Chirality Sensitive Effect on Surface States in Chiral $p$-Wave Superconductors

We study the local density of states at the surface of a chiral $p$-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the $p$-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.

Figure 1

$N(E=0)$ in a chiral $p$-wave superconductor in the presence of a vortex, which is situated at a distance of $x_V=2\xi$ from the surface. The vortex and the $p$-wave state have (a) the same chirality and (b) the opposite chirality. Clearly, there is a remarkable difference in the quasiparticle spectral weight at the surface ($x=0$) behind the vortex, showing a strong increase in (a) and a suppression in (b).

Figure 2

Local DOS at the point $x=y=0$ for different vortex to boundary distances $x_V$ as a function of energy. Again, $p$-wave state and Abrikosov vortex have the same chirality in (a) and the opposite in (b), resulting in peak and dip structures, respectively, around zero energy.