Evaluation of Doppler shifts in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductor tunneling junctions

The energy levels of quasiparticles in superconductors experience Doppler shifts due to the influence of a finite current flow. The influence of the Doppler shift is particularly pronounced in unconventional superconductors with gap nodes. In the case of a normal/insulator/superconductor junction of a $d$-wave superconductor, a zero-bias conductance peak exhibits a peak shift in an applied magnetic field. Although the shifts have been detected in past experiments, the shifts showed different field responses depending on each experiment. In this paper, we evaluate the magnitudes of the shift based on realistic junction shapes to elucidate the origin of the variability in experimental Doppler shifts. We find that the peak shift depends on the junction shape; the splitting is significantly suppressed when the junction is formed at a protruding position. Also, the shifts are suppressed by the penetration of magnetic flux quanta, resulting in nonlinear responses to the applied field. The present results explain the origin of the variability in experimental Doppler shifts.