Quantum effects of vortex in type-II superconductors

The vortex energy of type-II superconductors in mixed state is discussed based on the assumption that vortex can undergo quantum effect. The Hamiltonian of an isolated vortex of type-II superconductors in lower magnetic fields is calculated from the elasticity of vortex within the framework of weak collective pinning theory. The results indicate that the vortex can be described using the eigenvalue of a harmonic oscillator and the eigenvalue of the vortex energy can be reduced by the action of Lorentz force of the current acting on the vortex. The quantum effects of vortices in higher magnetic fields are also studied and two particular directions of the dispersion models of the two-dimension triangular vortex lattice are given.