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

电子-电子相互作用和拓扑学是理解量子材料和器件的基础，但目前还没有完全理解它们。纳米技术的最新进展使利用单个原子、电子和自旋构建人造量子材料、纳米结构和设备成为可能。我们广泛定义的研究计划旨在设计单粒子和最重要的多粒子水平的量子系统。这种人工可调结构将使人们能够从根本上了解电子-电子相互作用和拓扑结构的影响，并为它们在量子固态器件中的开发铺平道路，以解决信息处理、传感、安全和能量采集方面的重大技术挑战。**(I)由完全可调谐的扩展Hubbard模型描述的场效应晶体管中的量子点网络理论将被用来确定电子-电子相互作用是否可能导致强关联的拓扑相，并允许对固态量子计算机的前驱--小型量子模拟器所需的自旋进行电压控制。**(Ii)将发展嵌入纳米线的半导体量子点中相互作用电子和空穴的原子理论，以确定这些结构对于单光子源和纠缠光子源的势，在调制掺杂纳米线中，由于e-e相互作用，光子到自旋的转换和强健的宏观量子态的形成。**(Iii)由反带半导体组成的量子点的电学和光学性质的理论，如HgTe，将发展和确定出现受拓扑保护的自旋分辨表面态的必要条件。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以及它们作为应变、电荷和自旋传感器的应用将被确定。**(Iv)电子-电子相互作用、弱自旋轨道耦合的影响，因此石墨烯中没有拓扑效应和缺乏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，将半金属石墨烯转变为单原子层厚的“半导体”量子点，打破次晶格对称性产生磁矩，扭曲成莫比乌斯带状引入拓扑。我们将开发能够预测石墨烯量子点的电、光、磁和拓扑性质的理论和计算工具。这将使用于太阳能电池的胶体量子点的光学性质的确定、基于双层石墨烯中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成为可能。**这项研究计划将推动先进量子材料、纳米结构和用于量子和低功率信息处理、传感和能量收集的设备的进展。

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.