Rotational Symmetry Breaking in Sodium Doped Cuprates

For reasonable parameters a hole bound to a Na^{+} acceptor in Ca_{2-x}Na_{x}CuO_{2}Cl_{2} has a doubly degenerate ground state whose components can be represented as states with even (odd) reflection symmetry around the x(y) -axes. The conductance pattern for one 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 is reduced at higher voltages. Qualitative agreement with recent experiments leads us to propose this effect as an explanation of the broken local rotational symmetry.