Temperature dependence of the hole density in high-TC superconductors Bi2−yPbySr2CaCu2O8+δ

Highlights: ► We have done x-ray absorption spectra on the CuL3 edge of Bi(Pb)-2212 cuprates. ► We have measured the hole density nH in the CuO2 plane of Bi(Pb)-2212 cuprates. ► The measurements were performed from 10 K to 300 K. ► Gor'kov and Teitel'baums formula of nH consists of a linear and an exponential term. ► We have extended the Gor'kov and Teitel baum formula by a T3/2 term. -- Abstract: One of the most puzzling anomalies of high-TC cuprates is the strong temperature dependence of the Hall coefficient (RH) and the hole density (nH). Gor'kov and Teitel'baum (GT) proposed by using experimental data of La2−xSrxCuO4 (LSCO) a two fluid model. The number of holes per Cu atom nH, changes with temperature according to nH(T,x) = n0(x) + n1(x)exp(−Δ(x)/T) [1]. To clarify the temperature dependence of nH we have determined nH from X-ray absorption spectra (XAS) at the CuL3 edge for nearly optimum and slightly underdoped Bi2−yPbySr2CaCu2O8+δ single crystals yielding directly the absolute value of nH in the CuO2 planes and also its change with temperature nH(T). It shows pronounced structures between 10 K and 300 K. The temperature dependence puts constraints to the applicability of previously developed models: (i) the two-band model without any explicit temperature dependence and (ii) the formula of GT, because the latter is not able to fit our data over the whole temperature range from 10 K to 300 K. Instead the thermal behavior of nH proposes a function with at least three terms, i.e. a third term added to the formula of GT is of exponential form ∼T3/2