Low-Energy Optical Sum Rule in Moiré Graphene.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Few-layer graphene, particularly twisted bilayer graphene (TBG) at small twist angles, is a key system for exploring strong interaction physics.
• This system exhibits nearly quenched single-particle kinetic energy and non-trivial band topology, making it ideal for studying correlated electron phenomena.
• Understanding the interplay between interactions and band structure is crucial for predicting novel electronic properties.

Purpose of the Study:

• To develop an exact analytical theory for Coulomb interaction-induced low-energy optical spectral weight in twisted bilayer graphene.
• To investigate the behavior of optical spectral weight at integer fillings in the strong-coupling limit.
• To analyze the impact of strain-induced renormalization on optical spectral weight and its relation to superconductivity.

Main Methods:

• Exact analytical theory based on the strong-coupling limit of twisted bilayer graphene.
• Analysis of Coulomb interaction effects on low-energy optical spectral weight.
• Systematic inclusion of strain-induced renormalization of bandwidth and interlayer tunneling.

Main Results:

• In the strong-coupling limit, optical spectral weight vanishes identically at integer fillings, despite finite interaction-induced single-particle dispersion.
• Corrections to optical spectral weight were studied by considering strain effects.
• The relationship between optical spectral weight and diamagnetic response (controlling superconducting critical temperature, Tc) was examined.

Conclusions:

• The study highlights that specific parent insulating phases are crucial for enhancing superconductivity when doping away from integer fillings.
• The vanishing optical spectral weight at integer fillings provides insights into the insulating nature of these correlated states.
• Understanding these phenomena is vital for designing novel superconducting materials based on twisted bilayer graphene.