Quasiparticle coherence and the nature of the metal-insulator phase   transition in Na$_x$CoO$_2$
  Layered cobaltates embody novel realizations of correlated quantum matter on a spin-1/2 triangular lattice. We report a high-resolution systematic photoemission study of the insulating cobaltates (Na1/2CoO2 and K1/2CoO2). Observation of single-particle gap opening and band-folding provides direct evidence of anisotropic particle-hole instability on the Fermi surface due to its unique topology. Kinematic overlap of the measured Fermi surface is observed with the $\sqrt{3}$x$\sqrt{3}$ cobalt charge-order Brillouin zone near x=1/3 but not at x=1/2 where insulating transition is actually observed. Unlike conventional density-waves, charge-stripes or band insulators, the on-set of the gap depends on the quasiparticle's quantum coherence which is found to occur well below the disorder-order symmetry breaking temperature of the crystal (the first known example of its kind). 
D. Qian, L. Wray, D. Hsieh, D. Wu, L.J. Luo, N.L. Wang, A. Fedorov,   R.J. Cava, L. Viciu, M.Z. Hasan