非常规超导体量子临界涨落研究

The physics of the unconventional superconductors, the heavy-fermion superconductors, the cuprate superconductors and the Fe-based superconductors, is one main subject in the field of the modern condensed matter. One universal similarity of these unconventional superconductors is that the superconducting phase is proximate to an antiferromagnetic phase, and the superconductivity stems from non-BCS mechanisms. Another universal similarity is that there are novel mother normal states for superconductivity, such as the strange metallic state and the pseudogap state in cuprate superconductors, the quantum critical states in heavy-fermion superconductors, and the electronic nematic state in Fe-based superconductors. There are two unsolved associated problems, how the transition from the antiferromagnetic phase into the superconducting phase go on at zero temperature, and what relations between the superconducting state and the novel mother normal states are. In this project, we propose that all of these unsolved problems are deeply correlated to the quantum antiferromagnetic and/or electronic nematic fluctuations. .In this project, we will firstly establish the effective theory for the quantum critical fluctuations, and then study the roles of the quantum fluctuations in the novel mother normal states and in the superconductivity in the unconventional superconductors. There are three research plans in this project. In the first plan, we will restudy the Hertz-Millis theory. This theory established for the itinerant ferromagnetic and antiferromagnetic quantum phase transitions is not successful for the realistic quantum phase transitions in such as the unconventional superconductors. Some special issues will be systematically investigated: i) whether the correlation between the spatial and temporal rescaling transformations is necessary and reasonable in any quantum phase transition; ii) how to preserve both the scale invariance and the unbroken symmetries near critical fixed points; iii) how to make physical choice of the initial action in the renormalization theory; iv) what modification of the statistics of the order-parameter fields and whether any novel excitations emerge at quantum critical points. In the second plan, we will study the quantum critical antiferromagnetic and/or nematic fluctuations in unconventional superconductors. Our main focus is on the roles of the interplay between these quantum fluctuations and the quasiparticles in the anomalous non-Fermi liquid properties of the novel mother normal states and in the formation of the superconductivity. In the third plan, we assume that the critical phenomena with scale invariance can be regarded as fractal physics. With this assumption we will provide effective phenomenological fractal models to investigate the essential physics in the critical phenomena. .There are two potential contributions of our project to the field of the condensed matter. One is to provide appropriate theoretical formalisms to study the mechanisms for the novel mother normal states and the superconductivity in unconventional superconductors. The other is to find out the essential phenomenological physics in the complex quantum phase transitions and criticalities.

重费米子超导体、铜基超导体和铁基超导体等非常规超导体是凝聚态强关联领域的一个重要研究课题。这些非常规超导体表现出一些普适的共性：它们的超导相均与反铁磁相临近；它们都存在反常的超导母体态。这些普适共性背后涉及两个基本问题：一是反铁磁相和超导相之间的零温过渡是如何实现的；二是超导态和反常母体态的关系是怎样的。在本项目中，我们假设反铁磁涨落和电子向列型涨落等量子涨落与这些问题密切相关，并将基于量子相变思想，研究非常规超导体量子临界涨落物理。我们的研究计划主要包括，在重新审视Hertz-Millis量子相变理论基础之上，发展描述量子临界涨落的有效理论，并将之应用于研究非常规超导体超导母体态的反常物理（特别是非费米液体行为），以及超导态从这些反常母体态产生的微观机制。我们的研究有两个方面的意义，一是为理解非常规超导体物理提供理论支持，另一个是为建立普适量子相变与临界涨落理论探索正确的物理图像。

非常规超导体等强关联电子系统所展现出的非平凡反常物理，是多年来凝聚态领域的一个重要研究课题之一。本项目在重新审视Landau-Ginzburg-Wilson经典相变理论和Hertz-Millis量子相变理论基础之上，探索和发展描述非常规超导体非平凡反常物理的理论方法和实验技术。在本项目资助下，我们在该方面获得了一些有趣而有益的进展。一、我们重新审视了超越传统Landau序参量的复合粒子思想。基于复合粒子思想，我们进行了如下工作。(a)我们发展了一个直接测量复合粒子相关的本征两体关联的符合测量理论。这是首个为实现直接测量强关联电子系统本征多体关联而发展的符合测量理论；它将为研究非常规超导电性、巡游磁矩、电子向列性、量子自旋液体等带来新的实验方法和技术。(b)我们提出了一个two-step重整化方法，用于统一描述超导Cooper对内部自由度和质心自由度物理。该方法将为我们系统研究超导Cooper对内部自由度对宏观超导物理和超导量子相变的影响，提供一个基本的理论工具。目前该方法正在完善中。二、我们提出了一个超越Landau费米液体的广义思想：通过对Landau费米液体的电子自由度施加约束，可以得到破缺Landau费米液体的非常规反常物理。这一思想为理解和操控实现超越Landau费米液体新物理，提供了一个统一的指导原则。这些研究结果为非常规超导体等强关联电子系统领域带来了一些新的思想和技术。同时，我们的研究工作还开拓了三个研究方向：一、强关联电子系统本征多体关联的直接符合测量理论和技术研究；二、复合粒子内部自由度对质心自由度及相关相变物理的影响；三、从自由度约束视角，研究和寻找超越Landau费米液体新物理。