Superconductivity and Pseudogap Near Quantum Critical Points

该奖项是对量子临界点（QCP）附近系统行为的理论研究，在该点上，巡回费米子系统变得不稳定，相对于结构不稳定性，或者自旋或电荷密度波。 在所有这些情况下，量子跃迁都伴随着玻色子模式的软化。 主要研究者（PI）将研究玻色子模式为独立自由度的病例（例如，用于结构转变的声子模式），或者当它是费米子的集体模式并且其动力学由低能费米子产生时。 PI计划详细分析QCP附近系统行为的三个方面：（i）玻色子软化对费米传播子的影响-在许多情况下，这会导致临界状态下完全不相干的非费米液体行为;（ii）QCP处的配对不稳定性-这种配对如果发生，会在QCP顶部创建一个圆顶，在其下方临界行为会由于反馈效应而发生变化;（三）在何种条件下，长序（玻色子不稳定性的结果）和超导性共存，并且当它们被中间赝能隙相分离时，其中只有离散晶格对称性被破坏。从理论的角度来看，对这些问题的主要兴趣是由于QCP附近的配对问题是完全新颖的并且与BCS-Eliashberg理论有质的不同，因为它涉及通过交换无隙玻色子激发而相互作用的完全不相干的扩散费米子。 从实验的角度来看，拟议的研究旨在解释的起源的赝隙相位检测在多个实验测量欠掺杂的铜氧化物，也在一些重费米子和庞磁阻材料。 对于铜酸盐，这项研究将是以前努力发展反铁磁不稳定性附近低能行为完整理论的继续。将对强相互作用的电子系统进行理论研究，这些系统的行为被认为受到其接近所谓量子相变的影响。 在这些零温度临界点，所研究的材料可能会经历不稳定性并过渡到另一种特征状态。 虽然这项研究具有重大的根本意义，但其结果可能会影响我们对新材料的理解，并导致新材料的技术应用。

This award is for theoretical work on the system behavior near a quantum critical point (QCP), at which an itinerant fermionic system becomes unstable with respect to a structural instability, or to either a spin or charge density wave. In all of these cases, the quantum transition is accompanied by a softening of a bosonic mode. The principal investigator (PI) will study the cases when the bosonic mode is an independent degree of freedom (e.g., a phonon mode for a structural transition), or when it is a collective mode of fermions, and its dynamics is created by low-energy fermions. The PI plans to analyze in detail three aspects of the system behavior near a QCP: (i) the effect of bosonic softening on a fermionic propagator - in many cases this leads to a fully incoherent, non-Fermi liquid behavior at criticality; (ii) the pairing instability at the QCP - this pairing, if it occurs, creates a dome on top of the QCP beneath which the critical behavior changes due to feedback effects; (iii) the conditions under which long range order (the result of a bosonic instability) and superconductivity coexist, and when they are separated by an intermediate pseudogap phase in which only discrete lattice symmetry is broken.From a theoretical perspective, the primary interest in these issues is due to the fact that the pairing problem near a QCP is entirely novel and is qualitatively different from BCS-Eliashberg theory, as it involves fully incoherent, diffusive fermions that interact by exchanging gapless bosonic excitations. From an experimental perspective, the proposed research is aimed at explaining the origin of the pseudogap phase detected in multiple experimental measurements in the underdoped cuprates, and also in some heavy fermion and colossal magneto-resistance materials. For cuprates, this study will be a continuation of previous efforts to develop the full theory of the low-energy behavior near an antiferromagnetic instability.%%%Theoretical research will be conducted on strongly interacting electron systems whose behavior is believed to be affected by its proximity to so-called quantum phase transitions. At these zero-temperature critical points, the materials under study may experience an instability and transition into another characteristic state. While this study is of great fundamental interest, the results may impact our understanding of novel materials and lead to new materials with technological applications.***