Tunneling conductance and local density of states in tight-binding junctions

We study the relationship between the differential conductance and the local density of states in tight-binding tunnel junctions where the junction geometry can be varied between the point-contact and the planar-contact limits. The conductances are found to differ significantly in these two limiting cases. We also examine how the matrix element influences the tunneling characteristics and produces contrast in a simple model of scanning tunneling microscope (STM). Some implications regarding the interpretation of STM spectroscopic data in the cuprates are discussed. The calculations are carried out within the real-space Keldysh formalism.