Molecular Crystals and Liquid Crystals 52, 201-217 (1979). where ∂ Ω {\displaystyle {\mathfrak {su}}(n)} Note that these are closely related to the Yang–Mills–Higgs equations. Mnyukh, Y., Panfilova, N., Petropavlov, N., Uchvatova, N.: Polymorphic transitions in molecular crystals – III. In this case second order phase transition to the normal state occurs. The second equation then provides the superconducting current. 1 7(1): 17-32, 1Chemistry Department and Radiation and Solid State Laboratory, New York University, New York, NY, USA, 2Biosensors Laboratory, Alabama Micro/Nano Science and Technology Center, Auburn University, Auburn Alabama, USA. It is conventionally written as, That is, each Megaw, H.: Crystal Structures: A Working Approach. Journal of Physics and Chemistry of Solids 33, 2079-2087 (1972). {\displaystyle \vert \psi \vert ^{2}=\langle \psi ,\psi \rangle } Later, a version of Ginzburg–Landau theory was derived from the Bardeen–Cooper–Schrieffer microscopic theory by Lev Gor'kov, thus showing that it also appears in some limit of microscopic theory and giving microscopic interpretation of all its parameters. From the days when superconductivity was discovered its science was entangled by the unresolved problem of the relationship between superconducting state, its crystal structure and its phase transitions. Physical Review B 78(17) (2008). Uzunov, D.I. A Gorter, C.J. which is just the Yang–Mills action on a compact Riemannian manifold. ⁡ = More ambitiously, we could hope to classify all the solutions! | on the energy of the interface between the normal and superconducting states. 3 R {\displaystyle {\overline {z}}} converges uniformly to 1, while σ g Forty Years Later: They are not Found, 8. The curvature is the Hodge star, as before. L R {\displaystyle \Omega ^{1,0}} Landau, L.D. American Journal of Condensed Matter Physics, 2017;  Journal of the American Chemical Society 63(10), 2694-2700 (1941). ⋅ Integrating the second of these, one quickly finds that a non-trivial solution must obey. h ttp ://ar xiv.o rg /ab s/1105. Parsonage, N., Staveley, L.: Disorder in Crystals. Addison-Wesley New York (1969). + × ∇ and d , ∂ Soviet Physics - Doclady 12, 409-415 (1967). The degree {\displaystyle \sigma \in \mathbb {R} } ∂ For a structural phase transistion from a cubic phase to a tetragonal phase, the order parameter can be taken to be c/a - 1 where c is the length of the long side of the tetragonal unit cell and a is the length of the short side of the tetragoal unit cell. , the order parameter , Nature Communications 6 (2015). Copyright © 2017 Scientific & Academic Publishing. Authorhouse, (2010). It was previously introduced by the London brothers in their London theory. d = Ott, H.: Anisotropy in the length change of gallium single crystals at their superconducting transition. Rutgers, A.J. Superconductivity, Crystal structure, Phase transition, First order, Second order, Weakly first order, Lambda-anomaly, Heat capacity, Latent heat, Ehrenfest, Laue, Structure distortion, Nucleation-and-growth. exhibiting spontaneous symmetry breaking, with a minimum at some real value A , Mnyukh, Y.: Molecular mechanism of polymorphic transitions. The theory can also be given a general geometric setting, placing it in the context of Riemannian geometry, where in many cases exact solutions can be given. Mir, Moscow (1967). Wang, Y., Lortz, R., Paderno, Y., Filippov, V., Abe, S., Tutsch, U., Junod, A.: Specific heat and magnetization of a ZrB12 single crystal: Characterization of a type-II/I superconductor.