St-Jean P, Dauphin A, Massignan P, Real B, Jamadi O, Milicevic M, Lemaître A, Harouri A, Le Gratiet L, Sagnes I, Ravets S, Bloch J, Amo A
Centre de Nanosciences et de Nanotechnologies (C2N), CNRS-Université Paris-Sud/Paris-Saclay, Palaiseau 91120, France.
ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Avinguda Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain.
Phys Rev Lett. 2021 Mar 26;126(12):127403. doi: 10.1103/PhysRevLett.126.127403.
Topological materials rely on engineering global properties of their bulk energy bands called topological invariants. These invariants, usually defined over the entire Brillouin zone, are related to the existence of protected edge states. However, for an important class of Hamiltonians corresponding to 2D lattices with time-reversal and chiral symmetry (e.g., graphene), the existence of edge states is linked to invariants that are not defined over the full 2D Brillouin zone, but on reduced 1D subspaces. Here, we demonstrate a novel scheme based on a combined real- and momentum-space measurement to directly access these 1D topological invariants in lattices of semiconductor microcavities confining exciton polaritons. We extract these invariants in arrays emulating the physics of regular and critically compressed graphene where Dirac cones have merged. Our scheme provides a direct evidence of the bulk-edge correspondence in these systems and opens the door to the exploration of more complex topological effects, e.g., involving disorder and interactions.
拓扑材料依赖于对其体能带的全局性质进行调控，这些性质被称为拓扑不变量。这些不变量通常在整个布里渊区定义，与受保护的边缘态的存在有关。然而，对于一类重要的哈密顿量，它们对应具有时间反演和手征对称性的二维晶格（例如石墨烯），边缘态的存在与并非在完整二维布里渊区定义、而是在简化的一维子空间上定义的不变量相关。在此，我们展示了一种基于实空间和动量空间联合测量的新颖方案，以直接获取限制激子极化激元的半导体微腔晶格中的这些一维拓扑不变量。我们在模拟狄拉克锥已合并的规则和临界压缩石墨烯物理特性的阵列中提取这些不变量。我们的方案为这些系统中的体边对应提供了直接证据，并为探索更复杂的拓扑效应（例如涉及无序和相互作用的效应）打开了大门。
