Optical Selection Rule of Excitons in Gapped Chiral Fermion Systems

Area of Science:

• Condensed Matter Physics
• Topological Materials
• 2D Materials

Background:

• Exciton optical selection rules govern light-matter interactions in solids.
• Topological properties of Bloch bands, like winding number, influence electronic and optical behavior.
• Chiral fermion systems and 2D materials offer unique platforms for exploring novel quantum phenomena.

Purpose of the Study:

• To establish the relationship between the winding number (w) and exciton optical selection rules in gapped chiral fermion systems.
• To propose novel material systems exhibiting tunable exciton properties.
• To demonstrate a pathway for electrical control of optical transitions in two-dimensional materials.

Main Methods:

• Theoretical analysis of exciton optical selection rules based on topological invariants (winding number).
• Investigation of C_{N}-invariant chiral fermion systems.
• Proposal and theoretical characterization of gapped surface states in topological crystalline insulators and biased 3R-stacked MoS_{2} bilayers.

Main Results:

• The winding number (w) directly governs the exciton optical selection rule in gapped chiral fermion systems.
• The angular momentum of bright exciton states is determined by w±1+nN, where n is an integer.
• Gapped surface states of topological crystalline insulators and biased MoS_{2} bilayers are proposed to host dark s-like excitons.
• Electrical gating can tune s-like excitons from bright to dark states by altering the winding number in MoS_{2} bilayers.

Conclusions:

• The winding number is a fundamental quantity controlling exciton optical transitions in gapped chiral fermion systems.
• Topological crystalline insulators and engineered 2D heterostructures like MoS_{2} bilayers are promising platforms for realizing tunable excitonic effects.
• This work provides a theoretical framework for the electrical control of optical properties in advanced materials.