When magnetic flux penetrates a type-Ⅱ superconductor, it does so as quantized flux lines or vortex lines, so called because each is surrounded by a supercurrent vortex. Interactions between such vortices lead to a very rich and well characterized phenomenology for this 'mixed state'. But an outstanding question remains: are individual vortex lines 'strong', or can they easily be cut and made to pass through one another? The concept of vortex cutting was originally proposed to account for dissipation observed in superconducting wires oriented parallel to an applied magnetic field, where the vortex lines and transport current should be in a force-free configuration. Previous experiments, however, have been unable to establish the vortex topology in the force-free configuration or the size of the energy barrier for vortex cutting. Here we report magneto-optical images of YBa_2Cu_3O_(7-δ) samples in the force-free configuration which show that thousands of vortex lines can twist together to form highly stable structures. In some cases, these 'vortex twisters' interact with one another to produce wave-like dynamics. Our measurements also determine directly the current required to initiate vortex cutting, and show that it is much higher than that needed to overcome the pinning of vortices by material defects. This implies that thermodynamic phases of entangled vortices are intrinsically stable and may occupy a significant portion of the mixed-state phase diagram for type-Ⅱ superconductors.
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