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

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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.