Competing orders in low dimensional organic superconductors

这项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，该计划基本上是由在准一维有机超导体上进行的实验所激发的。尽管它们的分子结构复杂，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传统超导之间的密切联系。我们将利用RG方法的适宜性来研究与这类材料的压力-温度相图中的磁自旋密度波相邻近的超导电性有关的量子临界性质。RG方法将扩展到高阶，研究围绕量子临界性的集体激发及其对超导前金属相的准粒子态的影响。将特别强调准粒子激发的性质，它们的光谱特征进入输运量的行为，自从它们在非常规超导体中被发现以来，观察到的异常行为一直是一个持久的问题，包括硫化物、铜酸盐和重费米子系统。 我们打算进一步发展用于延迟电子-玻色子相互作用模型的RG方法。电子-声子耦合实际上与另一种量子临界性范式有关，该范式在某些类准一维有机物和压力下的无机物的相图中产生了具有超导电性的电荷密度波态。我们将研究延迟在量子临界性开始的相互作用中的作用，以及竞争序对金属态中准粒子激发性质的影响。 最后，我们将继续将RG方法扩展到相互作用电子的晶格1D和准1D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无法捕捉到长距离的正确关联物理或有限能量下的正确光谱性质。

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.