This award supports theoretical research on heavy fermion materials with a particular focus on quantum criticality. The strongly correlated many-electron systems of interest are in regimes that are not adiabatically connected to the limit of free-electron gas, and theoretical understanding of the pertinent non-perturbative physics of electron correlations are still at a very early stage. The PI will study model systems which are amenable to controlled theoretical studies and which may provide lessons for other more complex systems. The PI will pursue four specific research directions:
1.) Quantum Transition out of Magnetic Order in Heavy Fermions: The PI will study ways in which quantum transitions can take place from magnetically-ordered heavy fermion metals. This research is motivated by recent experiments in heavy fermion metals, which suggest at least three routes for such transitions. Another motivation is to shed new light on the nature of heavy fermion quantum criticality.
2.) Superconductivity in Quantum Critical Heavy Fermions: The PI will study whether and how unconventional superconductivity arises in heavy fermion metals near a Kondo-collapsing quantum critical point. This work will leverage advances of the past few years on quantum criticality beyond the Landau paradigm of order-parameter fluctuations, and will also aim to elucidate the interplay between quantum criticality and superconductivity in Ce-115 and related systems.
3.) Quantum Criticality from a Gravitational Perspective: The PI will seek to gain new insights into the Kondo-collapsing local quantum criticality from a dual picture formulated in terms of gravity in an anti-de Sitter space. The PI will explore the possibility that a heavy-fermion quantum critical point contains the factorization of spatial and temporal fluctuations as an emergent symmetry.
4.) Fluctuation and Dissipation of out-of-equilibrium Quantum Criticality: A quantum critical point is readily driven out of equilibrium, as its scale-invariant fluctuation spectrum implies the lack of any intrinsic energy scale. We will consider the fluctuations and dissipation of a magnetic nanostructure as a concrete setting to study the larger issues in non-equilibrium.
This research project will engage postdoctoral fellows, graduate students, and undergraduate students, and will contribute to the understanding of materials that may form the foundations of future technologies.
NON-TECHNICAL SUMMARY
This award supports theoretical research and education on a class of unusual materials. The discovery of complex metallic materials with unusual properties that lie outside the standard textbook description of metals has motivated intense research that aims to understand the physical origins of their properties. The PI will use advanced theoretical methods to attack this problem with a focus on elucidating the nature of a transformation from one state of matter to another that takes place at the absolute zero of temperature. In contrast to the familiar transformation of water to ice that takes place around 273K, or 0C, and in which temperature plays an important role, this transformation is driven by a fundamental principle of quantum mechanics ascribed to Heisenberg. The PI is developing a theory of these transformations and the unusual temperature dependent properties that they induce. The PI will develop new theoretical methods to study how textbook descriptions for the electronic states of metallic materials and for the transformation between electronic states can fail, and how new electronic states of matter can arise.
This research project will engage postdoctoral fellows, graduate students, and undergraduate students, and will contribute to the understanding of materials that may form the foundations of future technologies.
This grant has supported my research in the area of theoretical condensed matter physics. Our research addressed the effect of electron-electron interactions on the novel properties of strongly correlated electron systems. We carried out research on how transformation of phases at zero temperature influences the properties at finite temperatures, in a class of strongly correlated systems involving rare-earth elements. We found a new setting for quantum criticality that involves mixed valency, which was published in Physical Review Letters. Our theoretical studies also led us to a joint work with an experimental group on a class of cubic heavy fermion systems, which was published in Nature Materials. We also elucidated the role of isoelectronic doping on the quantum phase transitions in the iron-based high temperature superconductors, and reported the first microscopic studies of correlation effects on the newly discovered 122 iron selenides. We developed the method of a chiral anomaly to study the quantum phase transitions of the Kondo lattice model in one spatial dimension, which was published in Physical Review Letters. In a new direction of research, we developed the first holographic model for antiferromagnetic order. This is formulated on the gravity (bulk) of the so-called AdS/CFT duality, with a global SU(2) symmetry representing spin that is broken down to a U(1) by the presence of a finite electric charge density. This involves the condensation of a neutral scalar field in a charged AdS black hole. We found that the phase transition for both neutral and charged order parameters can be driven to zero temperature, resulting in a quantum phase transition. The quantum critical behavior has a surprising correspondence with local quantum criticality we have advanced for Kondo lattice systems. The grant resulted in about 30 publications in the refereed journals. The PI contributed to the dissemination of research by giving more than 40 invited talks invited talks on our NSF supported research. The PI co-organized several international workshops, and served on the advisory/program committees on several conferences/workshops. The PI continued to make efforts on some international collaborative efforts between Rice University and German/British/Chinese institutions. On the education front, the PI involved two undergraduate students research. One of them received a thesis award.
