Density of state and non-magnetic impurity effects in electron-doped cuprates

We analyze the density of state (DOS) and a non-magnetic impurity effect in electron-doped cuprates starting from two different scenarios: the $d_{x^{2}-y^{2}}$-wave superconductivity coexisting with antiferromagnetic spin density wave (SDW) order versus $d_{x^{2}-y^{2}}$-wave superconductivity with a higher harmonic. We find that in both cases the local density of state (LDOS) exhibits two impurity-induced resonance states at low energies. We also find that for the intermediate value of the SDW gap, the DOS looks similar to that obtained from the scenario of the $d_{x^{2}-y^{2}}$-wave gap with a higher harmonic, suggesting the presence of a non-monotonic $d_{x^{2}-y^{2}}$-wave gap. However, if the SDW gap is sufficiently large the DOS looks more conventional s-wave like. This obvious difference from the DOS resulted from the $d_{x^{2}-y^{2}}$-wave gap with a higher harmonic model, could differentiate the two above scenarios and is needed to be proved in the further doping dependence of tunneling spectrum measurement.