论文标题
高阶非铁皮皮肤效应
Higher-order non-Hermitian skin effect
论文作者
论文摘要
非铁皮皮肤效应是非热式系统的独特特征，其中在开放边界条件下出现了大量边界模式。在这里，我们发现了表现出新边界物理学的非铁皮皮肤效应的高阶对应物。在具有系统尺寸$ l \ times l $的二维系统中，而传统（一阶）皮肤效果伴随$ o \，（l^{2}）$皮肤模式，二阶皮肤效果伴随$ o \，（l）$角皮肤模式。这也与Hermitian二阶拓扑绝缘子形成鲜明对比，其中仅出现$ o \，（1）$ corter零模式。此外，对于三个维度的三阶皮肤效果，$ o \，（l）$ contry皮肤模式从所有$ o \，（l^{3}）$模式出现。我们证明，高阶皮肤效应源自由空间对称性保护的固有的非铁拓扑。我们还表明，它伴随着较高维度的非Bloch带理论的修改。
The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under the open boundary conditions. Here, we discover higher-order counterparts of the non-Hermitian skin effect that exhibit new boundary physics. In two-dimensional systems with the system size $L \times L$, while the conventional (first-order) skin effect accompanies $O\,( L^{2} )$ skin modes, the second-order skin effect accompanies $O\,( L )$ corner skin modes. This also contrasts with Hermitian second-order topological insulators, in which only $O\,( 1 )$ corner zero modes appear. Moreover, for the third-order skin effect in three dimensions, $O\,( L )$ corner skin modes appear from all $O\,( L^{3} )$ modes. We demonstrate that the higher-order skin effect originates from intrinsic non-Hermitian topology protected by spatial symmetry. We also show that it accompanies the modification of the non-Bloch band theory in higher dimensions.
