Electron-electron interactions and topology in semiconductor and graphene quantum dots

电子-电子相互作用和拓扑结构是理解量子材料和器件的基础，但目前两者都没有完全理解。纳米技术的最新进展使得从单个原子、电子和自旋构建人工量子材料、纳米结构和器件成为可能。我们广泛定义的研究计划旨在设计单粒子量子系统，最重要的是，在多粒子水平。这种人工可调结构将允许对电子-电子相互作用和拓扑结构的影响的基本理解，并为它们在量子固态设备中的开发铺平道路，以解决信息处理，传感，安全和能量收集方面的重要技术挑战。 将开展四个主要研究方向。 (i)由完全可调的扩展哈伯德模型描述的场效应晶体管中的量子点网络理论将用于确定电子-电子相互作用是否可能导致强相关的拓扑相，并允许在小型量子模拟器（固态量子计算机的前体）中所需的自旋的电压控制。 (ii)将发展嵌入纳米线中的半导体量子点中的相互作用电子和空穴的原子理论，以确定这些结构对于单个和纠缠光子源、光子到自旋转换以及由于调制掺杂纳米线中的e-e相互作用而形成鲁棒宏观量子态的潜力。 (iii)将发展由反能带半导体（如碲化汞）制成的量子点的电子和光学性质的理论，并确定拓扑保护自旋分辨表面态出现的必要条件。e-e相互作用在拓扑量子点的电子，光学和输运性质中的作用将被确定，以及它们作为应变，电荷和自旋传感器的应用。 (iv)电子-电子相互作用的影响、弱自旋轨道耦合以及因此在石墨烯中缺乏拓扑效应和磁性仍然是一个挑战。通过控制石墨烯的横向尺寸，可以打开能隙并将石墨烯（半金属）变成一个原子层厚的“半导体”量子点，打破亚晶格对称性产生磁矩，并扭曲成莫比乌斯带引入拓扑结构。我们将开发能够预测石墨烯量子点的电子，光学，磁性和拓扑特性的理论和计算工具。这将允许确定用于太阳能电池的胶体量子点的光学性质、基于双层石墨烯中的电子自旋的量子点网络的电子性质以及基于集成石墨烯量子点的电子电路的设计。 该研究计划将推动先进量子材料，纳米结构和量子和低功耗信息处理，传感和能量收集设备的进展。

Electron-electron interactions and topology are fundamental to the understanding of quantum materials and devices yet neither one is fully understood at present. Recent advances in nanotechnology make it possible to build artificial quantum materials, nanostructures and devices from single atoms, electrons, and spins. Our broadly defined research program aims at designing quantum systems both at the single particle and, most importantly, at the many-particle level. Such artificial tuneable structures will allow for the fundamental understanding of effects of electron-electron interactions and topology and pave the way toward their exploitation in quantum solid state devices addressing important technological challenges in information processing, sensing, security and energy harvesting. Four main research directions will be pursued. (i) theory of quantum dot networks in a field effect transistor described by fully tuneable, extended Hubbard model will be used to determine whether electron-electron interactions may lead to strongly correlated topological phases and allow for voltage control of spin needed in small quantum simulators, precursors of solid state quantum computers. (ii) atomistic theory of interacting electrons and holes in semiconductor quantum dots embedded in nanowires will be developed to determine the potential of these structures for single and entangled photon sources, photon-to-spin conversion and formation of a robust macroscopic quantum state due to e-e interactions in a modulation doped nanowire. (iii) theory of electronic and optical properties of quantum dots made of inverted band semiconductors, such as HgTe will be developed and conditions necessary for appearance of topologically protected spin-resolved surface states determined. The role of e-e interactions in the electronic, optical and transport properties of topological quantum dots will be determined as well as their application as strain, charge and spin sensors. (iv) the effects of electron-electron interactions, weak spin orbit coupling and hence absence of topological effects and lack of magnetism in graphene remain a challenge. By controlling lateral size of graphene one can open an energy gap and turn graphene, a semimetal, into a one atomic layer thick “semiconductor” quantum dot, breaking sublattice symmetry generates a magnetic moment and twisting into Mobius strip introduces topology. We will develop theoretical and computational tools enabling prediction of the electronic, optical, magnetic and topological properties of graphene quantum dots. This will allow the determination of optical properties of colloidal quantum dots for solar cells, electronic properties of quantum dot networks based on electron spin in bi-layer graphene and design of integrated graphene quantum dot based electronic circuits. This research program will advance progress in advanced quantum materials, nanostructures and devices for quantum and low power information processing, sensing and energy harvesting.