Superconductivity and Pseudogap Near Quantum Critical Points

该奖项是对在量子临界点(QCP)附近系统行为的理论工作，在该临界点，巡回费米子系统变得不稳定，无论是结构不稳定性，还是自旋或电荷密度波。在所有这些情况下，量子跃迁都伴随着玻色子模式的软化。首席研究员(PI)将研究当玻色子模是一个独立的自由度(例如，结构转变的声子模)时，或者当它是费米子的集体模时，其动力学是由低能费米子产生的情况。PI计划详细分析QCP附近系统行为的三个方面：(I)玻色软化对费米子传播子的影响--在许多情况下，这导致临界时的完全非相干、非费米液体行为；(Ii)QCP的配对不稳定性--如果发生这种配对，则在QCP的顶部创建一个圆顶，在该圆顶下，由于反馈效应，临界行为发生变化；(Iii)长程有序(玻色子不稳定性的结果)和超导电性共存的条件，当它们被一个只有离散晶格对称性被破坏的中间赝隙相分开时。从理论的角度来看，这些问题的主要兴趣是因为QCP附近的配对问题是全新的，与BCS-Eliashberg理论有质的不同，因为它涉及通过交换无间隙玻色激发而相互作用的完全非相干的扩散费米子。从实验的角度，这项研究的目的是解释在欠掺杂铜酸盐以及一些重费米子和巨磁电阻材料中多次实验测量中检测到的伪隙相的来源。对于铜酸盐，这项研究将是对以前工作的继续，以发展反铁磁不稳定性附近的低能行为的完整理论。%将对强相互作用电子系统进行理论研究，这些电子系统的行为被认为受到其接近所谓的量子相变的影响。在这些零温临界点，所研究的材料可能会经历一种不稳定并转变为另一种特征状态。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.***