Second order topology in a band engineered Chern insulator

Area of Science:

• Condensed Matter Physics
• Topological Materials
• Solid-State Physics

Background:

• The Haldane model describes a topological insulator with quantized Hall conductance without magnetic fields.
• Honeycomb lattices are crucial for realizing novel electronic properties.

Purpose of the Study:

• To investigate topological phase transitions in a deformed Haldane model.
• To characterize the properties of topological and second-order topological insulator phases.
• To analyze the impact of breaking time-reversal symmetry on topological states.

Main Methods:

• Smoothly deforming the Haldane model by varying a nearest-neighbor hopping parameter.
• Analyzing Berry curvature and Chern number evolution.
• Calculating Wannier charge center evolution.
• Diagonalizing the real-space Hamiltonian on a supercell.

Main Results:

• Identified two distinct topological phases: a topological insulator (TI) and a second-order topological insulator (SOTI).
• Observed a shift of Dirac cones and quantized Chern numbers (C=1) in the TI phase.
• Discovered in-gap zero-energy corner modes in the SOTI phase, characterized by quantized polarizations.

Conclusions:

• The deformed Haldane model hosts both TI and SOTI phases with distinct topological invariants.
• The SOTI phase exhibits quantized polarization and zero Berry curvature, analogous to the 2D Su-Schrieffer-Heeger model.