Synthetic many-body systems in artificially structured materials

人工结构材料中的合成多体系统。在这项提议中，我们的目标是设计在半导体和石墨烯器件中承载量子拓扑物质的合成多体系统。目前已知的多体系统表现出与它们的组成成分非常不同的有用性质。超导体在没有电阻的情况下导电，铁磁体被用来在计算机上存储数据，量子霍尔效应是电阻的标准。最近，正如2016年诺贝尔物理学奖所强调的那样，多体凝聚态物理中的新范式-量子拓扑物质，是多体物理与拓扑学相结合的产物。然而，潜在的多体问题仍然是一个巨大的挑战。我们建议通过构建和描述在人工结构材料中承载量子拓扑物质的设备来解决这一挑战。我们将追求三个主要目标。在第一个子项目中，将发展一种现实的理论，即在半导体纳米线的量子点阵列中合成霍尔丹自旋一链，这是拓扑量子物质的原型。这样的系统有望在其边缘支持拓扑自旋1/2激发，可用作宏观量子比特。第二个子项目涉及石墨烯中的电子相互作用。我们将发展一个由两个垂直堆叠的锯齿形边三角形量子点组成的合成双层量子霍尔系统(TGQD)中的电子理论。每个TGQD在费米能级支持一个简并态的壳层，其电子性质完全由电子-电子相互作用决定。我们将探索层间激子凝聚体的潜在存在，并希望发现新的相。第二个石墨烯子项目将探索由2D超导体和2D铁磁体夹在一起的门控、半导体或BG量子点链，旨在实现支持Majorana费米子的Kitaev链。第三条研究线将涉及载流子密度可控的2D半导体。我们将发展一个关于多谷2D半导体导带中激子、三子和相互作用电子的现实理论，特别是实现谷极化电子气的条件。这些合成量子系统将阐明多体问题，促进我们对量子拓扑物质的理解，当实现时，可能会对新兴的量子技术产生重大影响。例如，在霍尔丹和马约拉纳准粒子中编码的拓扑保护的量子比特可能会导致高效的量子处理器，石墨烯量子点可能形成碳电子学的基础：基于石墨烯的电子学、光子学和自旋电子学，原子薄的狄拉克材料可能形成下一代光电子学的基础。有了这些雄心勃勃的目标，我们希望吸引和培训加拿大经济中的信息和通信技术、先进制造、安全、软件和学术界所需的高素质人才。

Synthetic many-body systems in artificially structured materials. In this proposal we aim to design synthetic many-body systems hosting quantum topological matter in semiconductor and graphene devices. Currently known many-body systems exhibit useful properties very different from their constituents. Superconductors conduct electricity without resistance, ferromagnets are used to store data on computers and the quantum Hall effect is the standart of resistance. Recently, new paradigm in many-body condensed matter physics, quantum topological matter, emerged from the combination of many-body physics and topology as emphasized by the 2016 Nobel Prize in Physics. However, the underlying many-body problem remains a great challenge. We propose to address this challenge by constructing and describing devices hosting quantum topological matter in artificially structured materials. Three main objectives will be pursued. In the first subproject, a realistic theory of a synthetic Haldane spin one chain, a prototype of topological quantum matter, in an array of quantum dots in semiconductor nanowires will be developed. Such a system is expected to support topological spin 1/2 excitations at its edges which can be used as macroscopic qubits. The second subproject involves interacting electrons in graphene. We will develop a theory of electrons in a synthetic bilayer quantum Hall system built with two vertically stacked triangular quantum dots with zigzag edges (TGQD). Each TGQD supports a shell of degenerate states at the Fermi level and its electronic properties are entirely determined by electron-electron interactions. We will explore the potential existence of interlayer exciton condensates and hope to discover new phases. The second graphene subproject will explore a chain of gated, semiconductor or BG, quantum dots sandwiched by a 2D superconductor and a 2D ferromagnet aiming to realize a Kitaev chain supporting Majorana fermions. The third line of research will involve 2D semiconductors with controlled carrier density. We will develop a realistic theory of excitons, trions and interacting electrons in the conduction band of multi-valley 2D semiconductors, in particular the conditions for realizing Valley Polarised Electron Gas. These synthetic quantum systems will illuminate the many-body problem, advance our understanding of quantum topological matter and, when realised, may have significant impact on emerging quantum technologies. For example, topologically protected qubits encoded in Haldane and Majorana quasiparticles may lead to efficient quantum processors, graphene quantum dots may form a basis of carbonics: graphene based electronics, photonics and spintronics, and atomically thin Dirac materials may form the basis of next generation opto-electronics. With these ambitious goals, we hope to attract and train highly qualified personnel needed for the ICT, advanced manufacturing, security, software and academia sectors of the Canadian economy.