We performed high-resolution scanning tunneling microscopy/spectroscopy on an optimally-doped Ca2-xNaxCuO2Cl2 crystal with Tc ∼ 25 K. The so-called "checkerboard" local-density-of-state modulation previously found in heavily underdoped regime also manifests in the spectroscopic map of the optimally-doped sample. In addition, spatially-inhomogeneous energy gap with peaks at the gap edges is observed below about 10 meV. The gap tends to be buried at elevated temperatures and correlates with the checkerboard modulation.

Removing electrons from the CuO2 plane of cuprates alters the electronic correlations sufficiently to produce high-temperature superconductivity. Associated with these changes are spectral-weight transfers from the high-energy states of the insulator to low energies. In theory, these should be detectable as an imbalance between the tunneling rate for electron injection and extraction-a tunneling asymmetry. We introduce atomic-resolution tunneling-asymmetry imaging, finding virtually identical phenomena in two lightly hole-doped cuprates: Ca1.88Na0.12CuO 2Cl2 and Bi2Sr2Dy 0.2Ca0.8Cu2O8+δ.

We present studies of the electronic structure of La2-xBa xCuO4, a system where the superconductivity is strongly suppressed as static spin and charge orders or "stripes" develop near the doping level of x = 1/8. Using angle-resolved photoemission and scanning tunneling microscopy, we detect an energy gap at the Fermi surface with magnitude consistent with d-wave symmetry and with linear density of states, vanishing only at four nodal points, even when superconductivity disappears at x = 1/8.

Recent scanning tunneling microscopy (STM) experimentally observed strong gap inhomogeneity in Bi2Sr2CaCu2O8+δ (BSCCO). We argue that disorder in the pair potential underlies the gap inhomogeneity, and investigate its role in the Fourier-transformed inelastic tunneling spectra as revealed in the STM. We find that the random pair potential induces unique q-space patterns in the local density of states (LDOS) of a d-wave superconductor.

Formation of electron pairs is essential to superconductivity. For conventional superconductors, tunnelling spectroscopy has established that pairing is mediated by bosonic modes (phonons); a peak in the second derivative of tunnel current d2I/dV2 corresponds to each phonon mode. For high-transition-temperature (high-Tc) superconductivity, however, no boson mediating electron pairing has been identified. One explanation could be that electron pair formation and related electron-boson interactions are heterogeneous at the atomic scale and therefore challenging to characterize.

We study the effects of the electronic coupling to bosonic modes on scanning tunneling microscopy (STM) into a d -wave superconductor. We propose to investigate these effects by means of a different technique: a Fourier transformed inelastic electron tunneling spectroscopy (FT-IETS). Specifically, in this technique, the Fourier spectrum of the energy derivative local density of states is addressed, which is proportional to the (d2 I d V2) (q,eV) characteristics measured in FT-IETS STM.