Scanning tunneling spectroscopy gap maps of cuprate single crystals: k-space anisotropy as an alternative to nanoscale inhomogeneity

The results of a computer analysis of a simple two-dimensional quantum mechanical tunneling model are reported. These suggest that the spatial dependence of the superconducting energy gap observed by scanning tunneling spectroscopy (STS) studies of single crystals of the high T_c superconductor Bi₂Sr₂CaCu₂O_8+x is not necessarily caused by nanoscale inhomogeneity. Instead, the spatial dependence of the STS data could arise from the momentum (k) dependence of the energy gap, which is a defining feature of a d-wave superconductor. In other words, the superconducting properties of the CuO₂ layers could be spatially uniform. It is possible that this viewpoint could be exploited to obtain k-dependent information from STS studies.