Non-uniform square-octagon lattice: a new platform for quantum spin Hall insulator

Area of Science:

• Condensed Matter Physics
• Materials Science
• Topological Matter

Background:

• Investigating novel lattice structures is crucial for discovering new electronic properties.
• Spin-orbit coupling is a key factor in driving topological phase transitions in materials.

Purpose of the Study:

• To analyze the tight-binding model of a non-uniform square-octagon lattice.
• To understand the influence of two distinct spin-orbit couplings (λso1 and λso2) on electronic band structure and topological properties.
• To identify conditions for realizing the quantum spin Hall (QSH) phase.

Main Methods:

• Numerical evaluation of the topological invariant Z2 using the Fukui-Hatsugai method.
• Comprehensive analysis of electronic band structure modifications under varying spin-orbit couplings.
• Verification of topologically protected edge states.

Main Results:

• Both λso1 and λso2 induce band gap closure and reopening, signaling topological phase transitions.
• Spin-orbit coupling λso1 drives the system into a QSH phase at 1/8 and 3/8 filling fractions.
• Spin-orbit coupling λso2 stabilizes the QSH phase specifically at 3/8 filling.
• Topologically protected edge states confirm the nontrivial topological character.

Conclusions:

• The non-uniform square-octagon lattice is a promising platform for realizing nontrivial topological phases.
• This lattice expands the range of two-dimensional materials capable of hosting the quantum spin Hall effect.
• The study highlights the tunable nature of topological phases through controlled spin-orbit interactions.