Controlling Quantum Materials: Exotic Orders and Light-Induced Dynamics

什么原理支配着晶体固体中电子的集体量子行为？可以通过控制维度来调节电子的量子相吗？光能被用来控制电子的多体量子态并在它们之间切换吗？探索这些重要问题对于从根本上理解量子凝聚态系统至关重要，它是创造和控制量子材料的关键，可以为下一代量子技术奠定基础。晶体中电子的平衡和动力学性质受量子力学定律和泡利不相容原理中编码的量子统计的支配。这种晶体的例子，包括半导体工业的主力硅，在能带理论和费米液体理论的框架内是非常容易理解的。然而，当强电子相互作用在晶体中变得重要时，电子可以组织成显著的新状态，导致超导、巨磁电阻或电子液晶。过渡金属氧化物提供了这种“紧急”行为的典型例子，展示了过多的新集体相，以及固态驱动器、催化剂和光伏等一系列应用。近年来，人们认识到相对论自旋-轨道耦合可以赋予固体中的电子能带新的拓扑性质，为量子计算领域提供新的器件和新的发展方向。本提案中概述的五年研究方案侧重于两条相互交织的研究线索。第一条线索旨在探索和理解出现在重过渡金属氧化物、卤化物和硫化物等量子材料中的奇异有序的光学性质。这些量子材料表现出很强的原子自旋-轨道耦合，这导致了在大块晶体中以及在二维薄膜和界面中都出现了拓扑相、非常规超导和磁序。这项研究的第二条相互交织的线索涉及如何利用光来控制和操纵这种量子材料及其电子相。拟议的研究将集中在光学性质，如太赫兹电导率和克尔效应，超快泵浦-探测动力学，以及利用光学驱动声子模式在物质的电子态之间切换。这项拟议的研究将利用数值工具，包括古兹威尔投影波函数技术、高频展开、强耦合展开和新方法来处理关联电子的动力学。

What principles governs the collective quantum behaviour of electrons in a crystalline solid? Can one tune quantum phases of electrons by controlling dimensionality? Can light be used to control and switch between many-body quantum states of electrons? Exploring these important issues is crucial to gain a fundamental understanding of quantum condensed matter systems, and it holds the key to creating and controlling quantum materials which can lay the foundation for the next generation of quantum technologies. The equilibrium and dynamical properties of electrons in crystals are governed by the laws of quantum mechanics, together with quantum statistics as encoded in the Pauli exclusion principle. Examples of such crystals, which include silicon, the workhorse of the semiconductor industry, are extremely well-understood within the framework of band theory and Fermi liquid theory. However, when strong electron interactions become important in a crystal, the electrons can organize into remarkable new states leading to superconductivity, colossal magnetoresistance, or electronic liquid crystals. Transition metal oxides provide a canonical example of such ``emergent'' behavior, exhibiting a plethora of new collective phases, with a slew of applications such as solid state drives, catalysts, and photovoltaics. In recent years, it has been recognized that relativistic spin-orbit coupling can impart new topological character to electronic bands in solids with the potential for novel devices and the promise of new directions in the field of quantum computing. The five-year research programme outlined in this proposal focuses on two intertwined threads of research. The first thread aims to explore and understand the optical properties of exotic orders which appear in quantum materials such as heavy transition metal oxides, halides, and chalcogenides. These are quantum materials which exhibit strong atomic spin-orbit coupling, which leads to the emergence of topological phases, unconventional superconducting and magnetic orders, both in bulk crystals as well in two-dimensional thin films and interfaces. The second intertwined thread of the research deals with how one might control and manipulate such quantum materials and their electronic phases using light. The proposed research will focus on optical properties such as THz conductivity and Kerr effects, ultrafast pump-probe dynamics, and switching between electronic states of matter using optically driving of phonon modes. The proposed research will utilize numerical tools including Gutzwiller projected wavefunction techniques, high frequency expansions, strong coupling expansions, and novel methods to treat the dynamics of correlated electrons.