Rotational symmetry breaking in the ground state of sodium-doped cuprate superconductors

We use an extended t-J model to study a single hole bound to a Na+ acceptor in Ca2-xNaxCuO2Cl2. For parameters suitable to cuprates, the ground state has a twofold degeneracy, corresponding to even (odd) reflection symmetry around the x (y) axes. The conductance pattern of the broken symmetry state is anisotropic as the tip of a tunneling microscope scans above the Cu-O-Cu bonds along the x (y) axes. This anisotropy is pronounced at lower voltages but reduced at higher voltages. Our theory agrees qualitatively with recent data of scanning tunneling microscopy showing broken local rotational symmetry.