Universal disorder in Bi2Sr2CaCu2O8+x

The cuprates contain a range of nanoscale phenomena that consist of both local density of states (LDOS) features and spatial excitations. These phenomena can be measured with spectroscopic imaging scanning tunneling microscopy, and the phenomena's disorder can be mapped out by fitting the data with a phenomenological model to the LDOS(E). The use of such a model allows a reduction of the complicated LDOS(r, E) data to key parameters for which doping and spatial dependence can be quantitatively determined. In this paper, we present a study of the nanometer-scale disorder in single-crystal, cryogenically cleaved samples of Bi2Sr2CaCu2O8+x over a doping range of p = 0.19 to 0.06. The phenomenological model that we use to map out the disorder is the Tripartite model. This model has recently been successfully applied to the average LDOS(E), where its key energy scales have been shown to correspond to other observables. The application of the Tripartite model to the doping-dependent LDOS(r, E) data produces a series of energy scale maps that show a structured patchwork disorder of three energy scales. The spatial disorder structure is universal for all dopings and energy scales. It is independent of the oxygen dopants' negative energy resonance. The interface between the different patches takes the form of a shortened lifetime pseudogap/superconducting gap state. The relationship between the energy scales and the spatial modulations of the dispersive quasiparticle interference (QPI), static q(1)* modulation, and the pseudogap shows that the energy scales' signatures in the LDOS(r, E) are tied to the onset and termination of these spatial excitations. The application of the Tripartite model allows the static q(1)* modulation to have its local energy range measured and shows that its signature in the LDOS(E) is the kink, forwhich the total number of states is modulated by the wave vector of the q(1)* wave vector. This analysis of both the LDOS(r, E) and the spatial modulations in q-space reveals a picture of a single underlying disordered parameter that determines both the LDOS(E) structure as well as the energy ranges of the QPI, q(1)* modulation, and the pseudogap states. This underlying parameter represents a doping of chemical potential, if the patch is that of an infinite homogeneous superconductor. DOI: 10.1103/PhysRevB.87.104520