Semi-Meissner state and neither type-I nor type-II superconductivity in multicomponent superconductors

Abstract

Traditionally, superconductors are categorized as type-I or type-II. Type-I superconductors support only Meissner and normal states, while type-II superconductors form magnetic vortices in sufficiently strong applied magnetic fields. Recently there has been much interest in superconducting systems with several species of condensates, in fields ranging from Condensed Matter to High Energy Physics. Here we show that the type-I/type-II classification is insufficient for such multicomponent superconductors. We obtain solutions representing thermodynamically stable vortices with properties falling outside the usual type-I/type-II dichotomy, in that they have the following features: (i) Pippard electrodynamics, (ii) interaction potential with long-range attractive and shortrange repulsive parts, (iii) for an n-quantum vortex, a non-monotonic ratio E(n)/n where E(n) is the energy per unit length, (iv) energetic preference for non-axisymmetric vortex states, "vortex molecules". Consequently, these superconductors exhibit an emerging first order transition into a "semi-Meissner" state, an inhomogeneous state comprising a mixture of domains of two-component Meissner state and vortex clusters.The formation of vortices in type-II superconductors subjected to a magnetic field is one of the most remarkable phenomena occuring in condensed matter. In all type-II superconductors (i.e. superconductors where the GL parameter, which is the ratio of the magentic field penetration length to the coherence lenth, is κ > 1/ √ 2 [1]) these vortices share a set of properties: an n-quantum vortex is unstable with respect to decay into n onequantum vortices, two vortices have purely repulsive interaction, and invasion of vortices under normal conditions is a second order phase transition characterised by a critical value of the external magnetic field H c1 .Vortices as solutions of the GL equations also exist formally in a type-I superconductor (κ < 1/ √ 2), but these vortices are thermodynamically unstable. The special case κ = 1/ √ 2 is also very interesting since, at this value of κ, vortices do not interact [2,3]. One should note, however, that in real life systems the situation is more complicated; experiments [4] show that in certain materials with κ ≈ 1/ √ 2 there might exist a tiny attractive force between vortices at a certain distance. Such an interaction was reproduced in a modified one-component GL model with additional terms in the regime κ ≈ 1/ √ 2 [5]. We should also mention a long range van der Waals -type vortex attraction in layered systems produced by thermal fluctuations or disorder [6].Besides superconductivity, the vortex concept has a direct counterpart in High Energy Physics, called the Nielsen-Olesen string. Such strings have been considered in cosmology [7] where they are expected to form during a symmetry breaking phase transition in the early universe. There also exists a similar type-I/type-II division of semilocal cosmic strings in the Higgs doublet model [8].Recently, multicomponent superconducting systems hav...

Simulation of the phase diagram of magnetic vortices in two-dimensional superconductors: evidence for vortex chain formation

“…Also, for anisotropic superconductors, the theoretical calculation and analysis based on London theory and LowrenceDoniach theory has been shown that multiquanta vortex lattices will occur through changing titling angles of magnetic fields (equivalent to changing the value of q in this simulation) [25]. This suggests that our model is useful to study the vortex states for both low-κ type II superconductors and anisotropic superconductors, in addition to multiband or multicomponent superconductors [12].…”

“…Although large amount of experimental and theoretical efforts in this field has been made [10][11][12][13][14][15][16][17][18], the nature of the vortex clustering in multiband superconductors is still an intensely controversial issue now [17,[19][20][21][22]. In principle, the vortex cluster formation means that there might exist some type of attraction between vortices in addition to repulsion.…”

“…Besides, for layered superconductors, the intervortex attractions can also be induced by thermal fluctuations [29,30], or impurities [31]. (V) For multiband or multicomponent superconductors, the intervortex interaction is determined by the competition between the multiple fundamental length scales in GL theory [12,16,19]: leads to attractive interaction at a long range; yet the repulsive interaction is still dominating at a short range due to intercurrent and electromagnetic interaction. However, numerical simulations reveal that the nonmonotonic interaction potential with long-range attraction will result in the bubble-like rather than stripe-like vortex ground state [32].…”

Unconventional interaction between vortices in a polarized Fermi gas

“…It is worth mentioning that a non-monotonous interaction potential between vortices (albeit without oscillating character) has recently been found in multicomponent superconductors by Babaev and Speight. [51] The authors have also predicted the existence of exotic (non-triangular) vortex-lattice structures.…”

Composite Structures of d-Wave and s-Wave Superconductors (d-Dot): Analysis Using Two-Component Ginzburg-Landau Equations

“…heavy fermion superconductors [16][17][18] and Sr2RuO4 [19,20]. Also, recently, two components GL equations are studied for two-band or two-gap superconductors, such as MgB2 [21,22]. …”