At smaller dopings, a more reliable approach is to start from a Mott insulator. This approach also gives d-wave superconductivity, with the value of T c most likely determined by phase fluctuations and decreasing as a function of decreased doping. Because both approaches give d-wave superconductivity with comparable values of T c , the majority of researchers believe that the mechanism of superconductivity in the cuprates is understood, at least qualitatively. A more subtle issue is how to explain the so-called pseudogap phase in hole-doped cuprates figure 4.

Here, the system is neither magnetic nor superconducting, yet it displays properties that clearly distinguish it from a normal, even strongly correlated metal. One natural idea, pioneered by Philip Anderson, is that the pseudogap phase is a precursor to a Mott insulator that contains a soup of local singlet pairs of fermions: superconductivity arises if the phases of all singlet pairs are ordered, whereas antiferromagnetism arises if the system develops a mixture of spin singlets and spin triplets.

Several theoretical approaches, most notably dynamical mean-field theory, have been developed to quantitatively describe the precursors to a Mott insulator. The understanding of the pseudogap as the phase where electron states progressively get localised, leading to a reduction of T c , is accepted by many in the HTS community. Yet, new experimental results show that the pseudogap phase in hole-doped cuprates may actually be a state with a broken symmetry, or at least becomes unstable to such a state at a lower temperature.

Evidence has been reported for the breaking of time-reversal, inversion and lattice rotational symmetry.

Improved instrumentation in recent years also led to the discovery of a charge-density wave and pair-density wave order in the phase diagram and perhaps even loop-current order. Many of us believe that the additional orders observed in the pseudogap phase are relevant to the understanding of the full phase diagram, but that these do not change the two key pillars of our understanding: superconductivity is mediated by short-range magnetic excitations, and the reduction of T c at smaller dopings is due the existence of a Mott insulator near zero doping.

The cuprates have motivated incredible advances in instrumentation and experimental techniques, with fold increases in accuracy in many cases.

### BOOK SERIES

On the theoretical side, they have also led to the development of new methods to deal with strong interactions — dynamical mean-field theory and various metallic quantum-critical theories are examples. These experimental and theoretical methods have found their way into the study of other materials and are adding new chapters to standard solid-state physics books.

Some of them may even one day find their way into other fields, such as strongly interacting quark—gluon matter. We can now theoretically understand a host of the phenomena in high-temperature superconductors, but there are still some important points to clarify, such as the mysterious linear temperature dependence of the resistivity.

## Amplitude/Higgs Modes in Condensed Matter Physics

The community is coming together to solve these remaining issues. Yet, the cynical view of the cuprate problem is that it lacks an obvious small parameter, and hence a universally accepted theory — the analogue of BCS — will never be developed. Rather, a theory of cuprates should be judged by its ability to explain both superconductivity and a host of concomitant phenomena, such as the pseudogap, and its ability to provide design principles for new superconductors.

Indeed, this is precisely the approach that allowed the recent discovery of the highest-T c superconductor to date: hydrogen sulphide. At present, powerful algorithms and supercomputers allow us to predict quite accurately the properties of materials before they are synthesised. For strongly correlated materials such as the cuprates, these calculations profit from physical insight and vice versa. From a broader perspective, studies of HTS have led to renewed thinking about perturbative and non-perturbative approaches to physics.

Physicists like to understand particles or waves and how they interact with each other, like we do in classical mechanics, and perturbation theory is the tool that takes us there — QED is a great example that works because the fine-structure constant is small. In a single-band solid where interactions are not too strong, it is natural to think of superconductivity as being mediated by, for example, the exchange of antiferromagnetic spin fluctuations. When interactions are so strong that the wave functions become extremely entangled, it still makes sense to look at the internal dynamics of a Cooper pair to check whether one can detect traces of spin, charge or even orbital fluctuations.

At the same time, perturbation theory in the usual sense does not work. Instead, we have to rely more heavily on large-scale computer calculations, variational approaches and effective theories. Download references. To obtain permission to re-use content from this article visit RightsLink. Advanced Materials C Journal of Physics: Condensed Matter Physica C: Superconductivity and its Applications Nano Research By submitting a comment you agree to abide by our Terms and Community Guidelines.

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## Marco Grilli | Università degli Studi "La Sapienza" di Roma - giphycunori.cf

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Abstract THE discovery of superconductivity in potassium-doped C 60 ref. Rent or Buy article Get time limited or full article access on ReadCube. References 1. CAS Google Scholar 7. CAS Google Scholar 9. CAS Google Scholar Google Scholar Google Scholar Download references. Rights and permissions To obtain permission to re-use content from this article visit RightsLink. The first three chapters of this part cover generally accepted themes in the conventional theory of superconductivity and serve as a good introduction to the subject.

## Theory of Superconductivity

Chapter 4 describes what happens to the conventional theory when the coupling between electrons becomes strong. Part II describes key physical properties of high-temperature superconductors and their theoretical interpretation. Alternative viewpoints are discussed, but the emphasis is placed on the bipolaron theory.

Reviews "The book presents both a useful description of the fundamentals of the theory of supercondutivity and an example of the further evolution of the polaron concept. Request an e-inspection copy. Share this Title. Recommend to Librarian. Related Titles. Introduction to the Electronic Properties of Materials.

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