Quantum Criticality: Topology, Order, and Metallicity

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Metals are familiar to us in daily life, where the motion of electrons serves to conduct heat and electricity, in applications as diverse as cookware, microelectronics, and power distribution. Insulators are the opposite, where the absence of mobile electrons prohibits heat and electric currents. Recently, a new hybrid class of materials has been discovered where the interior of the material is insulating, while its surface readily conducts electricity and heat, but in ways that are distinct from normal metallic conduction. These materials are called topological insulators, and the separation of the surface and bulk conduction results from the topology of the electron states, where the bulk and surface states are as different as a sphere and a torus. The insulating interior restricts the mobile electrons to the surface, where their motion either covers the surface or must follow looplike orbits. These constraints make it nearly impossible for the electrons to change their energies, and so they conduct heat and electricity with significantly less dissipation than the three-dimensional electron motion found in normal metals. Interest in topological materials stems from their potential to reduce the power consumption of electronic devices, and to enable novel energy conversion devices. If the surface states are superconducting, they may form long-lived quantum states which could be the fundamental units of quantum information technologies. Before these technologies and others can be realized, there is a pressing need to understand how these topological constraints work and can be controlled. Our research seeks new materials where the topological character can be continuously modified by pressure or composition, and indeed entirely suppressed at a topological phase transition that separates conventional insulators without conduction from topological insulators with robust surface conduction. How does conduction emerge as the surface state is established, and the electrons transform from being spatially localized to completely mobile? Where is the conduction the largest and most sensitive to external forces? What are the thermodynamics that stabilize topological phases, and how do quantum fluctuations oppose them? Can we combine topological phases with more familiar sorts of order such as magnetism or superconductivity? We will use a variety of different electrical transport measurements backed by our arsenal of magnetic, thermal, and neutron scattering capabilities to address these questions in this research project. We will use the latest advances in crystal design to discover and modify new materials where we can explore these novel properties of topological insulators.