The local density of states ͑LDOS͒ and its Fourier component induced by a unitary impurity in a supercurrent-carrying d-wave superconductor are investigated. Both of these quantities possess a reflection symmetry about the line passing through the impurity site and along the supercurrent if it is applied along the antinodal or nodal direction. With increasing supercurrent, both the coherence and resonant peaks in LDOS are suppressed and slightly broadened. Under a supercurrent along the antinodal direction, the coherence peaks split into double peaks. The modulation wave vectors associated with the elastic scatterings of quasiparticles by the defect from one constant-energy piece of the Fermi surface to another are displayed as bright or dark spots in the Fourier space of the LDOS image, and they may be suppressed or enhanced and shifted, depending on the applied current and the bias voltage. The understanding of the local physics in cuprate or hightemperature superconductors ͑HTS͒ is one of the most challenging problems in condensed matter physics today. Different from the conventional s-wave superconductors, the HTS have very complex phase diagrams depending on doping and chemical composition. It is also well established that the superconducting order parameter in the cuprates has predominantly d-wave symmetry.1 The zero-bias conductance peak ͑ZBCP͒ in the tunneling spectroscopy of normal metalcuprate superconductor junction with non-͑n0m͒-directional contact provides one of the direct evidences for this symmetry.2 Due to the d-wave nature of the order parameter, impurities inserted into cuprates can serve as an important tool to explore the physics of HTS. Theoretical calculations of the local density of states ͑LDOS͒ predicted that a strong potential scatterer could induce a resonance peak near the Fermi level at sites near the impurity. 3,4 This resonant peak near zero-bias voltage was observed at and near the sites of Zn impurities in Bi 2 Sr 2 CaCu 2 O 8+␦ by scanning tunneling microscopy ͑STM͒.5 In addition, an interference pattern with fourfold symmetry was also detected in the STM image.
5When a superconductor carries a supercurrent ͑J s ͒, Cooper pairs with finite momentum appear in the system. This would drastically affect the electronic structure of the superconductor, including the elementary excitation spectrum, the order parameter symmetry, and the tunneling spectroscopy.6-8 With increasing supercurrent velocity, the superconducting order parameter can be depressed. Meanwhile, the supercurrent density first increases monotonously and then arrives at a maximum value, which is called the critical current density. Beyond that, superconductivity becomes unstable and collapses to the normal state. So the supercurrent in the stable regime can be also used as a probe to further understand the quasiparticle excitations in HTS. Moreover, a better understanding of the property of a superconductor under an applied J s may have the potential for device applications.In Ref. 7, we have studied the tunneling co...