##
**Theory of high temperature superconductivity. A conventional approach.**
*(English)*
Zbl 1242.82001

Hackensack, NJ: World Scientific (ISBN 978-981-4343-14-5/hbk; 978-981-4343-15-2/ebook). xiv, 259 p. (2011).

The book is devoted to the explanation of principles of high-temperature superconductor (HTS) physics presented in the form of an introductory monograph. It is divided into nine chapters. The first chapter analyzes the common features in the electron band structure of the layered perovskites within the tight-binding (TB) method. To address the conduction bands in the layered perovskites, a common Hamiltonian including the basis of valence states for ruthenates and cuprates is studied. After considering the generic Hamiltonian of the CuO2 plane, a Hamiltonian of the RuO2 plane is studied. Practical aspects in connecting the present theory with experiments are also considered.

Chapter 2 presents the traditional theory for superconductivity in overdoped and possibly also optimally doped cuprates. It is demonstrated how the s-d exchange can be incorporated into the standard Bardeen-Cooper-Schrieffer (BCS) scheme and how the d-wave superconducting gap can derived. For the case of the s-d pairing the analytical solution is compared with the ARPES data. In Chapter 3, an explicit interpolation formula for the temperature dependence of the specific heat is obtained. This formula is exact for factorizable pairing kernels which are a consequence of the approximate separation in superconducting order parameters derived in BCS weak-coupling approximations by Pokrovskii for arbitrary weak coupling kernels and Gor’kov and Melik-Barkhudarov results for the Ginzburg-Landau (GL) coefficients of an anisotropic superconductor. Moreover, the recent results of Kogan for the penetration depth are presented and new formulas are proposed for the zero-scattering case which may be used for experimental data processing. The fourth chapter is devoted to the study of some electrodynamic properties of HTS such as plasmons and electric field effects giving access to the Cooper pair effective mass. Among the main results presented in the chapter are formulae for vortex charge and vortex conductivity, surface Hall currents for bulk crystals, interface Hall conductivity for type-I superconductors and thermal-induced contact-potential difference. Chapter 5 systematizes the known classical results for the GL Gaussian fluctuations to derive new ones and gives formulae that are necessary for the further development of the Gaussian spectroscopy of fluctuations. By using the \(\zeta\)-function method for UV regularization, the authors obtain general expressions for the fluctuations heat capacity and magnetization. Moreover, it is discussed how systematic investigations of the fluctuation phenomena can lead to a reliable determination of fundamental material parameters of HTS. The next chapter derives the Boltzmann equation for fluctuation Cooper pairs and illustrates its work on the example of the fluctuation conductivity. The authors re-derive the frequency dependence of the Aslamazov-Larkin conductivity fluctuation, Hall effect at weak magnetic fields and magnetoconductivity. The test data are analyzed for indium oxide films and significant deviation from the BCS weak coupling prediction is found. Chapter 7 studies the effect of fluctuations of the superconducting order parameter on linear and non-linear conductivity near and above the bulk superconducting critical temperature. On the base of the time-dependent generalization of the Ginzburg-Landau theory (TDGL) the kinetics of the order parameter are studied in a strong electric field in the framework of a simple phenomenological approach and new test methods for determining the life-time of fluctuation Cooper pairs and coherence length are stated. Chapter 8 considers the electric field fluctuations between the CuO2 layers and explains the linear temperature dependence of the resistivity. The authors’ model is based on the strong anisotropy of the electrical resistivity in layered cuprates. In Chapter 9 it is discussed how HTS can be used as generators of high frequency electric oscillations including the THz range. It is shown that the negative differential conductivity presents a new opportunity for generation of THz oscillations.

In total, this very interesting book on theoretical approaches to HTS investigation and perspectives of its applications combines the clearness of physical methods and strictness of modern mathematics, it is written at a high methodical level and could be useful for students, post-graduate students and their teachers specializing in physics of superconductivity and related scientific areas.

Chapter 2 presents the traditional theory for superconductivity in overdoped and possibly also optimally doped cuprates. It is demonstrated how the s-d exchange can be incorporated into the standard Bardeen-Cooper-Schrieffer (BCS) scheme and how the d-wave superconducting gap can derived. For the case of the s-d pairing the analytical solution is compared with the ARPES data. In Chapter 3, an explicit interpolation formula for the temperature dependence of the specific heat is obtained. This formula is exact for factorizable pairing kernels which are a consequence of the approximate separation in superconducting order parameters derived in BCS weak-coupling approximations by Pokrovskii for arbitrary weak coupling kernels and Gor’kov and Melik-Barkhudarov results for the Ginzburg-Landau (GL) coefficients of an anisotropic superconductor. Moreover, the recent results of Kogan for the penetration depth are presented and new formulas are proposed for the zero-scattering case which may be used for experimental data processing. The fourth chapter is devoted to the study of some electrodynamic properties of HTS such as plasmons and electric field effects giving access to the Cooper pair effective mass. Among the main results presented in the chapter are formulae for vortex charge and vortex conductivity, surface Hall currents for bulk crystals, interface Hall conductivity for type-I superconductors and thermal-induced contact-potential difference. Chapter 5 systematizes the known classical results for the GL Gaussian fluctuations to derive new ones and gives formulae that are necessary for the further development of the Gaussian spectroscopy of fluctuations. By using the \(\zeta\)-function method for UV regularization, the authors obtain general expressions for the fluctuations heat capacity and magnetization. Moreover, it is discussed how systematic investigations of the fluctuation phenomena can lead to a reliable determination of fundamental material parameters of HTS. The next chapter derives the Boltzmann equation for fluctuation Cooper pairs and illustrates its work on the example of the fluctuation conductivity. The authors re-derive the frequency dependence of the Aslamazov-Larkin conductivity fluctuation, Hall effect at weak magnetic fields and magnetoconductivity. The test data are analyzed for indium oxide films and significant deviation from the BCS weak coupling prediction is found. Chapter 7 studies the effect of fluctuations of the superconducting order parameter on linear and non-linear conductivity near and above the bulk superconducting critical temperature. On the base of the time-dependent generalization of the Ginzburg-Landau theory (TDGL) the kinetics of the order parameter are studied in a strong electric field in the framework of a simple phenomenological approach and new test methods for determining the life-time of fluctuation Cooper pairs and coherence length are stated. Chapter 8 considers the electric field fluctuations between the CuO2 layers and explains the linear temperature dependence of the resistivity. The authors’ model is based on the strong anisotropy of the electrical resistivity in layered cuprates. In Chapter 9 it is discussed how HTS can be used as generators of high frequency electric oscillations including the THz range. It is shown that the negative differential conductivity presents a new opportunity for generation of THz oscillations.

In total, this very interesting book on theoretical approaches to HTS investigation and perspectives of its applications combines the clearness of physical methods and strictness of modern mathematics, it is written at a high methodical level and could be useful for students, post-graduate students and their teachers specializing in physics of superconductivity and related scientific areas.

Reviewer: I. A. Parinov (Rostov-na-Donu)

### MSC:

82-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistical mechanics |

82D55 | Statistical mechanics of superconductors |