A recent Scanning Tunneling Spectra (STS) measurement on underdoped Bi-2201 by Cai et al., discovered large energy in-gap states between Oxygen band and upper Hubbard band (UHB) of Cu. There is a strong interplay between the spectral weights and energies of the UHB and these in-gap states. We proposed a simple theory to explain the origin of these states by constructing explicitly the in-gap states and UHB states for a one-band Hubbard model. Our results show that the spatial variation of in-gap states and its evolution of spectral weight transfer from UHB are associated with the inhomogeneous local hole density.
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