Elasticity-driven interaction between vortices in type-II superconductors

The contribution to the vortex lattice energy which is due to the vortex-induced strains is calculated covering all the magnetic field range which defines the vortex state. This contribution is compared with previously reported ones what shows that, in the most part of the vortex state, it has been notably underestimated until now. The reason of such underestimation is the assumption that only the vortex cores induce strains. In contrast to what is generally assumed, both core and non-core regions are important sources of strains in high-$\kappa$ superconductors.Comment: 10 pages, 1 figure, revtex

Universal mechanism of discontinuity of commensurate-incommensurate transitions in three-dimensional solids: Strain dependence of soliton self-energy

We show that there exists a universal mechanism of long-range soliton attraction in three-dimensional solids and, therefore, of discontinuity of any commensurate-incommensurate (C-IC) phase transition. This mechanism is due to the strain dependence of the soliton self-energy and specific features of the solid-state elasticity. The role of this mechanism is studied in detail for a class of C-IC transitions where the IC modulation is one-dimensional, the anisotropy in the order parameter space is small, and the symmetry of the systems allows the existence of the Lifshitz invariant. Two other mechanisms of soliton attraction are operative here but the universal mechanism considered in this paper is found to be the most important one in some cases. Comparison with the most extensively studied C-IC transition in $\rm K_2SeO_4$ shows that the experimentally observed thermal anomalies can be understood as a result of the smearing of the theoretically predicted discontinuous transition.Comment: 8 pages (extended version, title changed

Loss of elastic stability and formation of inhomogeneous states at phase transitions in thin films on substrates

Within the Landau-like approach we study stability of homogeneous states near phase transitions in thin films on substrates. The order parameter is electrically neutral in order to exclude the effects of the depolarizing fields and concentrate on the elasticity effects. We consider the case where the first-order transition in free crystal would convert into a second order when in the film on a substrate if the system remained homogeneous. Limit of stability of the homogeneous state is found analytically. Numerical simulations show that inhomogeneity arises somewhat before the limit of stability is reached

Elastic anomalies at structural phase transitions : a consistent perturbation theory. I. One component order parameter

The perturbation theory of elastic anomalies near structural phase transitions is revisited. It is shown that expressions more often used to interpret ultrasonic attenuation anomalies are not correct, particularly below the phase transition temperature $T_{\rm c}$. A consistent perturbation theory is worked out and it is shown that the sound wave attenuation coefficient takes a form less simple in the general case than that usually assumed. The explicit results for the temperature and frequency dependence of the sound attenuation coefficient are given for two extreme cases : order-disorder systems and displacive systems. It is found that for the order-disorder transitions, which are not too far from the tricritical point the main part of the sound attenuation anomaly can be described by the Landau-Khalatnikov (LK) formula with the order parameter exhibiting a nonmean field behaviour. For displacive transitions for both LK and fluctuation, contributions have the same temperature dependence and the same order of magnitude within the perturbative region. As a result the low frequency sound attenuation coefficient has the same “critical index” for the two phases but different “critical amplitudes”, the ratio of the amplitudes A_{T<T_{\rm c}}/A_{T>T_{\rm c}} going to zero when the tricritical point is approached. At tricritical phase transition the “critical index” in the low-temperature phase is different from that in the high-temperature one.La théorie perturbative des anomalies élastiques près des transitions de phase structurales est réexaminée. On montre que les expressions utilisées le plus souvent pour interpréter les anomalies ultrasonores ne sont pas correctes, en particulier en dessous de la température de transition de phase $T_{\rm c}$. Une théorie de perturbation auto-cohérente est établie et on montre que l'atténuation du son est donnée par une expression beaucoup moins simple que celle utilisée d'habitude. Les résultats explicites quant à la dépendance de l'atténuation ultrasonore en fonction de la température et de la fréquence, sont donnés pour les deux cas extrêmes suivants : systèmes ordre-désordre et systèmes displacifs. Pour les transitions ordre-désordre, qui ne se produisent pas trop loin du point tricritique, l'atténuation est décrite par le formule de Landau-Khalatnikov (LK) où l'expression du paramètre d'ordre n'est pas donnée par la théorie du champ moyen. Pour les transitions displactives, la partie de type LK et celle due aux fluctuations ont la même dépendance en température (dans la région où le calcul de perturbations est valable). En conséquence l'atténuation basse fréquence a le même indice critique pour les deux phases, mais des amplitudes critiques différentes. Le rapport de ces amplitudes ({A_{T<T_{\rm c}}})/({A_{T>T_{\rm c}}}) tend vers zéro au point tricritique. En ce point les indices critiques ne sont plus égaux entre eux

Loss of elastic stability and formation of inhomogeneous states at phase transitions in thin films on substrates

Within the Landau-like approach we study stability of homogeneous states near phase transitions in thin films on substrates. The order parameter is electrically neutral in order to exclude the effects of the depolarizing fields and concentrate on the elasticity effects. We consider the case where the first-order transition in free crystal would convert into a second order when in the film on a substrate if the system remained homogeneous. Limit of stability of the homogeneous state is found analytically, though approximately. Numerical simulations provide qualitatively similar results and reveal temperature evolution of the arising inhomogeneities

Negative bulk modulus and possibility of loss of elastic stability near tricritical transitions in thin films on substrates

Within the Landau-like approach we study anomalies of elastic moduli at phase transitions in thin films on substrates. We consider the case where, similar to many experimental cases, the first-order transition in free crystal would convert into a second order in the film if the system remained homogeneous. It is shown, however, that apart from its questionable thermodynamic advantages, the homogeneous state of low-symmetry phase may become absolutely unstable which is signaled by changing of sign of its bulk modulus