Theoretical search for quantum intermediate phases in condensed matters

在这个研究项目中，我们从理论上研究了一对量子凝聚态系统，其中可能包含一种低温下的量子中间态。我们选择的主题如下：1)从理论上确定气凝胶中超流氦-3的类A相，2)研究无序颗粒超导体中量子金属相(玻色金属相)的可能性，3)了解涨落对正常相和FFLO相之间相变的影响。在1)受最近气凝胶中液态氦-3的实验事实的启发，我们研究了气凝胶中准粒子的随机散射事件如何影响A相中的配对对称性和超流长程有序。通过基于常规微观分析的自由能计算表明，只要气凝胶没有全局各向异性，大块A相的ABM配对态不受气凝胶的影响，并且…更重要的是，只要无序足够弱，产生的类A相就是具有准长程超流有序的超流-玻璃。这些研究结果发表在《物理评论》上的两篇论文中。在2)中，受颗粒系统特有的零温度玻璃相中电阻率有限的提议的启发，我们研究了无序颗粒超导体中存在量子金属相的可能性。我们的结论在这方面是否定的：我们发现颗粒系统玻璃相的电阻率为零，这与在这个问题上的传统看法是一致的。在3)中，讨论了重费米子超导体CeCoIn5中正常态和FFLO态之间一阶跃迁行为的起源。我们已经在确凿的证据上证明，法线到FFLO跃迁的不连续性质是平均场性质的，而不是由于临界涨落。较少

In this research project, we have theoretically studied a couple of quantum condensed matter systems which may include a kind of quantum intermediate state at low temperatures. The subjects we have chosen are in the following ;1)Identifying theoretically the A-like phase of superfluid Helium-three in aerogel,2)Examining a possibility of a quantum metallic phase (Bose-metal) in disordered granular superconductors,3)Understanding effects of fluctuation on the phase transition between the normal and FFLO phases.In 1),motivated by recent experimental facts on liquid Helium-three in aerogels, we have examined how the pairing symmetry and the superfluid long range order in the A-phase are affected by the random scattering events of quasiparticles provided by the aerogel. Through free energy calculations based on the conventional microscopic analysis, we have shown that, as far as the aerogel has no global anisotropy, the ABM pairing state of the bulk A-phase is unaffected by the aerogel, and … More that, as far as the disorder is weak enough, the resulting A-like phase is a superfluid-glass with quasi long-ranged superfluid order. These research results were reported in two papers published in the Physical Review.In 2),inspired by a proposal that the resisitvity remains finite in a glass phase at zero temperature peculiar to the granular systems, we have examined a possibility of a quantum metallic phase in disordered granular superconductors. Our conclusion is negative on this respect : We find that the resistivity in the glass phase of granular systems is zero in agreement with the conventional wisdom on this issue. Due to this conclusion, no reliable theory favoring the presence of a quantum bole - metal phase is present.In 3),an origin of the first - order transition behavior between the normal and the FFLO state in the heavy-fermion superconductor CeCoIn5 was discussed. We have shown on a firm evidence that the discontinuous nature of the normal to FFLO transition is of the mean-field character and not due to the critical fluctuation. Less