Fermi surface investigation in the scanning tunneling microscopy of Bi ₂Sr₂CaCu₂O₈

Within the ideal Fermi liquid picture, the impurity-induced spatial modulation of local density of states (LDOS) in the d-wave superconductor Bi₂Sr₂CaCu₂O₈ is investigated at different superconducting (SC) gap sizes. These LDOS spectra are related to the finite-temperature dI/dV spectra in scanning tunneling microscopy (STM), when the Fermi distribution factor is deconvoluted away from dI/dV. We find stripe-like structures even in the zero gap case due to a local-nesting mechanism. This mechanism is different from the octet-scattering mechanism in the d-wave SC (dSC) state proposed by McElroy et al. [K. McElroy, R.W. Simmonds, J.E. Huffman, D.H. Lee, J. Orenstein, H. Eisaki, S. Uchida, J.C. Davis, Nature 422 (2003) 592]. The zero gap LDOS is related to the normal state dI/dV. The zero gap spectra when Fourier-transformed into the reciprocal space, can reveal the information of the entire Fermi surface at a single measuring bias voltage, in contrast to the point-wise tracing out proposed by McElroy et al. This may serve as another way to check the reality of Landau quasiparticles in the normal state. We have also re-visited the octet-scattering mechanism in the dSC state and pointed out that, due to the Umklapp symmetry, there are additional peaks in the reciprocal space that experimentally yet to be found.