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We use an extended t-J model to study a single hole bound to a Na⁺ acceptor in Ca_2-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.
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Chen et al. (2006) studied this question.
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