论文标题
魔术费米斯：卡洛尔和扁平乐队
Magic Fermions: Carroll and Flat Bands
论文作者
论文摘要
Carroll代数被构造为庞贝里代数的$ c \ to0 $限制，与通用无效表面上的对称性相关。在本文中，我们开始研究在通用无效表面上定义的卡洛利亚费米子或费米子。由于卡罗尔（Carroll）空位上有两个不同的（退化）指标，因此可能有两个不同版本的Carroll Clifford代数。我们考虑了Carrollian Gamma矩阵的可能性和构建明确表示，并展示了如何从较低的时代构建更高的时空表示。 Carroll Fermions的作用是用这些伽马矩阵构建的，并研究了这些动作的特性。 我们表明，在凝结物质系统中，分散关系变得琐碎，即能量不依赖动量，并且频段扁平，而Carroll Symmetry通常会出现。我们给出了这一点的明确示例，包括扭曲的双层石墨烯，其中超导性以所谓的魔术角出现并将其连接到卡罗尔·费米子（Carroll Fermions）。
The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions.
