ON SINE-GORDON VORTICES IN HIGH-TEMPERATURE SUPERCONDUCTORS

摘要

In this paper we considered vortex states in high-temperature superconductors. Multilayered systems of superconducing planes coupled by Josephson effect are realised in the high-temperature superconductors. Layered superconductors of the high temperature type are coupled due to intrinsic Josephson effect. The Lawrence -Doniach free energy functional describes the order parameters in all layers, in the n-th layer the order parameter is dependent on the two-dimesional position R = (r, z).r 1 is the Josephson coupling constant between neighbouring layers. The coherence length in the c-direction and the penetration depths define the anisotropy ratio. We assume that the interlayer coupling is weak, ζ_c s, and this corresponds with layered materials in which the in-plane distance is shorter than the inter-layer distance. We assume further that the constant amplitude approximation | ψ |~2= 1 holds and, when temprature is near the transition temperature the amplitude has the form |ψ |~2= |α|/β, where the Φ_n(r) is the phase of the order parameter. Lawrence-Doniach functional for the order parameter leads to a set of coupled sine-Gordon equations for difference of phases in the neighbouring planes. The inductance coupling between planes exponentially decreases. Thus we consider firstly ground state and other order parameter configurations of the in-layer type. An homogeneous state with a vortex of the same type and position in every layer is one type of the state. In this case the order parameter phases are either the same either differing by π. The gauge invariant difference of phases between neighbouring planes is found of the soliton and vortex type /single, dipole, lattice/. Coupling between planes leads to coupling of these solitons and vortices. The interlayer Josephson current has its corresponding forms, which may be easily found. The mutual interlayer inductance for nearest neighbouring planes is a small parameter which leads to renormalized coupling of solitons and vorices in neighbouring planes. The boundary conditions for the Lagrange -Euler equations are known.