The quasiparticle energy spectra of the KHM from the direction Γ′(π3,π3)→K(2π3,2π3)→M′(π3,2π3) for NN electron hopping but with NNN hole hopping, the blue dashed line denotes the Fermi energy level, where the parameters are t = 1, t₁/t = 0.3, n_c = 0.9, J_K = 2.5.