Engineering Corner States from Two-Dimensional Topological Insulators.

Area of Science:

• Condensed matter physics
• Topological materials science
• Quantum phenomena

Background:

• Topological insulators possess unique electronic properties protected by time-reversal symmetry.
• Higher-order topological insulators exhibit protected states at lower-dimensional boundaries (e.g., corners).
• Z_{2} topological insulators are a key class of topological materials.

Purpose of the Study:

• To theoretically demonstrate the realization of second-order topological insulators with robust corner states.
• To investigate the role of Zeeman fields in creating higher-order topological phases.
• To explore the experimental feasibility of these corner states.

Main Methods:

• Theoretical modeling using the Kane-Mele model and the Bernevig-Hughes-Zhang model.
• Application of an in-plane Zeeman field to break time-reversal symmetry.
• Analysis of crystalline symmetries protecting higher-order topological phases.

Main Results:

• An in-plane Zeeman field gaps out spin-helical edge states in 2D Z_{2} topological insulators.
• Robust in-gap corner states emerge at the intersection of zigzag edges, independent of field orientation.
• Corner states show robustness against various perturbations including out-of-plane fields and lattice imperfections.

Conclusions:

• Second-order topological insulators with robust corner states are achievable in 2D Z_{2} topological insulators via Zeeman field.
• Crystalline symmetries play a crucial role in protecting these higher-order topological phases.
• The demonstrated robustness makes these corner states promising for experimental realization and potential applications.