Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model

TL;DR

This paper derives Lorentz-invariant interactions from the Haldane-Hubbard model and studies how they induce charge density wave and superconducting phase transitions, highlighting the roles of chemical potential, magnetic flux, and initial topological states.

Contribution

It introduces Lorentz-invariant four-fermion interactions in the honeycomb lattice and analyzes their impact on phase transitions, considering topological effects and experimental verification methods.

Findings

Charge-density-wave and superconducting phases are mainly controlled by chemical potential.

Magnetic flux influences the domain of phase transition.

Initial topological states significantly affect phase transition behavior.

Abstract

We derive Lorentz-invariant four-fermion interactions, including Nambu-Jona-Lasinio type and superconducting type, which are widely studied in high-energy physics, from the honeycomb lattice Hamiltonian with Hubbard interaction. We investigate the phase transitions induced by these two interactions and consider the effects of the chemical potential and magnetic flux (Haldane mass term) on these phase transitions. We find that the charge-density-wave and superconductivity generated by the attractive interactions are mainly controlled by the chemical potential, while the magnetic flux delimits the domain of phase transition. Our analysis underscores the influence of the initial topological state on the phase transitions, a facet largely overlooked in prior studies. We present experimental protocols using cold atoms to verify our theoretical results.