Temperature Effect and Fermi Surface Investigation in the Scanning Tunneling Microscopy of Bi$_2$Sr$_2$CaCu$_2$O$_8$

TL;DR

This study investigates how temperature affects impurity-induced LDOS modulations in Bi$_2$Sr$_2$CaCu$_2$O$_8$ using STM, revealing stripe structures in both normal and superconducting states and proposing new methods to analyze the Fermi surface.

Contribution

It introduces a Fermi liquid-based model for temperature effects on LDOS modulations and suggests a novel reciprocal space analysis to examine the Fermi surface in the normal state.

Findings

Stripe-like LDOS structures exist in the normal state due to local nesting.

Fourier-transformed spectra can reveal the entire Fermi surface at a single bias.

Additional reciprocal space peaks are predicted due to Umklapp symmetry, yet to be observed.

Abstract

Based on a Fermi liquid picture, the temperature effect on the impurity-induced spatial modulation of local density of states (LDOS) is investigated for the d-wave superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$, in the context of scanning tunneling microscopy (STM). It is found that stripe-like structure exists even in the normal state due to a local-nesting mechanism, which is different from the octet scattering mechanism proposed by McElroy $et al$. {[Nature {\bf 422}, 592 (2003)]} in the d-wave superconducting ($d$SC) state. The normal-state spectra, when Fourier-transformed into the reciprocal space, can reveal the information of the entire Fermi surface at a single measuring bias, in contrast to the point-wise tracing 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 spectra in the $d$SC state and pointed out that, due to the Umklapp symmetry of the lattice, there should exist additional peaks in the reciprocal space, but experimentally yet to be found.