**Author details**

Valerij A. Shklovskij *Institute of Theoretical Physics, NSC-KIPT, 61108 Kharkiv Physical Department, Kharkiv National University, 61077 Kharkiv, Ukraine*

Oleksandr V. Dobrovolskiy *Physikalisches Institut, Goethe-University, 60438 Frankfurt am Main, Germany*

### **6. References**

[1] L. V. Shubnikov, V. I. Khotkevich, Yu. D. Shepelev, and Yu. N. Ryabinin. Magnetic properties of superconductors and alloys. *Zh. Eksper. Teor. Fiz.*, 7:221–237, 1937.

[2] L. V. Shubnikov, V. I. Khotkevich, Yu. D. Shepelev, and Yu. N. Ryabinin. Magnetic properties of superconductors and alloys. *Ukr. J. Phys.*, 53:42–52, 2008.

22

**5.2. Extension of the theory for non-zero temperature**

to elucidate the physics in the problem under consideration.

*Institute of Theoretical Physics, NSC-KIPT, 61108 Kharkiv*

*Physical Department, Kharkiv National University, 61077 Kharkiv, Ukraine*

*Physikalisches Institut, Goethe-University, 60438 Frankfurt am Main, Germany*

**Acknowledgements**

Oleksandr V. Dobrovolskiy

**Author details** Valerij A. Shklovskij

**6. References**

(DFG) through Grant No. DO 1511/2-1.

Finally, let us compare the results presented in the chapter with the analogous but more general results obtained by the authors [25] on the basis of a stochastic model for arbitrary temperature *T* and densities *j*<sup>0</sup> and *j*1. In that work, the Langevin equation (1), supplemented with a thermofluctuation term, has been *exactly* solved for *γ* = 1 in terms of a matrix continued fraction [52] and, depending on the WPP's tilt caused by the dc current, two substantially different modes in the vortex motion have been predicted. In more detail, at low temperatures and relatively high frequencies in a *nontilted* pinning potential each pinned vortex is *confined* to its pinning potential well during the *ac* period. In the case of superimposed strong ac and dc driving currents a *running* state of the vortex may appear when it can visit several (or many) potential wells during the ac period. As a result, two branches of new findings have been elucidated [25, 27]. First, the influence of an ac current on the usual *E*0(*j*0) and ratchet *E*0(*j*1) CVCs has been analyzed. Second, the influence of a dc current on the ac nonlinear impedance response and nonlinear power absorption has been investigated. In particular, the appearance of Shapiro-like steps in the usual CVC and the appearance of phase-locking regions in the ratchet CVC has been predicted. At the same time, it has been shown that an anomalous power absorption in the ac response is expected at close-to critical currents *j*<sup>0</sup> *jc* and relatively low frequencies *ω ωp*. Figure 8 shows the main predictions of these works. Namely, predicted are (i) an enhanced power absorption at low frequencies, (ii) a temperature- and current-dependent minimum at intermediate frequencies. (iii) At substantially low temperatures, the absorption can acquire negative values which physically corresponds to the generation by vortices. However, a more general and formally precise solution of the problem in terms of a matrix-continued fraction does not allow the main physical results of the problem to be investigated in the form of explicit analytical functions of the main physical quantities (*j*0, *j*1, *ω*, *α*, *T*, *�*, and *γ*) which, we believe, has helped us greatly

The authors are very grateful to Michael Huth for useful comments and critical reading. O.V.D. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft

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**1. Introduction**

http://dx.doi.org/10.5772/46073

theories.

The discovery and further development of superconductivity is extremely interesting because of its pragmatic (practical) and purely academic reasons. At the same time, the superconductivity science is very remarkable as an important object for the study in the framework of the history and methodology of science, since all the details are well documented and well-known to the community because of numerous interviews by participants including main heroes of the research and the fierce race for higher critical temperatures of the superconducting transition, *Tc*. Moreover, the whole science has well-documented dates, starting from the epoch-making discovery of the superconducting transition by Heike Kamerlingh-Onnes in 1911 [1–7], although minor details of this and, unfortunately, certain subsequent discoveries in the field were obscured [8–11]. As an illustrative example of a senseless dispute on the priority, one can mention the controversy between the recognition of Bardeen-Cooper-Schrieffer (BCS) [12] and Bogoliubov [13]

**dc Josephson Current Between an Isotropic and** 

**Chapter 12**

**a d-Wave or Extended s-Wave Partially Gapped** 

**Charge Density Wave Superconductor** 

Alexander M. Gabovich, Suan Li Mai,

Henryk Szymczak and Alexander I. Voitenko

Additional information is available at the end of the chapter

If one looks beyond superconductivity, it is easy to find quite a number of controversies in different fields of science [14, 15]. Recent attempts [16–18] to contest and discredit the Nobel Committee decision on the discovery of graphene by Andre Geim and Kostya Novoselov [19, 20] are very typical. The reasons of a widespread disagreement concerning various scientific discoveries consist in a continuity of scientific research process and a tense competition between different groups, as happened at liquefying helium and other cryogenic gases [9, 21–24] and was reproduced in the course of studying graphite films [25, 26]. At the same time, the authors and the dates of major discoveries and predictions in the science of

Macroscopic manifestations of the superconducting state and diverse properties of the plethora of superconductors are consequences of main fundamental features: (i) zero

> ©2012 Gabovich et al., licensee InTech. This is an open access chapter 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

©2012 Gabovich et al., licensee InTech. This is a paper 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.

superconductivity are indisputable, fortunately to historians and teachers.

cited.
