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Evolution of Fermi surface and normal-state gap in chemically substituted cuprates Bi$_{2}$Sr$_{2-x}$Bi$_{x}$CuO$_{6+δ}$

We have performed a systematic angle-resolved photoemission study of chemically substituted cuprates Bi$_{2}$Sr$_{2-x}$Bi$_{x}$CuO$_{6+δ}$. We observed that the Fermi surface area shrinks linearly with Bi substitution content $x$, reflecting the electron doping nature of this chemical substitution. In addition, the spectral linewidth broadens rapidly with increasing $x$, and becomes completely incoherent at the superconducting-insulating boundary. The d-wave-like normal-state gap observed in the lightly underdoped region gradually evolves into a large soft gap, which suppresses antinodal spectral weight linearly in both the excitation energy and temperature. Combining with the bulk resistivity data obtained on the same samples, we establish the emergence of the Coulomb gap behavior in the very underdoped regime. Our results reveal the dual roles, doping and disorder, of off-plane chemical substitutions in high-$T_c$ cuprates and elucidate the nature of the quantum electronic states due to strong correlation and disorder.