In-gap states in lightly doped cuprate superconductors
Recent scanning tunneling spectroscopy (STS)[1,2] on very underdoped Mott insulators with AFM order unveiled the spectral function across the CT gap. Particularly, in Ref. [1], finite density of states appear throughout the CT gap and only a small portion at the chemical potential remains empty of spectral weight after holes are doped into the sample. These in-gap states have energy scales, about $0.1 \sim 0.5$eV, much larger than the localization gap at chemical potential. Besides the presence of in-gap states when the system is doped with holes, there is also a systematic evolution in the spectral weight distribution or local density of states (LDOS) measured at different positions. The in-gap states with higher spectral weight are situated more closer to the chemical potential and they obtain larger spectral weight transferred from the UHB. Moreover, the positions are anti-correlated between sites with higher spectral weight for UHB and in-gap states. This is consistent with an effective doping picture. That is, at the position where the UHB has strong intensity, the effective doping is close to $x=0$ and the in-gap states aren't seen. On the other hand, at the position where the in-gap states show up, $x>0$ and the intensity of the UHB becomes weaker.