**Author details**

Roberto Zivieri

Address all correspondence to: roberto.zivieri@unife.it

INdAM-GNFM Rome, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Messina University, Messina, Italy

**Superfluidity: Theory and Observation**

circulation in multiply-connected superfluids. Quantized vortex structures are characterized by a singularity in the center and the vortex core is quantified by means of vorticity, a topological charge otherwise called winding number characterizing the strength of a vortex and identifying superfluid and superconducting vortices as topological defects. This description is an important step forward in both fields because the study of the topological properties is crucial to fully understand the underlying physics in the systems exhibiting either superconductivity or superfluidity.

In the next six chapters of the book, some of the recent novelties in the two fields of superconductivity and superfluidity are reviewed both from a theoretical and an experimental point of view. The book is organized into two sections: (1) the first section contains three chapters dealing with the recent developed theoretical models and measurements carried out in superconductors and (2) the last three chapters contained in the second section report on the theoretical advancement together with the most sophisticated experimental techniques in superfluidity. In more detail, Chapter 2 reviews the main properties of the intermediate state in type-I superconductors and the main theoretical models to interpret it. Chapter 3 reports the recent experiments on some emerg-

with special regard to the correlation between crystal structure and superconductivity. Chapter 4 reports on the effect of isovalent substitutions and heat treatments on some physical properties of high-critical temperature superconductors by means of advanced experimental techniques. Chapter 5 presents an advanced theory in the field of superfluids on the Kelvin wave and knot dynamics on three-dimensional deformed knot-crystal and its relation with deformed space-time. Chapter 6 outlines an effective field theory applied to study vortices and solitons in superfluid Fermi gases. Chapter 7 describes an experimental technique that is able to produce hydrogen-free

Finally, I would like to express my personal gratitude to all authors who have contributed with their efforts to this book. I am sure that all the contributions can give interesting insights

INdAM-GNFM Rome, Department of Mathematical and Computer Sciences, Physical


**3. Contents and organization of the book**

4 Superfluids and Superconductors

ing superconductors, the bismuth chalcogenides, and the BiS<sup>2</sup>

into the condensed matter physics scientific community.

Address all correspondence to: roberto.zivieri@unife.it

Sciences and Earth Sciences, Messina University, Messina, Italy

**Acknowledgements**

**Author details**

Roberto Zivieri

liquid helium and illustrates how to solve the flow impedance blocking issue.

**Chapter 2**

Provisional chapter

**An Effective Field Description for Fermionic Superfluids**

DOI: 10.5772/intechopen.73058

In this chapter, we present the details of the derivation of an effective field theory (EFT) for a Fermi gas of neutral dilute atoms and apply it to study the structure of both vortices and solitons in superfluid Fermi gases throughout the BEC-BCS crossover. One of the merits of the effective field theory is that, for both applications, it can provide some form of analytical results. For one-dimensional solitons, the entire structure can be determined analytically, allowing for an easy analysis of soliton properties and dynamics across the BEC-BCS interaction domain. For vortices on the other hand, a variational model has to be proposed. The variational parameter can be determined analytically using the EFT, allowing to also

study the vortex structure (variationally) throughout the BEC-BCS crossover.

Keywords: fermionic superfluids, superfluidity, effective field theory, solitons, vortices

When cooling down a dilute cloud of fermionic atoms to ultralow temperatures, particles of different spin type can form Cooper pairs and condense into a superfluid state. The properties and features of these superfluid Fermi gases have been the subject of a considerable amount of theoretical and experimental research [1, 2]. The opportunity to investigate a whole continuum of inter-particle interaction regimes and the possibility to create a population imbalance result in an even richer physics than that of superfluid Bose gases. In this chapter, we present an effective field theory (EFT) suitable for the description of ultracold Fermi gases across the BEC-BCS interaction regime in a wide range of temperatures. The merits of this formalism mainly

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

An Effective Field Description for Fermionic Superfluids

Wout Van Alphen, Nick Verhelst,

Wout Van Alphen, Nick Verhelst,

http://dx.doi.org/10.5772/intechopen.73058

Jacques Tempere

Abstract

1. Introduction

Jacques Tempere

Giovanni Lombardi, Serghei Klimin and

Giovanni Lombardi, Serghei Klimin and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Chapter 2** Provisional chapter

#### **An Effective Field Description for Fermionic Superfluids** An Effective Field Description for Fermionic Superfluids

DOI: 10.5772/intechopen.73058

Wout Van Alphen, Nick Verhelst, Wout Van Alphen, Nick Verhelst,

Giovanni Lombardi, Serghei Klimin and Giovanni Lombardi, Serghei Klimin and

Jacques Tempere Jacques Tempere

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73058

#### Abstract

In this chapter, we present the details of the derivation of an effective field theory (EFT) for a Fermi gas of neutral dilute atoms and apply it to study the structure of both vortices and solitons in superfluid Fermi gases throughout the BEC-BCS crossover. One of the merits of the effective field theory is that, for both applications, it can provide some form of analytical results. For one-dimensional solitons, the entire structure can be determined analytically, allowing for an easy analysis of soliton properties and dynamics across the BEC-BCS interaction domain. For vortices on the other hand, a variational model has to be proposed. The variational parameter can be determined analytically using the EFT, allowing to also study the vortex structure (variationally) throughout the BEC-BCS crossover.

Keywords: fermionic superfluids, superfluidity, effective field theory, solitons, vortices
