Synthetic many-body systems in artificially structured materials

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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.