LOFF态是在中等重子数密度下被提出作为夸克物质基态的候选者中的一种。其它候选者包 括同色磁不稳定性相关的均匀的无能隙超导态（g2SC或者gCFL），还有多种不具有费米能不相等的BCS相混合状态和正常态。其中LOFF态产生一个库珀对需要的自由能很低，被认为是中等密度色超导基态的强力候补。零温下LOFF态可存在的条件下所有的磁极化张量都是非零的，也就意味着同无能隙态相关的色磁不稳定性消失了。考虑到中子星内部条件，本项目将对两味LOFF色超导中的迈斯纳效应讨论扩展到非零温和色电中性约束条件。本项目的另一关注点为拓扑半金属这一当今物理学界热点问题，探讨格点模型下手征磁效应在Weyl半金属中是否存在。

LOFF（Larkin-Ovchinnikov-Fudde-Ferrell）state is one of the several states that were proposed as a possible ground states for quark matter at moderately high baryon density. Others include the homogeneous gapless states(g2SC or gCFL) which are associated with a chromomagnetic instability and the heterogeneous mixture of BCS states with Fermi sea displacement and normal phases. It is shown that at zero temperature, all the eigenvalues of the magnetic polarization tensor in LOFF are non-negative, therefore the chromomagnetic instability pertaining to gapless states disappear. We will investigate the Meissner effect in a two flavor LOFF color superconductor at a non-zero temperature and under the charge neutrality constraint.Integrates with the topological semimetal which have attracted considerable attention in condensed matter physics，the progect will investigate if the chiral magnetic effect exists in Weyl semimetal.