Disorder and quantum criticality in itinerant antiferromagnets

• Applicant: Professor Dr. Jörg Schmalian
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2013 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 225437397

The overall goal is to develop a theory for dynamic excitations and transport near a quantum critical point that takes into account critical fluctuations of all soft modes and disorder due to impurities and imperfections. The recently discovered iron-based high-temperature superconductors as well as investigations of inter-metallic heavy-electron systems and transition-metal oxides demonstrate the need to establish a theoretical framework that accounts for disorder in itinerant antiferromagnets close to criticality. In these systems it is important to analyze simultaneously the impact of disorder on the collective order-parameter degrees of freedom and on the electrons near the Fermi energy. Metals, being governed by gapless electronic excitations, give rise to new critical behavior compared to insulating quantum magnets. In addition to the formal development of a new theoretical framework, our project will be concerned with a detailed comparison with experiments in the mentioned materials. In the limit of vanishing disorder the theory should recover the results obtained from the analysis of fluctuating spin density waves. In the limit of vanishing electron-electron interactions the theory will recover the known behavior of disordered electrons, including weak and strong localization. To develop such a theory is important for a number of reasons: i) it enables us to judge whether some or all of the observations that puzzle the community can be rationalized as being due to the subtle interplay of criticality and disorder, ii) experiments in some systems seem to agree with the conventional theory and our work will make clear predictions with regards to disorder induced novel physics, and iii) the theory that we propose to develop promises to constitute novel critical behavior.We plan to formulate a well-controlled theory to make robust and reliable predictions for thermodynamic, spectroscopic and transport properties of metals near antiferromagnetic quantum phase transitions. We will then develop a controlled calculation where critical fluctuations and disorder are treated on the same footing. The small parameter of the theory is 1/N, where N is the number of fermion flavors (bands). This expansion allows the investigation of the limit of strong disorder and large spin-electron coupling. It was successfully used to solve disordered problems without interactions and includes the physics of localization in strongly disordered or two dimensional systems. It was also used in clean quantum critical systems, where it leads to non-Fermi liquid behavior. We will also address the role of statistically rare regions and droplets that lead to quantum Griffith behavior, activated scaling and smearing of the phase transition.

• DFG Programme: Research Grants
• International Connection: USA
• Participating Persons: Professor Dr. Andrey Chubukov; Professor Dr. Peter Wölfle