Quantum Criticality: Topology, Order, and Metallicity

金属在日常生活中是我们所熟悉的，在各种应用中，如炊具、微电子和电力分配，电子的运动起到了传导热量和电力的作用。绝缘体正好相反，因为没有可移动电子，所以无法产生热量和电流。最近，一种新的混合材料被发现，这种材料的内部是绝缘的，而其表面很容易导电和导热，但其方式与正常的金属导电不同。这些材料被称为拓扑绝缘体，表面和体导电的分离是由电子态的拓扑引起的，其中体态和表面态就像球体和环面一样不同。内部绝缘将可移动电子限制在表面，在那里它们的运动要么覆盖表面，要么必须沿着类似Lopli的轨道。这些限制使得电子几乎不可能改变它们的能量，因此它们传导热量和电能的耗散比正常金属中发现的三维电子运动要少得多。 人们对拓扑材料的兴趣源于它们有可能降低电子设备的功耗，并使新型能量转换设备成为可能。如果表面态是超导的，它们可能会形成长寿命的量子态，这可能是量子信息技术的基本单位。 在实现这些技术和其他技术之前，迫切需要了解这些拓扑约束是如何工作和可以控制的。我们的研究寻找新的材料，在这种材料中，拓扑性可以被压力或组成连续改变，并且实际上在将传统的无导电绝缘子与具有良好表面导电性的拓扑绝缘子分开的拓扑相变处完全被抑制。当表面态建立，电子从空间定域转变为完全移动时，传导是如何出现的？哪里是传导最大、对外力最敏感的地方？什么是稳定拓扑相的热力学，量子涨落又是如何对抗它们的？我们能否将拓扑相与更常见的有序相结合，比如磁性或超导性？在这个研究项目中，我们将使用各种不同的电传输测量方法，并以我们的磁力、热力和中子散射能力为后盾来解决这些问题。我们将利用晶体设计的最新进展来发现和修饰新材料，在那里我们可以探索拓扑绝缘体的这些新特性。

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.