npj Quantum Materials ( IF 5.7 ) Pub Date : 2021-01-04 , DOI: 10.1038/s41535-020-00300-7 Sander Kooi , Guido van Miert , Carmine Ortix
The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional topological properties that do not yield surface spectral features, but manifest themselves as (fractional) quantized electronic charges localized at the crystal boundaries. Here, we formulate such bulk-corner correspondence for the physical relevant case of materials with time-reversal symmetry and spin-orbit coupling. To do so we develop partial real-space invariants that can be neither expressed in terms of Berry phases nor using symmetry-based indicators. These previously unknown crystalline invariants govern the (fractional) quantized corner charges both of isolated material structures and of heterostructures without gapless interface modes. We also show that the partial real-space invariants are able to detect all time-reversal symmetric topological phases of the recently discovered fragile type.
中文翻译:
时间对称绝缘子的体角对应
绝缘子的拓扑通常通过无间隙边界模式的存在来揭示:这就是所谓的体边界对应。但是,晶体绝缘体的多体波函数具有附加的拓扑特性,这些拓扑特性不会产生表面光谱特征,而是表现为位于晶体边界的(分数)量化电子电荷。在这里,我们为具有时间反转对称性和自旋轨道耦合的材料的物理相关情况制定了这种体角的对应关系。为此,我们开发了部分实空间不变式,既不能用Berry相表示,也不能使用基于对称的指标表示。这些先前未知的晶体不变量控制无间隙界面模式的隔离材料结构和异质结构的(分数)量化角电荷。我们还显示部分实空间不变量能够检测到最近发现的脆弱类型的所有时间逆对称拓扑阶段。