FIG. 4: Doping evolution of the electronic structure along the nodal direction near E$_{F}$ . (a)-(d): Blow up of Fig. 1 near E$_{F}$ . Vertical bars indicate the position of the LHB. (e): Position of the LHB and the “QP” band obtained from MDCs. The plots have been shifted vertically so that the chemical potential µ shifts the average of the shift in the LHB at ∼ ( π/ 2 , π/ 2) and ∼ ( π, 0) in Fig. 3 for each doping. The chemical potential µ is also displayed. (f): Doping dependence of Fermi momentum k$_{F}$ positions in Bi2212, LSCO $^{14}$, Bi22015 and Na-CCOC $^{8}$. -0.6 -0.4 -0.2 0  = 0.075 -0.6 -0.4 -0.2 0  = 0.06 -0.6 -0.4 -0.2 0  = 0.05 -0.6 -0.4 -0.2 0  = 0.03 Energy relative to E$_{F}$ (eV) -0.6 -0.4 -0.2 0.0 Relative Energy (eV) 0.6 0.5 0.4 0.3 0.2 0.1 k$_{x}$( a)  = 0.03  = 0.05  = 0.06  = 0.075 0.03 0.05 0.06 0.075 (a) (b) (c) (d) (e) (f) 0.50 0.45 0.40 0.35 k F x  = k F y ( a) 0.30 0.25 0.20 0.15 0.10 0.05 0.00 Hole concentration  p  Bi2212  LSCO  Bi2201  Na-CCOC 13