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

TL;DR

This paper demonstrates that the lowest Landau level approximation remains valid over a wider range of magnetic fields in strongly type II superconductors than previously thought, due to symmetry-induced cancellations and smaller higher Landau level contributions.

Contribution

It provides a detailed calculation of higher Landau level effects and shows the extended validity of the LLL approximation in the mean field regime, including fluctuation effects.

Findings

Range of LLL validity extends down to H = Hc2/13

Higher Landau levels contribute less than expected

Lattice excitation spectrum is softer, enhancing fluctuations

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.