Fractal Spectrum in Twisted Bilayer Optical Lattice

Area of Science:

• Condensed Matter Physics
• Quantum Optics
• Materials Science

Background:

• Twisted bilayer optical lattices (TBOLs) are crucial for studying quantum phenomena.
• Conventional moiré physics often assumes continuum theory and small twist angles.

Purpose of the Study:

• To explore the full spectrum of TBOLs across all twist angles.
• To challenge the conventional moiré physics paradigm.
• To uncover the underlying physics of fractal band structures in TBOLs.

Main Methods:

• Departing from continuum theory, we analyzed the complete spectrum of TBOLs.
• Mapped TBOLs to a generalized Hofstadter model with long-range hopping.
• Provided numerical evidence for infinite recursive spectral structures.

Main Results:

• Discovered an astonishing fractal spectrum in TBOLs, similar to Hofstadter's butterfly.
• Observed vanishing first Chern numbers in these fractal bands.
• Fractal bands emerge from geometric moiré effects, independent of magnetic fields.

Conclusions:

• TBOLs exhibit a universal algebraic structure linked to generalized Hofstadter models.
• The geometric moiré effect is key to generating complex fractal band structures.
• Developed an algorithm for computing these infinite recursive spectral structures.