Why the lowest Landau level approximation works in strongly type II superconductors

Abstract

Higher than the lowest Landau level contributions to magnetization and specific heat of superconductors are calculated using Ginzburg - Landau equations approach. Corrections to the excitation spectrum around solution of these equations (treated perturbatively) are found. Due to symmetries of the problem leading to numerous cancellations the range of validity of the LLL approximation in mean field is much wider then a naive range and extends all the way down to $H=H_{c2}(T)/13$. Moreover the contribution of higher Landau levels is significantly smaller compared to LLL than expected naively. We show that like the LLL part the lattice excitation spectrum at small quasimomenta is softer than that of usual acoustic phonons. This enhanses the effect of fluctuations. The mean field calculation extends to third order, while the fluctuation contribution due to HLL is to one loop. This complements the earlier calculation of the LLL part to two loop order.

arXiv comment20 pages, Latex file, three figures

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• Structure and Orientation of the Moving Vortex Lattice in Clean Type II Superconductors
• Supercooled vortex liquid and quantitative theory of melting of the flux line lattice in type II superconductors
• Precision calculation of magnetization and specific heat of vortex liquids and solids in type II superconductors
• Covariant gaussian approximation in Ginzburg - Landau model
• Improved perturbation theory in the vortex liquids state of type II superconductors
• Study of diamagnetic fluctuations in YBa_2Cu_3O_{7-x} and Bi_2Sr_2CaCu_2O_{8+x}: Possible observation of phase correlations persisting above T_c
• Thermal fluctuations and disorder effects in vortex lattices
• Flux-lattice melting in two-dimensional disordered superconductors
• An effective lowest Landau level treatment of demagnetization in superconducting mesoscopic disks
• High-frequency dynamical response of Abrikosov vortex lattice in flux-flow region