Nobel Lecture: Type-II superconductors and the vortex lattice

In 1950 Vitaly Ginzburg and Lev Landau published their famous paper on the theory of superconductivity sGinzburg and Landau, 1950d. The approach was based on the general theory of the second-order phase transitions proposed by Landau in 1937 sLandau, 1937d. There Landau introduced the main variable, the so-called order parameter, which was finite below the transition and zero above it. Different phase transitions had different order parameters, and whereas it was evident for, e.g., the ferromagnetic transitions, namely, the spontaneous magnetization, it was far less evident for the superconducting transitions. Ginzburg and Landu had a stroke of genius when they chose, as the order parameter, some sort of wave function. At that time nobody knew about Cooper pairs or about their Bose condensates, where all particles become coherent, i.e., described by the same wave function. This assumption was the basis of the new theory, which managed to solve the main contradiction of the old theory by Fritz and Heinz London s1935d, namely, the positive surface energy. Besides, it made many useful predictions, such as the critical magnetic field of thin films, the critical current in thin wires, etc. All these predictions required experimental verification, and my friend and University mate, Nikolay Zavaritskii, started to measure the critical field of thin films. Theory and experiment fitted perfectly, including the change of the nature of the transition: first order at larger thicknesses and second order at smaller ones. Everything seemed OK but Alexander Shalnikov, Zavaritskii’s boss, was not satisfied. He said that the films used by Zavaritskii were bad, since they were prepared at room temperature. The atoms of the metal, evaporated on a glass substrate, could agglomerate, and therefore the film actually consisted of small droplets. In order to avoid that, Shalnikov recommended maintaining the glass substrate at helium temperatures during evaporation and until the measurements were finished. Then every metal atom hitting the surface would stick to its place, and the film would be homogeneous. Zavaritskii followed this advice, and the result was a surprise: the dependence of the critical field on the thickness, or temperature sthe theory contains the ratio of the thickness to the penetration depth, which depends on temperatured, did not fit the predictions of the Ginzburg-Landau theory. Discussing these results with Zavaritskii, we could not believe that the theory was wrong: it was so beautiful and fitted so well the previous data. Therefore, we tried to find some solution in the framework of the theory itself, and we found it. The equations of the theory, where all entering quantities were expressed in corresponding units, depended only on one dimensionless “material” constant k, which was later called the Ginzburg-Landau parameter. The value of k could be defined from the surface energy between the normal and superconducting phases. The latter, in its turn, could be calculated from the period of the structure of the intermediate state. These data for conventional superconductors led to very small values of k, and therefore the calculations in the paper by Ginzburg and Landau were done for this limiting case. It was also established that with increasing value of k the surface energy between the superconducting and normal layers would become negative, and since this contradicted the existence of the intermediate state, such a case was not considered. Therefore I decided to look at what would happen if k.1/I2, when the surface energy became negative. The transition in this case became second order for any thickness. The theory fitted completely Zavaritskii’s experimental data, and this led us to the conclusion that there exists a special kind of superconductor, which we called “superconductors of the second group,” with k.1/I2 and negative surface energy. Now they are called type-II superconductors. I published my derivation in the Russian journal Doklady Akademii Nauk SSSR in 1952 sAbrikosov, 1952d. This was the earliest introduction of type-II superconductors. Since, however, this journal was never translated into English, there is a considerable confusion on this point, and the most common is just a statement that “there exist two types of superconductors... .” In Russia the idea of type-II superconductors raised no objections, although such materials were considered as exotic. In this connection it is worthwhile to mention that virtually all new superconducting compounds, discovered since the early 1960s up to the present time, are type-II superconductors. They include organics, A-15, Chevrel phaes, heavy fermionic materials, fullerenes, and high-temperature superconductors. One could say that now type-I superconductors have become exotic. After the work on films I decided to look at the magnetic properties of bulk type-II superconductors. It was definite that the transition to the normal state in a mag*The 2003 Nobel Prize in Physics was shared by A. A. Abrikosov, Vitaly L. Ginzburg, and Anthony J. Leggett. This lecture is the text of Dr. Abrikosov’s address on the occasion of the award. REVIEWS OF MODERN PHYSICS, VOLUME 76, JULY 2004