Low-lying excitations induced by non-magnetic impurities in d-wave superconductors

This theoretical study shows low-lying excitations induced by a non-magnetic impurity in a d-wave superconductor. Results in the real coordinate are fully calculated by using the Bogoliubov-de Gennes theory. For the same condition other results are also calculated by using the Born approximation. The comparison with the Fourier transformation shows that these results are almost identical. We have performed numerical calculations for low-lying excitations induced by a single non-magnetic impurity in a d-wave superconductor on the basis of two different frameworks. One is the Bogoliubov-de Gennes theory in real coordinates, while the other is the Born approximation in wave-number coordinates. This paper shows that these results for low-lying excitations are identical by using Fourier transformations.