Wigner crystallization at large fine structure constant

At low electron density, massive Dirac electrons can form a Wigner crystal phase if the ratio of interaction energy to Fermi energy is very large. The strength of Coulomb interactions in Dirac systems is characterized by the effective fine structure constant, α=e²/∈_rhv, where h is the reduced Planck’s constant, v is the Dirac velocity, and ∈_r is the dielectric constant. We discuss the fate of the Wigner crystal, including its quantum and thermal melting, as α is increased. We show that in the limit of large α, the critical density and critical temperature associated with melting approaches a constant universal value due to the renormalization of the electron charge by the interband dielectric response. Our results have implications for twisted bilayer graphene, where α becomes very large near the magic angle.