Topological invariant of multilayer Haldane models with irregular stackings

Area of Science:

• Condensed matter physics
• Topological materials science
• Quantum mechanics

Background:

• The Haldane model is a foundational concept in topological insulator research.
• Understanding topological invariants in multilayer systems is crucial for designing novel quantum materials.
• Irregular stacking introduces complexities not present in standard hexagonal lattices.

Purpose of the Study:

• To investigate the topological properties of multilayer Haldane models with irregular stacking.
• To determine how interlayer hopping affects topological invariants and phase transitions.
• To explore the conditions under which phase transitions can occur in these systems.

Main Methods:

• Theoretical analysis of multilayer Haldane models.
• Calculation of topological invariants for various stacking configurations.
• Investigation of the role of nearest and next-to-nearest interlayer hopping.

Main Results:

• For irregular stacking (excluding AA), the topological invariant scales with the number of layers and the monolayer invariant.
• Nearest interlayer hopping does not close the band gap or induce phase transitions.
• Inclusion of next-to-nearest interlayer hopping can lead to band gap closing and topological phase transitions.

Conclusions:

• The topological properties of multilayer Haldane models are robust to irregular stacking under nearest interlayer hopping.
• Next-to-nearest interlayer hopping is the key mechanism for inducing topological phase transitions in these systems.
• This research provides insights into the design principles for tunable topological materials.