Impurities in carbon nanotubes give rise to rich physics due to the honeycomb lattice structure. We concentrate on the conductance through a point-like defect in metallic zigzag carbon nanotube via the Landauer-B‥uttiker approach. At low bias, the conductance is suppressed due to the presence of an additional impurity state existing only on one of the sublattices. In consequence, the suppression is exactly half of the perfect conductance without impurity. Furthermore, there exists a transport resonance at larger bias where the perfect conductance is recovered as if the impurity were absent. Implications of these conductance
anomalies are elaborated and experimental detections in realistic carbon nanotubes are also discussed.

1 Introduction
2 Impurity states in zigzag carbon nanotubes
2.1 Partial Fourier transformation application in zigzag carbon nanotubes
2.2 Generalized Bloch theory
2.3 Electronic property in zigzag nanotubes
2.4 Speci‾c cases in zigzag nanotubes
2.4.1 Single vacancy defect in zigzag nanotubes
2.4.2 Single point-like defect in semiconducting zigzag nan-
otubes
3 Transport properties in metallic zigzag carbon nanotubes
with single defect
3.1 Landauer-Buttiker formula
3.2 Friedel sum rule
3.3 Conductance for metallic zigzag nanotube with single defect in low energy regime
3.4 Conductance, Backward conductance and scattering phase analysis
4 Theoretical analysis of conductance and phase
4.1 Traditional scattering theory
4.1.1 S matrix and T matrix
4.1.2 Optical theorem
4.2 Tunneling regime for single dot problem
4.3 Scattering regime for single channel one dimensional case
5 Conclusion and outlook

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