Hall effect in the normal phase of Bi2Sr2CaCu2O8+δ single crystals

The pseudogap is a general phenomenon occurring in the cuprate superconductors that manifest itself as anomalies in several properties of the normal and superconducting states of these systems [1, 2, 3]. Basically, the pseudogap characterizes a depression in the electronic density of states near the Fermi level. Its effects are observed below a certain temperature $T^*$. Depending on the carrier density $T^*$ may be located much above the critical temperature $T_C$. An important property that is sensitive to Fermi surface modifications is the Hall effect. In fact, in the normal state of the superconducting cuprates, the Hall coefficient presents a strong dependence with temperature, contrasting with observations in conventional metals. The unusual behavior of the Hall coefficient is particularly evident in the underdoped regime of the cuprates, where the pseudogap effects are prominent. Despite this fact, few discussions on the relation between the Hall effect and the pseudogap phenomenon are available in the literature [4, 5]. In this communication, we report on Hall effect experiments in the normal phase of $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212) single crystals with different carrier concentrations. The single crystals were grown by self-flux method and were structurally characterized by x-ray diffraction and scanning electron microscopy (SEM). The as-grown single crystals were submitted to a heat treatment in oxygen pressure or vacuum in fixed temperatures in order to modify the carrier content. Crystals could be obtained within a large range of carrier densities. Longitudinal resistivity and Hall resistivity measurements were performed with a Quantum Design Physical Properties Measuring System (PPMS). Magnetic fields up to 9T were applied perpendicularly to the samples plane. Temperatures were varied between $T_C$ and 300 K. The total Hall coefficient for all insvestigated samples is quite well described by an empirical expression with small number of adjustable parameters. This expression implies that the Hall resistivity is composed by an ordinary term plus an anomalous contribution. The anomalous term has the form of a cut-off law, in which the characteristic parameter reproduces the pseudogap temperature as a function of the carrier concentration. This finding evidences the strong correlation between the Hall effect and the pseudogap phenomenon in the studied cuprates. A phase diagram could be traced for the Bi-2212 superconductor where the pseudogap temperature $T^*$ was represented as a function of the doping and compared with previous determinations. In addition, the obtained ordinary Hall coefficient presents a strong hole doping dependence with a minimum occurring at the concentration $p$ = 0.14, possibly caused by a partial Fermi surface reconstruction.