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Flux Pinning
Published in David A. Cardwell, David C. Larbalestier, I. Braginski Aleksander, Handbook of Superconductivity, 2023
Kees van der Beek, Peter H. Kes
In superconductors with very weak bulk pinning, the vortex Bragg glass phase transforms to the vortex liquid through a first-order transition, often denoted “vortex lattice melting” (Brezin, Nelson, and Thiaville 1985, Brandt 1989, Zeldov et al. 1995). The transition to the liquid state is driven by the excess entropy of the latter; as a result, the liquid has a higher vortex density than the Bragg glass. On the contrary, upon cooling the Bragg glass is stabilised through the gain in elastic deformation energy associated with the arrangement of vortices into a regular array. The first-order melting transition is hysteretic, with the vortex liquid showing supercooling. The transition is enabled by thermal fluctuations of vortex segments (or kinks) around their equilibrium positions, until at the transition, plastic barriers of height Uc can be overcome (Fendrich et al. 1995, López et al. 1997). At that point, thermal cutting and reconnection leads to the demise of the “identity” of vortices, and to entanglement in the vortex liquid state( López et al 1996). The first-order transition has often been described by a Lindemann criterion: the vortex lattice “melts” when the thermal displacements become larger than a fraction cLa0 of the inter-vortex spacing (Brandt 1989). Here cL is the Lindemann constant, cL≈0.2. This criterion, which is tantamount to a modified Ginzburg criterion for superconducting fluctuations, gives rise to a transition line in the (T,B) phase diagram which, for conventional superconductors, is located near the upper critical field Hc2(T). For layered superconductors such as Bi2Sr2CaCu2O8+δ, the transition lies at fields below 1 T.
Studies of de Vries SmA* type phase in chiral thiobenzoates
Published in Phase Transitions, 2023
Janusz Chruściel, Arkadiusz Rudzki, Mirosława D. Ossowska-Chruściel, Sławomir Zalewski
Smectic phases, such as SmA, in which the rod-like molecules are characterized by a layered structure and the mesogens are oriented with their long axes perpendicular to the layer plane, constitute the most basic structure of the layer. In an ideal arrangement of the molecules, the length of the molecules l should be equal to the thickness of layer d. However, it has been found that in the orthogonal phase of SmA, the thickness of the layer is approximately 1.7 Å smaller than the length of the molecules in the all-trans conformation [1]. The SmA liquid crystal phase is usually considered as system where the molecules are packed in two-dimensional layers in which the molecular director n is parallel to the layers normal. Decreasing the temperature may cause the transition to smectic C (SmC) phase, where the molecular direction is tilted. A model proposed by de Gennes suggests that the SmA–SmC and SmA*–SmC* phase transition belong to the 3D XY universality class [2]. Later experimental results on the SmA*–SmCα* (or SmC*) were described by the Landau theory (e.g. [3,4]) or using the Ginzburg criterion [5]. The SmA*–SmCα* phase transition shows a very deviation from the Landau mean-field theory [6] or is incompatible with the Landau model [7]. The SmCα* phase as subphase, the intermediate phase between the paraelectric SmA* and the ferroelectric SmC* phases was observed for the first time in MHPOBC [8]. Paragraph: use this for the first paragraph in a section, or to continue after an extract.