Inelastic tunneling spectroscopy in a d-wave superconductor

We propose a mechanism to use inelastic tunneling spectrosopy scanning tunneling microscope (STM) to detect a single spin in a d-wave superconductor and in a pseudogap state, based on a direct exchange coupling J between the surface electrons and the local spin S in a magnetic field. This coupling will produce a kink in a dI/dV characteristic at Zeeman energy of the spin ω₀. We find that for relevant values of parameters signal scales as dI²/dV² ≃ (JN₀)²Θ(eV − ω₀) and could be in the range of 10⁻² of the bare density of states where N₀ is the density of states for surface electrons. Scattering in superconductor with the coherence peak at gap maximum Δ leads also to strong features at Δ + ω₀. This suggests a different technique for a detection of a local spin excitation with STM. We also consider a detection of a local vibrational mode as a simple extension of the spin case.