Coulomb interaction between holes confined in copper-oxide planes is crucial to explaining superconductivity in cuprates.

d-Wave is the New Wave

By the early 1990s, the amassed experimental data provided further evidence that there was something different about the pairs carrying the supercurrent in high-temperature cuprate superconductors than in low-temperature superconductors. Experiments carried out by David Wollman and colleagues in 1993 indicated a new electron pairing symmetry in cuprate superconductors called d wave.

For their experiments Wollman et al. fabricated superconducting-normal-superconducting “sandwiches” and connected two of these sandwiches together. This system allowed them to measure the phase of the energy gap for bound electron pairs, not just its magnitude as in earlier experiments. In low-temperature superconductors there is no phase shift, but in these cuprates the team observed a nonzero phase shift of approximately π, indicating a different pairing state symmetry for the material.

Prior to these experiments, Phillippe Monthoux and colleagues had predicted d-wave pairing in high-temperature cuprate superconductors when the d orbitals of copper ions were antiferromagnetically aligned in the copper-oxide planes. The work built on theoretical calculations by Douglas Scalapino et al., who had also predicted d-wave pairing in spin-density-wave instabilities.

More Weird Behavior

The relatively high temperature of superconductivity in cuprates isn’t their only weird behavior. In their nonsuperconducting, or “normal state,” these materials do not behave like ordinary metals. For example, in many cuprates their normal-state resistivity increases linearly with temperature, while in metals, resistivity deviates from linearity, saturating at higher temperatures. But experiments showed that normal-state cuprates do have a Fermi surface—a surface in reciprocal space that defines the momentum distribution of conduction electrons—a characteristic of metals, also termed Fermi liquids.

To explain the appearance of a Fermi surface in normal-state cuprates, Chandra Varma and colleagues hypothesized that excitations existed in the polarizability of spin- and charge-density waves at low frequencies. Accounting for these “quasiparticles,” the group was able to show that a Fermi-like surface appeared in the cuprates’ normal state. They called this state a marginal Fermi liquid. The theory also provided a mechanism for pair-formation in the superconducting state.

Phys. Rev. Lett. 100, 047004 (2008)

The Superconducting Fermi Surface

The conducting properties of cuprates depend on the level of doping of the material: Overdoped cuprates behave like conventional metals with a Fermi surface, while underdoped cuprates behave like superconductors and display only disconnected Fermi “arcs.” In two studies published in 2007 and 2008, scientists set out to probe the Fermi arcs of underdoped superconducting cuprates experimentally.

To do this, Doiron-Layraud and colleagues measured variations in the electric resistance of the underdoped cuprate YBa₂Cu₃O_6.5 as a function of an applied magnetic field. The team observed quantum oscillations in the electrical resistance of the material—a direct indication of a Fermi surface—when the superconductivity was suppressed by the applied magnetic field. In a second study, Alimamy Bangura and colleagues observed the same oscillations, but this time in thin films of the underdoped cuprate YBa₂Cu₄O₈. These measurements established the presence of a Fermi surface in underdoped cuprates. The low frequency of the quantum oscillations indicated that the Fermi surfaces of these materials consisted of distinct “pockets,” rather than a continuous surface measured for overdoped cuprates.

Phys. Rev. B 40, 7391(R) (1989)

The Appearance of Stripes

In the late 1980s, scientists observed that undoped compounds of cuprates are antiferromagnetic Mott insulators: they should conduct electricity but they don’t. When charge carriers are introduced by doping, the length scale over which antiferromagnetic order is observed slowly decreases and eventually disappears. This breakdown in antiferromagnetic order corresponds to a switch from insulating to conducting behavior in the material. Jan Zaanen and Olle Gunnarsson studied the breakdown of antiferromagnetism theoretically. The duo calculated that the excessive holes introduced by doping condense into charged magnetic domain lines forming “stripes.”

John Tranquada and colleagues later presented experimental evidence for stripes in a superconducting neodymium-doped lanthanum cuprate. Using neutron scattering techniques, the team demonstrated that stripe and superconducting states coexist in this material, fueling a debate on whether the two states are connected.

Enter the Pseudogap

The antiferromagnetic region of the phase diagram of cuprates is bordered by the underdoped region. In the underdoped region, the material’s band structure exhibits a pseudogap—partial suppression of the density of states—below some characteristic temperature. The pseudogap transition temperature has been shown experimentally to extend above the superconducting transition temperature, leading scientists to question how and if the two phenomena are related.

To answer this question, Christoph Renner and colleagues used scanning tunneling microscopy techniques to probe the evolution of one state into the other. Their measurements indicate that the pseudogap evolves continuously into a superconducting gap and it is therefore a precursor of the superconducting state. However, in a Comment on this paper, Jeffery Tallon and Grant Williams point out that nuclear magnetic resonance and heat capacity data show that the pseudogap phenomenon and superconductivity are not directly related, raising doubt about the interpretation of Renner et al. The exact nature of the pseudogap has yet to be confirmed. The majority of the community now believes that understanding the nature of the pseudogap would be a major step forward in pinning down the origin of high-temperature superconductivity in cuprates.

Gadolinist/Wikimedia

A Glassy State for Superconductors

Cuprate superconductors are not only characterized by a high T_c, but also by short coherence lengths, deep magnetic penetration depths, and two-dimensional layered structures. In 1989, Matthew Fisher showed theoretically that when combined with microscopic disorder in the material, these unusual characteristics lead to a new magnetic vortex-glass phase appearing when a strong magnetic field is applied to the material. Fisher’s predictions suggested that this glassy state was also a superconducting state with zero electrical resistance.

Later that year, Roger Koch and colleagues provided experimental evidence that supported Fisher’s predictions. In detailed measurements of the current-voltage characteristics of Y-Ba-Cu-O subjected to strong external magnetic fields, the team mapped out the equilibrium phase boundary between a normal “vortex-liquid” and a superconducting “vortex-glass” as a function of temperature.

Daniel Fisher, Matthew Fisher, and David Huse then presented a complete theory for the vortex glass and studied other magnetic phases in high-T_c cuprates. Their work provided further evidence that the vortex-glass state is a true zero-resistance superconducting state, with magnetic vortices pinned by quenched point defects.