Many-Body Problems in High Temperature Superconductivity

Tao Xiang

High-temperature superconductivity, a fundamental topic in condensed matter physics, presents one of the critical scientific challenges of this century. The potential for breakthroughs in this field not only promises to reveal numerous novel quantum phenomena and deepen our understanding of quantum many-body physics but also to significantly drive advancements in experimental techniques, theories, and methodologies in probing correlated quantum systems. More importantly, as a non-perturbative quantum system, high-temperature superconductivity offers an ideal platform and a crucial driving force for systematically establishing non-perturbative quantum field theory. Currently, research on high-temperature superconductivity stands at a critical turning point. Achieving significant breakthroughs requires the development of cutting-edge detection technologies built upon novel concepts, the establishment of innovative theoretical frameworks and methodologies, and insightful elucidation of the physical pictures revealed by experimental findings. Such extensive exploration is vital for unveiling fundamental relationships and identifying the governing principles. By integrating these efforts, we can gain profound insights into the mechanisms of high-temperature superconductivity and significantly expand the horizons of quantum many-body theory.

H. Forehlich

Alexandre M. Zagoskin

Luis Benet, M. Bienert, S. Yu. Kun

A characteristic feature of thermalized non-equilibrated matter is that, in spite of energy relaxation- equilibration, a phase memory of the way the many-body system was excited remains. As an example, we analyse data on a strong forward peaking of thermal proton yield in the Bi(γ, p) photonuclear reaction. A new analysis shows that the phase relaxation in highly-excited heavy nuclei can be eight orders of magnitude or even much longer than the energy relaxation. We argue that thermalized non-equilibrated matter resembles a high temperature superconducting state in quantum many-body systems. We briefly present results on the time-dependent correlation function of the many-particle density fluctuations for such a superconducting state. It should be of interest to experimentally search for manifestations of thermalized non-equilibrated matter in many-body mesoscopic systems and nanostructures.

A. S. Alexandrov

Motivation With few exceptions [131] it is widely accepted that the conventional Bardeen–Cooper–Schrieffer (BCS) theory [12] and its intermediate-coupling Eliashberg extension [14] do not suffice to explain high-temperature superconductivity. As shown in the preceding chapters the true origin of high-temperature superconductivity could be found in a proper combination of the bare Coulomb repulsion with the bare electron–phonon interaction in the framework of the many-body polaron theory [51] beyond the BCS–Eliashberg approximation. Nevertheless some researchers have maintained that the repulsive electron–electron interaction alone should provide pairing at high temperatures without phonons despite substantial experimental evidence that the EPI is an important player and needs to be included in the successful theory of high- T c superconductivity. Following the original proposal by P. W. Anderson, many authors [22, 74] argued that the electron–electron interaction in high-temperature superconductors was strong but repulsive providing high T c without phonons via superexchange and/or spin fluctuations in the d -wave pairing channel ( l = 2). A motivation for this concept can be found in the earlier works by Kohn and Luttinger (KL) [132, 133] who showed that the Cooper pairing of fermions with any weak repulsion was possible since the two-particle interaction induced by many-body effects is attractive for pairs with large orbital momenta, l ≫ 1.

Alexandre M. Zagoskin