Hofstadter Butterfly and Broken-Symmetry Quantum Hall States in α-Type Organic Dirac Fermion Systems

The electronic state under magnetic fields in the α-type organic Dirac fermion systems, α-(ET)2I3 and α-(BETS)2I3, has been studied to clarify the spatial order in the quantum Hall state. The four-band tight-binding model with Peierls phase factors was employed, and the generated Hofstadter butterfly and its Chern numbers confirmed the validity of the Dirac fermion picture in these materials. The four-component envelope function of the N = 0 Landau level with valley degeneracy was investigated. It was found that the two degenerate valley states have different weights on A and A′ molecules connected by inversion. This valley-site correspondence is also recognized for the N = 0 spin-split Landau levels under the Zeeman effect and the spin–orbit interaction. The spontaneous valley symmetry breaking in the N = 0 Landau levels due to the exchange interaction results in the ν = ±1 quantum Hall states accompanied by the spatial modulation of charge and spin densities at A and A′ sites in a unit cell.