Spin Dynamics in Graphene Quantum Dots

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Graphene is a very specific host material to study the dynamics of localized electron spins (in quantum dots) coupled to a bath of nuclear spins. Interestingly, only 1% of all carbon nuclei (at natural abundance) carry a nuclear spin ½. The coupling between the electron spins and these nuclear spins is mediated by the hyperfine interaction. In a typically sized graphene quantum dot, the number of nuclear spins is still quite large (1000-100000). However, isotopic purification enables us to reduce the 13C-content versus the 12C-content that does not carry any nuclear spin. Therefore, it is possible to constantly reduce the number of bath degrees of freedom down to 1-10 nuclear spins per quantum dot.We would like to study the dynamics of electron and nuclear spins in a graphene quantum dot. This analysis is interesting both from a quantum computing as well as a fundamental physics point of view. To do so, we will employ a combination of numerical methods (based on exact diagonalization) and analytical methods (based on the Nakajima-Zwanzig equation). We plan to analyze concepts of quantum thermodynamics such as typicality, thermalization, and quantum Darwinism in graphene quantum dots. This research will allow us to predict observable consequences of these abstract concepts in real material systems. Eventually, we expect that our findings may lead to a better understanding of the microscopic description of thermodynamics in mesoscopic systems.