Electronic states around a columnar defect in d-wave superconductors

Electronic states around a columnar defect in d-wave superconductors are studied within a quasi-classical approximation. It is shown that the local density of states at zero energy has peaks near (1, 1; 0) and ((1) over bar, 1, 0) direction boundaries of the columnar defect. In contrast to the zero energy the local density of states at the gap (peak) energy is lower near these directions. These properties are qualitatively consistent with an experiment which has been recently performed to study the local electronic structure around a columnar defect in Bi2Sr2CaCu2Ox using scanning tunneling spectroscopy.