Topological Graphene Multiterminal Josephson Junctions

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Topological properties of quantum systems have recently attracted considerable theoretical and experimental attention. Nontrivial topological properties usually follow from intrinsic material properties, e.g., topological band structures in materials with strong spin-orbit interaction. Another possibility is the combination of different materials in hybrid structures to create topological band structures. These implementations require complex materials which are often difficult to synthesize.Recently, it has been predicted that multiterminal Josephson junctions made of conventional materials host topologically nontrivial states in an artificial band structure controlled by the macroscopic phases of the superconducting terminals. These systems offer the possibility to tune topological properties in situ by external parameters, and therefore allow considerable flexibility for the investigation of topology.The aim of this project is a joint experimental and theoretical effort to implement and understand artificial topological band structures in multiterminal Josephson junctions. The material of choice for our project is graphene. Due to its two-dimensional nature, graphene offers full flexibility of design, while its intrinsic high quality and gate tunability allows control of ballistic transport down to single quantum channels. Therefore, graphene is a prime candidate for the investigation of topological multiterminal Josephson junctions. We plan to unambiguously identify and characterize topological Andreev states via quantized nonlocal conductance and microwave spectroscopy in a minimal system, a four-terminal Josephson junction. A long-term goal is to use graphene multiterminal junctions to simulate topology in higher effective dimensions.