A dichotomy between nodal and antinodal excitations and competing order in high temperature superconductors

ARPES and STM reveal that the electronic excitations near the nodes and antinodes have very different characteristics. The nodal excitations are quasiparticle-like and the nature of antinodal excitations depends on temperature, doping, and other material details. This nodal-antinodal dichotomy is manifested most dramatically in the recent recent STM experiment that reveal a checkerboard order in the Na doped Ca$_2$CuO$_2$Cl$_2$. The constraint of this dichotomy on theories will be discussed.