Scale-dependent theory of the disordered electron liquid

About This Grant

NONTECHNICAL SUMMARY This award supports fundamental theoretical research and education on the transport of electric charges and heat in disordered materials. These systems contain scatterers, such as impurities or lattice imperfections, which can cause electrons to frequently change directions. The presence of disorder is often unavoidable in complex materials, including quantum materials. Conversely, disorder leads to fascinating phenomena, especially when quantum mechanical effects are important and interactions between the electrons are strong. The project focuses on two key systems: 1. The disordered electron liquid: The disordered electron liquid near where a metallic state transforms to an insulator in silicon-based transistors is a system for which the strength of interactions and disorder can be tuned by changing the density of electrons. Depending on the density, the material can either act like a metal at low temperatures, allowing electrons to flow freely, or like an insulator by blocking the electron flow. Despite much effort, the physical mechanisms causing this metal-insulator transition are still under debate. The aim of this project is to derive refined theoretical predictions for the transport of charges and heat on the metallic side of the metal-insulator transition with the goal to enable interpretation of experimental data that can advance understanding of this phenomenon. 2. Disordered quantum critical metals: The transport of heat in disordered quantum critical metals represents another focus of this project. In these systems, the interplay of disorder and the complex electron motion that arises from strong electron-electron interactions near a zero-temperature phase transition can cause anomalies in the flow of charge and heat through the material. This research aims to compare charge transport and heat transport in quantum critical metals and to contrast the findings with conventional metals. The proposed research will advance basic knowledge, and add to our understanding of semiconductors, a class of materials that are of great technological importance. In addition to its scientific merit, better knowledge of the fundamental mechanisms of charge and heat transport holds promise for improving energy efficiency in electronic devices. This project also includes educational initiatives, including the development a new mathematical physics course for undergraduates, and a K-12 outreach activity that will be associated with the University of Alabama high school physics contest. In addition, the project will provide research training for undergraduate and graduate students. TECHNICAL SUMMARY This award supports fundamental theoretical research and education on transport and thermodynamics in two paradigmatic disordered electron systems: the two-dimensional electron liquid, and quantum critical metals. The disordered electron liquid near the metal-insulator transition is an electron system close to a quantum phase transition, for which the strength of the two main factors, interaction and disorder, can be tuned externally. The physical mechanisms underlying the observed non-monotonic behavior of the resistance on the metallic side of the transition as well as the metal-insulator transition itself are under debate. Progress in the interpretation of the experimental data requires refined theoretical predictions. The aim of this project is to develop a comprehensive theory of transport and thermodynamics near the metal-insulator transition. Thermal transport in disordered quantum critical metals represents another backbone of the project. In these systems, the interplay of disorder and the effective long-range interaction mediated by collective bosonic modes can result in characteristic non-Fermi liquid behavior of transport properties. A goal of this project is to obtain results for the Lorenz ratio, the ratio of thermal and electric conductivities, which is often used to quantify deviations from Fermi-liquid theory observed in experiments. The main goals of the proposed research are: 1. Disordered electron liquid near the metal-insulator transition: to derive detailed theoretical predictions for the temperature dependence of the resistance, the thermopower, the specific heat and the spin susceptibility of the disordered two-dimensional electron liquid near the metal-insulator transition. An important aim of this project is the interpretation of experimental findings in silicon metal-oxide-semiconductor field effect transistors. 2. Thermal transport in strange metals: to explore thermal transport in a strange metal described by a two-dimensional generalization of the Sachdev-Ye-Kitaev model with potential disorder and spatially random Yukawa coupling. Both studies will be based on the nonlinear sigma-model formalism for disordered interacting systems. Deepening knowledge of fundamental mechanisms of thermal transport may help improve energy efficiency in electronic devices. In synergy with the scientific plan, this project includes an education and outreach effort. This includes the development of a new course on mathematical physics tailored to undergraduates, and a K12 outreach activity that will be associated with the University of Alabama high school physics contest. Further impact of this project will lie in research training of undergraduate and graduate students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.