Atomic scale rotational symmetry breaking in lightly doped Ca2−xNaxCuO2Cl2

We study the ground state and the conductance in the single hole t-t′-J model with impurity potential on center square of small clusters using an exact diagonalization method. The ground state may be doubly degenerate with each state breaking the rotational symmetry. The interference of tunneling in one of the degenerated states may explain the origin of atomic scale rotational asymmetry. The asymmetry is pronounced at lower voltages but is reduced at higher voltages. Our results agree qualitatively with recent STM experiments in Ca2−xNaxCuO2Cl2.