Collaborative Research: Non-linear Response for Quantum Materials

NONTECHNICAL SUMMARY Electrons are very light and move very fast in materials: if one tries to drive them out of their equilibrium steady state, for example by using an applied voltage, they reorganize rapidly and establish a new steady state. Until very recently, experimenters were incapable of measuring materials on fast-enough timescales to see how electrons behave when they are far out of equilibrium before they reach a new steady state. This restriction to studying electrons in materials at or near equilibrium has fundamentally limited understanding of the physical mechanisms governing charge and heat conduction, magnetism, and other topics. In the past decade, developments in ultrafast laser technology have made it possible to study far-from-equilibrium systems of electrons. Apart from isolated examples, however, there is no theoretical framework for interpreting such experiments, i.e., for understanding what they can tell us about the underlying quantum mechanical dynamics of the electrons, or how we can use this knowledge to guide the search for materials with new functionalities. This is the theoretical gap that the present project aims to fill. This project has two main thrusts. First, for broad classes of systems — such as superconductors and thin wires — the researchers will develop explicit predictions for out-of-equilibrium behavior based on state-of-the-art theoretical descriptions. In materials that exhibit exotic phenomena, there are often multiple theoretical models that agree on what equilibrium behavior looks like, but in general make distinct predictions for out of equilibrium. The researchers will use out-of-equilibrium dynamics as a way for distinguishing between these various models. Also, many fundamental aspects of the physics of complex quantum systems have largely been studied with computer simulations because they have no nontrivial implications for near-equilibrium dynamics. Out of equilibrium, however, such phenomena appear to have concrete and testable implications; the researchers will establish what these implications are, and how they can be unambiguously identified in present-day experiments. This project aims to establish a theoretical framework to exploit new experimental capabilities to yield new insights into quantum materials. Alongside the research, the educational and outreach component of this activity includes the training of students in this new field and the organization of conferences. In addition, the researchers intend to write a monograph on nonequilibrium quantum dynamics, intended to make the dramatic developments that have taken place in this field over the past two decades accessible to a broad audience. TECHNICAL SUMMARY Most current experimental probes of quantum materials employ linear response. Recent experimental developments enable interrogation of materials through nonlinear response, offering a wealth of opportunities for materials characterization, and for resolving fundamental questions that could not be unambiguously settled through linear-response techniques. However, exploiting this opportunity requires a theoretical foundation, which is currently absent. The researchers will develop the necessary theoretical foundation for applying nonlinear response techniques to correlated quantum materials. The research consists of three principal thrusts. The first thrust will address both clean and disordered superconductors to investigate how nonlinear response may be used to probe intrinsic lifetimes of excitations, as well as how to use nonlinear response to resolve fundamental questions regarding energy localization. The second thrust will consider one-dimensional systems at low temperatures. Specific problems include how nonlinear response may be used to probe disorder-driven localization in Luttinger liquids, how nonlinear response may be used to characterize the spin incoherent Luttinger liquid (with and without disorder), and nonlinear corrections to Luttinger liquid physics. The third thrust aims at developing a crisp means of characterizing chaos, addressing formal theoretical concepts like eigenstate thermalization, and understanding how nonlinear response could be used to gain insight into strange-metal phases without good quasiparticles. In addition to the research, this project will train students in this new field, and disseminate the key developments through conference organization and summer-school lectures. Furthermore, the researchers intend to write a monograph on quantum dynamics. Quantum dynamics has witnessed dramatic advances over the past two decades, yet these advances are scattered across a wide literature. A monograph that collects the key developments in one place will play a key role in making this field accessible to a broad audience. 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.