The spatial variation of the local density of states in optimally doped Bi 2 Sr 1:6 La 0:4 CuO 6þ (superconducting transition temperature is 34 K) is studied by scanning tunneling spectroscopy at 4.2 K in zero magnetic field. Two-dimensional density-of-states modulation aligned with the Cu-O-Cu bond with a periodicity of about five lattice constants is observed. It is found that this modulation accompanies the appearance of a new energy gap of approximately 10 meV, whose gap edge peak is spatially modulated in intensity. This gap coexists with the superconducting gap, the value of which ranges from 10 meV to 60 meV.The addition of a relatively small number of carriers into a Mott insulator realizes d-wave high-temperature superconductivity in cuprates. The doped cuprates show unconventional electronic states. This unconventional nature has been investigated extensively in both momentum and real space. Angle-resolved photoemission spectroscopy (ARPES) revealed that states in different parts of momentum space, i.e., nodal and antinodal regions, show contrasting features, such as different temperature and doping dependences. 1) Furthermore, the line shape of photoemission spectra indicates dichotomy; a broad line shape in the antinodal region changes abruptly to a sharp one near the nodal region. 2) In addition, the superconducting gap structure along the Fermi surface considerably deviates from the prismatic d-wave functional form. 3,4) On the other hand, scanning tunneling spectroscopy (STS), which measures integrated spectral weight in momentum space, revealed spatial evolution of the electronic states. The superconducting gap varies on a length scale of about 5 nm and the tunneling spectrum changes distinctly in its shape. 5,6) It is claimed that coherence peaked spectra are observed in the region to be occupied by a canonical d-wave superconductor (dSC), while the spectra without clear coherence peaks, attributed to the destruction of antinodal coherence peaks, is characteristic of the electronic phase at the zero temperature limit of the pseudogap (ZTPG) region. 7) Furthermore, an anomalous local density-of-states (LDOS) modulation with a periodicity of about four lattice constants has been observed in Bi 2 Sr 2 CaCu 2 O 8þ (Bi2212) and Ca 2Àx Na x CuO 2 Cl 2 (Na-CCOC). 7-13) This modulation was first observed by Hoffman et al. in a magnetic field around vortex cores. 8) In zero magnetic fields, both energydispersive and nondispersive LDOS modulations were reported. The former, observed at low energy, is attributed to the interference of the quasi particles at the Fermi arc regions. 9,14) The dispersion of the quasi particles obtained in the STS experiments and the ARPES results are in excellent agreement. The origin of the latter, however, is still controversial. Since the nondispersive LDOS modulation has been observed in pseudogap states above the superconducting transition temperature, T c , and in the underdoped non-superconducting region, 10,15) it is claimed that this modulation is associated with the p...
