The nodal band-dispersion in (Bi,Pb)2(Sr,La)2CuO 6+δ (Bi2201) is investigated over a wide range of doping by using 7-eV laser-based angle-resolved photoemission spectroscopy. We find that the low-energy band renormalization ("kink"), recently discovered in Bi2Sr2CaCu2O 8+δ (Bi2212), also occurs in Bi2201, but at a binding energy around half that in Bi2212, implying its scaling to Tc. Surprisingly the coupling-energy dramatically increases with a decrease of carrier concentration, showing a sharp enhancement across the optimal doping. This strongly contrasts to other modecouplings at higher binding-energies (∼20, ∼40, and ∼70 meV) with almost no doping variation in energy scale. These nontrivial properties of the low-energy kink (material-and doping-dependence of the coupling-energy) demonstrate the significant correlation among the mode-coupling, the Tc, and the strong electron correlation.PACS numbers: 74.25.Jb, 71.18.+y The band renormalization or "kink" in cuprates have been attracting huge interest in the condensed matter physics because of a prospect that the associated collective mode plays an essential role in the pairing of electrons causing the high temperature superconductivity. However, the nature of the kink, particularly whether it is due to phonon or spin excitations, remains controversial mostly because the different modes occur at almost the same energy [1]. Previously it was reported that the nodal group velocity within 50 meV of Fermi energy (E F ) is independent of the cuprate family or the number of CuO 2 layers in the crystal unit cell, and it is almost constant across the entire phase diagram [2]. Recent ARPES technique with low-energy photons (hν = 6-8 eV) has extensively improved the momentum and energy resolutions [3,4], and uncovered a remarkable band renormalization very close to the E F (< 20 meV) [5][6][7][8][9][10], in addition to the well-studied kinks seen at 40-80The new fine band-feature (or "low-energy kink") determines the nodal Fermi velocity of Bi2212, thus it is crucial for the understanding of the electronic properties, which are dominated by the conduction electrons close to the E F .A recent theoretical study has suggested that coupling to phonons is too small to produce the observed band renormalization [11]. On the other hand, it has been pointed out that the strong electron correlation or reduced screening can significantly enhance the phononelectron coupling [10,[12][13][14][15]. A systematic study of the fine band-feature from the metallic overdoped-region to the poorly screened underdoped-region is crucial to reveal the mechanism of the mode-couplings in cuprates. To address the issue, we chose (Bi,Pb) 2 (Sr,La) 2 CuO 6+δ (Bi2201) [T max c = 35 K] for a study, where a wide doping range from the underdoped-to the heavily overdopedregion up to outside the T c -dome is accessible. The studying of Bi2201 with a T c , which is ∼2.5 times lower than that of Bi2212, is also important to confirm the universality of the low-energy kink in cuprates.In this letter, we find...