Preface

Chapter 7 **Effects of Isovalent Substitutions and Heat Treatments on Tc,**

Abdelhakim Nafidi

**VI** Contents

**Orthorhombicity, Resistivity, AC Magnetic Shielding and Irreversibility Line in High-Tc Superconductors 129**

> Two of the main phenomena occurring in condensed matter systems are superfluidity and superconductivity. The two phenomena can be considered as two faces of the same coin. Indeed, superfluidity is the property of a fluid with zero viscosity and no losses of fluid ki‐ netic energy, while superconductivity occurs as the property of a conductor having zero electrical resistance and exhibiting the total expulsion of a magnetic field. Below a critical temperature, viscosity in a superfluid and resistance in a superconductor drop to zero. In the former case, there is the appearance of a superfluid phase, while in the latter case, a su‐ perconducting phase arises.

> Since the first discovery of superfluidity in the two isotopes of helium, helium-3 and heli‐ um-4, and the observation of superconductivity, many efforts have been done to understand the underlying physics characterizing these two remarkable phenomena. A step forward for the comprehension of superfluidity on a microscopic level has been the connection between superfluid helium-4 and a boson particle and between superfluid helium-3 and a fermion particle with the pairing between two helium-3 atoms occurring at low temperatures and leading to the superfluid phase below the critical temperature. The pairing mechanism rep‐ resents the analogous of the electron Cooper pairs that are at the basis of the microscopic theory of superconductivity for superconductors of the first kind and allows a superfluid behavior below a critical temperature with zero resistance. The discovery of superconduc‐ tors of the second kind exhibiting a higher critical temperature and two critical values for the external magnetic field has been an important advancement in the field of superconduc‐ tivity. Finally, for both phenomena, one of the most important implications is the formation of vortex configurations that are linked to their topological properties.

> I would like to thank all the authors for their efforts in writing the chapters included in this book. Each of them contains the recent advances in the topics of superfluidity and supercon‐ ductivity both from the theoretical and experimental points of view catching the attention not only of specialists but also of nonspecialists working in the field of condensed matter physics. Special thanks go to the Publishing Process Manager, Mr. Julian Virag, for his kind help and for his precious and devoted assistance during all the production steps. I would also like to acknowledge the National Institute of Advanced Mathematics (INdAM) and the National Group for the Mathematical Physics (GNFM) in Rome for their kind support of‐ fered to me during this project.

> > **Prof. Roberto Zivieri** INdAM and GNFM, Rome Department of Mathematical and Computer Sciences Physical Sciences and Earth Sciences Messina University, Messina, Italy

**Section 1**

**Introduction**

**Section 1**
