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Doping evolution of chemical potential, spin-correlation gap, and charge dynamics in Nd$_{2-x}$Ce$_x$CuO$_4$

We report optical reflectivity study on Nd$_{2-x}$Ce$_x$CuO$_4$ over a broad doping range 0$\leq x\leq$0.20. The study reveals a systematic shift of chemical potential with doping. A pronounced peak structure specific to the electron-doped cuprate is observed in optical scattering rate based on the extended Drude model analysis. The energy scale of the peak could be very different from that of the peak in conductivity spectrum. We clarify that the "hot spots" gap probed in photoemission experiments correlates directly with the sharp suppression feature in scattering rate rather than conductivity spectra. The gap is associated with the short-range antiferromagnetic correlation, and disappears in a manner of fading away with increasing doping and temperature. In the heavily overdoped region, a dominant $ω^2$-dependence of the scattering rate is identified up to very high energy.