Assoc ProfessorAndrew Mitchell

Theoretical nanoelectronics: When nanoscale components are incorporated into electronic circuits, the laws of quantum mechanics govern their basic properties. Striking phenomena such as entanglement and quantum interference can appear, and have no classical analogue. The next generation of miniaturized electronics will overcome the limitations of traditional design paradigms by exploiting the novel functionality of the nano. I am interested in developing and applying state-of-the-art theoretical and computational techniques, working closely with experimental collaborators to study and direct development of new nanoelectronic devices. The group is currently working on two key areas of emerging potential. First, we are exploring the rich physics of nanostructures such as semiconductor quantum dots, where strong electron interactions lead to new emergent physics appearing in electron transport measurements. Such devices also represent a paradigm for designer nanophysics, providing a route engineer previously elusive states through quantum simulation of abstract models. We are also interested in molecular electronics -- especially single molecule junctions. Here, new possibilities arise from the complex interplay between quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Our aim is to address the challenge of how to harness the robust and reproducible chemical complexity provided by nature in single molecule devices. Topological Quantum Matter: The last decade has seen enormous activity in the research of electronic topological states of matter, sparked by the discovery of topological insulators (TIs), protected by time-reversal symmetry. The nontrivial bulk band topology of 3D strong TIs causes the crossing of surface states at time-reversal invariant points in the surface Brillouin zone, and gives rise to a 2D surface metal. In the vicinity of such crossing points, the effective surface theory takes the form of a Dirac equation of massless fermions, with spin-momentum locking. Many of the intriguing properties of such systems are however elusive to direct local measurement since, by their very nature, topological features are not local in real-space. However, topological systems can be characterized by their nontrivial response to defects or spin qubits. We are interested in studying such defects in topological materials such as graphene, topological insulators, Dirac and Weyl semimetals, and spin liquids. In particular we develop the theory of experimentally-relevant measurable quantities such as those probed by scanning tunneling spectroscopy (STM) and related quasiparticle interference (QPI), especially in disordered and/or interacting systems.