BCS Theory of Time-Reversal-Symmetric Hofstadter-Hubbard Model

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Ultracold Atomic Gases

Background:

• The interplay between lattice periodicity and magnetic fields creates complex quantum phenomena like the Hofstadter butterfly.
• Understanding many-body physics in optical lattices is crucial for quantum simulation and condensed matter research.

Purpose of the Study:

• Investigate the impact of opposing synthetic magnetic fields on a two-component Fermi gas in a square optical lattice.
• Explore the many-body Bardeen-Cooper-Schrieffer (BCS) pairing phenomenon under these conditions.
• Map the low-temperature phase diagrams and identify distinct superfluid transitions.

Main Methods:

• Utilizing a two-component Fermi gas model on a square optical lattice.
• Applying opposite synthetic magnetic fields to each component.
• Analyzing superfluid transitions from semimetal, quantum spin-Hall insulator, and normal phases.
• Characterizing low-temperature phase diagrams.

Main Results:

• Observed intricate competition between lattice length scales and cyclotron radius.
• Identified distinct superfluid transitions from various insulating and metallic phases.
• Revealed phase diagrams with lobe structures analogous to Mott insulator transitions in Bose-Hubbard models.

Conclusions:

• The synthetic magnetic fields significantly influence BCS pairing in Fermi gases.
• The resulting phase diagrams exhibit rich structures with potential for quantum simulation.
• This work provides insights into many-body physics in interacting quantum systems under magnetic frustration.