标题： 有限尺寸拓扑超导体的大环绕数异常现象 显示英文标题

标题： Exceptionally large winding number of a finite-size topological superconductor

摘要： 我们研究了非传统超导体中由有限尺寸效应引起的拓扑现象。 具体来说，我们关注的是在一种高-$T_{\text{c}}$ 铜氧化物 $d_{xy}$-波超导体上制造的具有持续自旋纹理的薄膜。 在二维 $d_{xy}$-波超导体中，平带的安德烈夫束缚态出现在边缘。 随着系统变窄，由于有限尺寸导致的杂化作用和持续自旋纹理的自旋轨道耦合，这些束缚态获得了能量间隙。 这种诱导的间隙导致了一种拓扑相的出现，其特征是异常大的一维缠绕数，该缠绕数与薄膜宽度成比例。 我们展示了高度简并的零能态的出现，从而在脏超导结中导致了异常完美的电荷传输。 这些发现为探索由开隙安德烈夫束缚态驱动的迷人拓扑超导相提供了有希望的平台。 显示英文摘要

摘要： We study finite-size-induced topological phenomena in unconventional superconductors. Specifically, we focus on a thin film with a persistent spin texture, fabricated on a high-$T_{\text{c}}$ cuprate $d_{xy}$-wave superconductors. In two-dimensional $d_{xy}$-wave superconductors, flat-band Andreev bound states appear at the edges. As the system narrows, these bound states acquire an energy gap due to finite-size hybridization and spin-orbit coupling of the persistent spin texture. This induced gap gives rise to the emergence of a topological phase, characterized by an exceptionally large one-dimensional winding number that scales with the film width. We demonstrate the appearance of highly degenerate zero-energy states, leading to anomalous perfect charge transport in dirty superconducting junctions. These findings provide a promising platform for exploring fascinating topological superconducting phases driven by gapped Andreev bound states.