BCS-BEC crossover on the two-dimensional honeycomb lattice.

Area of Science:

• Condensed Matter Physics
• Quantum Materials

Background:

• The attractive Hubbard model on a honeycomb lattice features a quantum critical point at half filling, transitioning between a semimetal with Dirac fermions and an s-wave superconductor.
• Understanding the Bardeen-Cooper-Schrieffer/Bose-Einstein condensate (BCS-BEC) crossover is crucial for various condensed matter systems.

Purpose of the Study:

• Investigate the BCS-BEC crossover away from half filling in the attractive Hubbard model at zero temperature.
• Analyze the behavior of the crossover line and the underlying Fermi surface of the superconductor.
• Examine fluctuations and emergent phenomena, such as the Leggett mode, in both superconducting and semimetal phases.

Main Methods:

• Theoretical study of the attractive Hubbard model on the honeycomb lattice.
• Analysis of the BCS-BEC crossover in the interaction-density plane.
• Investigation of quasiparticle excitations and Fermi surface properties.
• Study of superconducting and semimetal fluctuations.

Main Results:

• The BCS-BEC crossover line passes through the quantum critical point at half filling.
• The underlying Fermi surface area of the superconductor exhibits non-monotonic behavior with interaction strength near half filling.
• An undamped Leggett mode emerges deep in the superconducting phase.

Conclusions:

• The BCS-BEC crossover is intimately linked to quantum criticality in this model.
• Non-monotonic Fermi surface behavior suggests complex emergent phenomena.
• Findings have potential implications for ultracold atoms in optical lattices and high-temperature superconductors.