Spin Dynamics in Graphene Quantum Dots

石墨烯是一种非常特殊的主体材料，用于研究与核自旋浴耦合的局部电子自旋（在量子点中）的动力学。有趣的是，只有1%的碳核（在自然丰度下）具有1/2的核自旋。 电子自旋和这些核自旋之间的耦合是由超精细相互作用介导的。在典型尺寸的石墨烯量子点中，核自旋的数量仍然相当大（1000-100000）。然而，同位素纯化使我们能够减少13 C含量，而12 C含量不携带任何核自旋。因此，我们可以不断地将量子点的自由度减少到1-10个核自旋。我们希望研究石墨烯量子点中电子和核自旋的动力学。从量子计算和基础物理学的角度来看，这种分析都很有趣。为此，我们将采用数值方法（基于精确对角化）和分析方法（基于Nakajima-Zwanzig方程）的组合。我们计划分析量子热力学的概念，如典型性，热化和量子达尔文主义在石墨烯量子点。这项研究将使我们能够预测这些抽象概念在真实的物质系统中的可观察结果。最终，我们希望我们的研究结果可能会导致更好地理解介观系统中热力学的微观描述。

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.