Competing orders in low dimensional organic superconductors

该研究计划将主要集中在基于弱耦合重整化群（RG）理论的理论工具的开发和应用上，该理论基本上是由准一维有机超导体上进行的实验刺激的。尽管它们的分子结构很复杂，但这些相关系统作为一个简单的范例脱颖而出，展示了反铁磁性和非常规超导性之间的紧密联系。我们将利用RG方法的适用性来研究与超导性相关的量子临界性的性质，在这种材料的压力-温度相图中的磁自旋密度波相位附近。RG方法将扩展到高阶，以研究量子临界周围的集体激发及其对超导之前的金属相的准粒子态的影响。特别强调的是准粒子激发的性质，它们的光谱特征，进入运输量的行为， 自从它们在非常规超导体包括磷属元素化物、铜酸盐和重费米子系统中被发现以来，所观察到的异常行为一直是一个持久的问题。 我们打算进一步发展RG方法的延迟电子玻色子相互作用的模型。电子-声子耦合实际上与量子临界的另一种范式有关，它在压力下的某些类准一维有机物和无机物的相图中引入了具有超导性的电荷密度波态。 我们将研究延迟的作用，在相互作用的量子临界性的发病和竞争秩序的影响，准粒子激发的性质在金属状态。 最后，我们将沿着将RG方法扩展到相互作用电子的晶格一维和准一维模型，而不是通常的连续统方法，后者在几个有文献记载的场合中未能捕获长距离相关的正确物理或有限能量下的正确光谱特性。

This research program will be mainly focused on the development and application of theoretical tools grounded on the weak coupling renormalization group (RG) theory, a plan essentially stimulated by experiments that are carried out on quasi-one-dimensional organic superconductors. In spite of their complex molecular structure, these correlated systems stand out as a paradigm of simplicity to exhibit a close proximity between antiferromagnetism and unconventional superconductivity. We shall exploit the aptness of the RG method to study the nature of quantum criticality associated with superconductivity in the close vicinity of a magnetic spin-density wave phase in the Pressure-Temperature phase diagram of such materials. The RG method will be extended to high order to investigate the collective excitations surrounding quantum criticality and their influence on quasi-particles states of the metallic phase that precedes superconductivity. Particular emphasis will be put on the nature of quasi-particle excitations, their spectral features that enter in the behavior of transport quantities, whose observed anomalous behaviors have remained an enduring question since their discovery in unconventional superconductors including pnictides, cuprates and heavy-fermion systems. We intend to further develop the RG method for models of retarded electron-boson interactions. Electron-phonon coupling is actually relevant for another paradigm of quantum criticality, which brings into interplay a charge-density-wave state with superconductivity in the phase diagram of some classes of quasi-1D organics and inorganics under pressure. We shall investigate the role of retardation in interactions for the onset of quantum criticality and the impact of competing orders on the nature of quasi-particle excitations in the metallic state. Finally, we shall go along with extending the RG method to lattice 1D and quasi-1D models of interacting electrons instead of the usual continuum approach, which fails in several documented occasions to capture either the correct physics of correlations at long distance or the correct spectral properties at finite energy.