Superconductivity and Pseudogap Near Quantum Critical Points

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.

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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.

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