Topological and geometrical aspects of condensed matter systems

凝聚态系统的最新理论进展揭示了量子材料的可观测特征与拓扑学和微分几何等复杂数学之间的深刻联系。这些不同的科学分支被统一在热力学系统的场论方法中。在这个项目中，我们将研究由具有不同性质的2D材料组成的范德华异质结构模型。一个例子是RuCl3/石墨烯异质结构。RuCl3最近被发现表现出量子自旋液体的特征，特别是它的激发既不像玻色子也不像费米子。它们是任意子。相似粒子在量子计算中的潜在应用引起了人们的兴趣，人们越来越有兴趣寻找具有这种不寻常和奇异性质的物质的相，用于量子技术。目标是找到新的方法来产生、探测和操纵传统电子学中的这种奇异准粒子。这就是与石墨烯相互作用的地方，因为石墨烯是研究最多的2D导体。希望我们能够通过测量石墨烯电子与上述系统的激发相互作用来检测诸如RuCl3等强关联系统的量子相的异常性质。因此，我们的项目位于量子材料设计、量子技术和(由于电子与量子磁相之间的相互作用)自旋电子学领域的交叉点。学生将使用量子场论和动力学方程技术来研究(石墨烯)电子-(RuCl3)自旋相互作用的影响。他们将推导出这两个量的运动方程，描述它们之间的能量/动量交换。然后将求解方程，以找到与实验相关的可观测数据。

Recent theoretical advances in condensed matter systems unveiled deep connections between observable features of quantum materials and sophisticated mathematics like topology and differential geometry. These distinct branches of science are united within field-theoretical approach to thermodynamic systems. In this project we will study models of van der Waals heterostructures comprising 2D materials with different properties. One example are RuCl3/graphene heterostructures. RuCl3 has been recently found to exhibit features of a quantum spin liquid, in particular its excitations behave as neither bosons nor fermions. They are anyons. Similar particles have attracted interest for potential use in quantum computation and there is a growing interest in finding phases of matter exhibiting such unusual and exotic properties for applications to quantum technology.The goal is to find novel ways to generate, detect and manipulate such exotic quasiparticles with conventional electronics. This is where the interaction with graphene comes into place, because graphene is the most studied 2D conductor. The hope is that we will be able to detect the unusual properties of quantum phases of strongly-correlated systems such as RuCl3 by measuring graphene electrons, when they interact with the excitations of the aforementioned systems. Thus, our project sits at the intersection between the fields of quantum material design, quantum technology and (because of the interactions between electrons with quantum magnetic phases) spintronics. The student will use quantum field theory and kinetic equation techniques to study the effect of the (graphene)electron-(RuCl3)spin interaction. They will derive equations of motions for the two quantities describing the exchange of energy/momentum between them. Equations will then be solved to find observables that can be related to experiments.