CAREER: Wave Mechanics of Complex, Correlated, and Driven Quantum Materials

William Marsh Rice University, Houston TX

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education to advance understanding Quantum materials which hold great promise for technology. These are compounds in which quantum physics plays an essential role in enabling exceptional electronic or magnetic properties. Quantum materials may enable new electronic devices, perhaps based on high temperature superconductivity or topologically robust quantum circuits. Superconductors can carry electric current without dissipation while topological states are new states of electronic matter that may enable quantum computation. An obstacle to realizing this potential has been the complexity often exhibited by these systems. This CAREER award supports the investigation of a new theoretical paradigm to tackle this issue, inspired by so-called many-body localization. In quantum physics, particles can behave like waves. Many-body localization is the idea that the interference between quantum waves can "freeze" the dynamics of interacting electrons, producing different classes of quantum states with different properties. In this project, ideas from the theory of localization will be applied to systems of many interacting electrons, with the view that the statistical classification of different types of excited many-body states may prove essential for determining properties in complex materials. This is very different from the usual approaches that stress the properties of the ground state at the absolute zero of temperature. In particular, if successful, the statistical approach developed here will provide new theoretical tools to characterize the complex behavior that arises from the melting of competing electronic phases. Understanding the latter may be a key to unlocking the potential of quantum materials for technological applications. The PI will also investigate the role of strong electron-electron interactions on the transport of electric charge and heat in quantum materials. An educational component of the project aims to make modern mathematical tools more accessible to undergraduate physics majors by emphasizing algorithms and visualization. In the U.S., physics majors are currently taught mathematics developed prior to the 20th century, yet research now employs many more modern mathematical tools. These can be presented to undergraduates using an algorithmic, problem-solving, approach. The PI will create learning modules that will be tested in the classroom and openly disseminated via a permanent Rice-hosted web repository. TECHNICAL SUMMARY This CAREER award supports theoretical research and education to advance understanding Quantum materials. The rich variety of collective phenomena exhibited by quantum materials holds great promise for technology. An obstacle to realizing this potential has been the complexity often exhibited by these systems. Due to the interplay of interactions, frustration, and material disorder, many compounds exhibit competing low temperature phases. These are often found in proximity to quantum critical regimes that may arise from fluctuations of the many different ordered states. It is now believed that quantum wave interference can induce the Anderson localization of a many-particle interacting system, in the presence of disorder or frustration. This many-body localization suggests a paradigm shift to the statistical classification of many-particle states, instead of a singular focus on the ground state. Transport measurements are the primary probe of quantum interference, but understanding transport in correlated materials remains a challenge. Project goals include: bringing statistical methods developed in one-body Anderson localization physics to bear on quantum many particle systems, and revealing correlation-dominated transport effects in non-Fermi liquids. The focus is on low-dimensional quantum critical regimes and driven topological systems. The goal of the educational component is to make available more modern mathematical tools to physics and STEM students and workers. Specific research and education objectives are to: 1) Test the hypothesis that the many-body localization transition can be continuous, and investigate the physics of the "bad metal" phase predicted to occur above it. 2) Test the hypothesis that "clustering" between the probability peaks of different many-body states determines the relaxation dynamics in the bad metal phase, and investigate competing orders in the presence of inhomogeneity and one-body state Chalker scaling. 3) Investigate new transport effects that directly reveal the influence of correlations, by exploiting novel geometries for edge loop drag and quantum quench dynamics in 2D topological insulators, and by sharpening the roles of virtual and real collisions in the thermoelectric transport of correlated electron fluids. 4) Develop and disseminate virtual learning modules for topics in modern mathematics accessible to undergraduate physics majors, emphasizing algorithms and visualization. The PI will create learning modules starting with Lie algebra representation theory, and these will be tested in the classroom and openly disseminated via a permanent Rice-hosted web repository. Ideas germinated from many-body localization may lead to insight into the interplay of competing orders, disorder, and frustration in correlated electron systems; however, many fundamental questions regarding the nature or even the existence of the many-body localization transition currently are unanswered, particularly in dimensions higher than one. The approaches will (a) introduce improved models amenable to exact numerical or analytical solutions, and (b) exploit the proximity of a 2D many-body localization transition to a special zero temperature Anderson-Mott transition. Competing orders and critical delocalization will be studied in an interacting version of an integrable quasicrystal model. The PI's investigation of thermoelectric transport will be in collaboration with experimentalists who are experts on graphene, and will help disentangle the roles of hydrodynamics, quasiparticle and transport lifetimes in marginal Fermi liquids.