Theory of order and fluctuations in quantum materials

Stanford University, Stanford CA

Investigators

Abstract

NONTECHNICAL SUMMARY The Division of Materials Research funds this award on theoretical research and education in the physics of strongly interacting electron systems. The study of emergent properties in these systems, i.e. properties that the system displays as a whole but which are not characteristic of the constituents, is one of the central thrusts of theoretical physics, and currently a key area of inquiry in a broad range of subfields including condensed matter, string theory and quantum gravity, cold-atom condensates, and quantum information theory. More generally, quantum materials play an increasingly important role in a range of more applied sciences, so increased understanding of these problems has the potential to influence broader developments in science and technology as well. Theoretical work in this field ranges from highly focused "microscopic" studies that attempt to provide a quantitative understanding of specific properties of particular interesting materials, to more abstract studies of simple models that shed light on the possible qualitative behaviors of quantum materials. The bulk of the work that will be supported by this award is of the latter variety. Both analytic and newly developed numerical methods will be deployed to compute the equilibrium and near-equilibrium properties of paradigmatic models of many interacting electrons. That knowledge could enable qualitative contact with measured properties of materials that have so far proven too complex to be understood from a more microscopic perspective. All of the proposed research will be carried out in collaboration with PhD students and post-doctoral scholars. The combination of theoretical precision and phenomenological relevance of the proposed studies makes them ideal for training future condensed matter theorists, and more generally for producing scholars able to grapple with complex, open-ended problems in a broad range of venues. TECHNICAL SUMMARY The Division of Materials Research funds this award on theoretical research and education in the physics of strongly interacting electron systems. One of the striking characteristics of systems of strongly interacting electrons is the complex interplay between competing or coexisting forms of order including magnetism, superconductivity, and electronic liquid crystalline order. Understanding the inter-relations between these ordering tendencies and the fluctuations associated with them may well be the key to understanding the physics of highly correlated quantum materials, including various high-temperature superconductors. Many aspects of the emergent low-energy physics of such materials are qualitatively similar despite their chemical and structural diversity. In the vicinity of a zero temperature quantum critical point (where an electronic order onsets as a function of an external tuning parameter), the microscopic physics is averaged out, giving rise to universal scaling behavior. More generally, many of the materials of interest show surprisingly simple scaling laws, such as a linear dependence of the resistivity on temperature, over broad regimes which may or may not be influenced by a "nearby" quantum critical point. In this proposal, the PI will undertake a theoretical investigation of the qualitative aspects of the interplay of order and fluctuations in correlated materials. The work will focus on simple models that can illuminate the generic behavior of systems of strongly correlated electrons. Among the directions to be pursued are: 1) Determinantal quantum Monte Carlo (DQMC) methods will be employed to study models of interacting electrons that do not suffer from the fermion minus sign problem, and can thus be solved efficiently in a broad range of temperatures and system sizes. A large part of the effort will be devoted to models of quantum criticality in metallic systems. In addition, the problem of electrons interacting strongly with phonons, which is at the heart of the physics of conventional superconductors, will be revisited in order to understand, among other things, what limits the maximum superconducting transition temperature. 2) Novel regimes of electron transport, not described by the traditional nearly-free-electron theory of metals, will be investigated. In particular, the PI will identify regimes in which electrons in solids behave hydrodynamically, i.e. as a locally-equilibrated collective "fluid" with a nearly-conserved momentum and energy. In addition, the "bad metal" transport regime, where the resistivity of a material is too high to be accounted for by a model of nearly-independent quasi-particles, will be explored in simple theoretical models that can be controlled in certain limits. All of the proposed research will be carried out in collaboration with PhD students and post-doctoral scholars. The combination of theoretical precision and phenomenological relevance of the proposed studies makes them ideal for training future condensed matter theorists, and more generally for producing scholars able to grapple with complex, open-ended problems in a broad range of venues.