主讲人：骆训江 博士（武汉大学）

题目：Higher-order topological phases: realization, construction, and topological characterization

时间：2024年7月10日（周三）上午10：00

地 点：理工楼1227

联系人：贾伟

报告摘要：

The abundance of bulk and boundary topologies in higher-order topological phases offer remarkable tunability and diversity to boundary states but also pose a challenge to their unified topological characterization. This talk is composed of two parts: one is about the realization and construction of higher-order topological phases; another is about the universal topological characterization of higher-order topological insulators and superconductors with chiral symmetry.

In the first part, we propose to realize and engineer higher-order topological superconductors based on weak topological insulators [1]. Motivated by the realization mechanism, we further generally construct higher-order topological phases by utilizing Gamma matrices [2,3]. In these discussed higher-order topological phases, the certain boundaries behave as first-order topological states and the whole system’s topology can be characterized by boundary topological invariants.

In the second part, we establish a comprehensive framework for characterizing topological zero-energy corner states in systems with chiral symmetry by using a series of Bott indices invariants with exact correspondence [4]. A key feature of our framework is its ability to capture the real-space patterns of zero-energy corner states in arbitrarily shaped systems. Motivated by the invalidation of a direct application of the defined invariants to the DIII symmetry class systems, we further develop new framework based on the spin-resolved Bott indices to characterize Majorana kramers pair of corner states [5]. As an application of our theory, we study the Kane-Mele model with the sublattice-dependent superconducting pairings.

References:

[1] Xun-Jiang Luo, et.al, Phys. Rev. B 104, 104510 (2021)

[2] Xun-Jiang Luo, et.al, Phys. Rev. B 107, 045118 (2023)

[3] Xun-Jiang Luo, et.al, Phys. Rev. B 108, 075143 (2023)

[4] Jia-Zheng Li*, Xun-Jiang Luo*,et.al, arXiv:2404.19757 (2024)

[5]Xun-Jiang Luo, et.al, Higher-Order Topological Invariants For Time-Reversal Invariant Topological Superconductors (In prepared)

个人简介：

骆训江，武汉大学重点资助博士后。2016年获湖北大学物理学学士学位，2021年获华中科技大学凝聚态物理博士学位。目前在武汉大学从事博士后研究工作，其研究方向为高阶拓扑物理，转角过度金属硫化物，拓扑超导和拓扑量子计算等。已在National Science Review，PRB等期刊发表论文10余篇。