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Register a new userCasimir Force between two Half Spaces of Vortex Matter in Anisotropic Superconductors
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We present a new approach to calculate the attractive long-range vortex-vortex interaction of the van der Waals type present in anisotropic and layered superconductors. The mapping of the statistical mechanics of two-dimensional charged bosons allows us to define a Casimir problem: Two half spaces of vortex matter separated by a gap of width R are mapped to two dielectric half planes of charged bosons interacting via a massive gauge field. We determine the attractive Casimir force between the two half planes and show that it agrees with the pairwise summation of the van der Waals force between vortices.
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High-T_c superconductors in small magnetic fields directed away from the crystal symmetry axes have been found to exhibit inhomogeneous chains of flux lines (vortices), in contrast to the usual regular triangular flux-line lattice. We review the experimental observations of these chains, and summarize the theoretical background that explains their appearance. We treat separately two classes of chains: those that appear in superconductors with moderate anisotropy due to an attractive part of the interaction between tilted flux lines, and those with high anisotropy where the tilted magnetic flux is created by two independent and perpendicular crossing lattices. In the second case it is the indirect attraction between a flux line along the layers (Josephson vortex) and a flux line perpendicular to the layers (pancake vortex stack) that leads to the formation of chains of the pancake vortex stacks. This complex system contains a rich variety of phenomena, with several different equilibrium phases, and an extraordinary dynamic interplay between the two sets of crossing vortices. We compare the theoretical predictions of these phenomena with the experimental observations made to date. We also contrast the different techniques used to make these observations. While it is clear that this system forms a wonderful playground for probing the formation of structures with competing interactions, we conclude that there are important practical implications of the vortex chains that appear in highly anisotropic superconductors.
Here we use highly sensitive magnetisation measurements performed using a Hall probe sensor on single crystals of highly anisotropic high temperature superconductors $Bi_{2}Sr_{2}CaCu_{2}O_{8}$ to study the dynamic interactions between the two species of vortices that exist in such superconductors. We observe a remarkable and clearly delineated high temperature regime that mirrors the underlying vortex phase diagram. Our results map out the parameter space over which these dynamic interaction processes can be used to create vortex ratchets, pumps and other fluxonic devices.
Several experimental demonstrations of the Casimir force between two closely spaced bodies have been realized over the past two decades. Extending the theory to incorporate the behavior of the force between two superconducting films close to their transition temperature has resulted in competing predictions. To date, no experiment exists that can test these theories, partly due to the difficulty in aligning two superconductors in close proximity, while still allowing for a temperature-independent readout of the arising force between them. Here we present an on-chip platform based on an optomechanical cavity in combination with a grounded superconducting capacitor, which overcomes these challenges and opens up the possibility to probe modifications to the Casimir effect between two closely spaced, freestanding superconductors as they transition into a superconducting state. We also perform preliminary force measurements that demonstrate the capability of these devices to probe the interplay between two widely measured quantum effects: Casimir forces and superconductivity.
We report the direct imaging of a novel modulated flux striped domain phase in a nearly twin-free YBCO crystal. These domains arise from instabilities in the vortex structure within a narrow region of tilted magnetic fields at small angles from the in-plane direction. By comparing the experimental and theoretically derived vortex phase diagrams we infer that the stripe domains emerge from a first order phase transition of the vortex structure. The size of domains containing vortices of certain orientations is controlled by the balance between the vortex stray field energy and the positive energy of the domain boundaries. Our results confirm the existence of the kinked vortex chain phase in an anisotropic high temperature superconductor and reveal a sharp transition in the state of this phase resulting in regular vortex domains.
A simple variational model is proposed to analyze the superconducting state in long cylindrical type-II superconductor placed in the external magnetic field. In the framework of this model, it is possible to solve the Ginzburg-Landau equations for the states with axially symmetric distributions of the order parameter. Phase transitions between different superconducting states are studied in the presence of external magnetic field and an equilibrium phase diagram of thin cylinder is obtained. The lower critical field of the cylindrical type-II superconductor with arbitrary values of radius and Ginzburg-Landau parameter is found. The field dependence of the magnetization of thin cylinder, which can carry several magnetic flux quanta, is calculated.
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