Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries

Area of Science:

• Condensed matter physics
• Topological materials
• Quantum matter

Background:

• Higher-order topological insulators (HOTIs) exhibit unique boundary phenomena.
• Momentum-space nonsymmorphic (k-NS) symmetries offer new routes to topological phases.
• Synthetic gauge fields enable the construction of novel quantum materials.

Purpose of the Study:

• To theoretically construct a higher-order topological insulator (HOTI) on a real projective plane.
• To explore the role of momentum-space nonsymmorphic (k-NS) symmetries in realizing HOTI phases.
• To propose an experimental platform for realizing and detecting these topological states.

Main Methods:

• Theoretical construction of a checkerboard Z_{2} flux model with anicommutative k-NS glide reflections.
• Analysis of Berry curvature and nonlocal polarization quantization.
• Investigation of bulk quadrupole phase diagram and ribbon geometry for edge phenomena.

Main Results:

• Demonstrated intrinsic HOTI features arising from bulk gap closure.
• Observed simultaneous intrinsic and extrinsic HOTI characteristics.
• Identified boundary-obstructed topological phases due to k-NS symmetry breaking in ribbon geometries.
• Proposed a concrete design for a real projective plane quadrupole insulator.

Conclusions:

• The study establishes a new paradigm for HOTIs on deformed Brillouin manifolds using k-NS symmetries.
• The proposed acoustic resonator array offers a feasible experimental platform for verification.
• This work expands the understanding of topological phases in synthetic quantum matter.