Model for Vortex-Core Tunneling Spectroscopy of Chiral $p$-Wave Superconductors via Odd-Frequency Pairing States

The local density of states is studied theoretically in terms of the odd-frequency (odd-$\omega$) Cooper pairing induced around a vortex core. We find that a zero energy peak in the density of states at the vortex center is robust against nonmagnetic impurities in a chiral $p$-wave superconductor owing to an odd-$\omega$ $s$-wave pair amplitude. We suggest how to discriminate a spin-triplet pairing symmetry and spatial chiral-domain structure by scanning tunneling spectroscopy via odd-$\omega$ pair amplitudes inside vortex cores.

Figure 1

(a) Spatial dependence of the odd-$\omega$ pair amplitudes (${\omega }_{n=0}$), and (b) the corresponding LDOS for the $s$-wave vortex with $\Gamma =0.1{\Delta }_0$ (left panel) and $0.3{\Delta }_0$ (right panel).

Figure 2

Spatial dependence of the pair potentials and the odd-$\omega$ pair amplitudes (${\omega }_{n=0}$) for the chiral $p$-wave vortices with $\Gamma =0.1{\Delta }_0$ (left panel) and $0.3{\Delta }_0$ (right panel). The $p$-wave pair potentials are normalized by bulk value of the $p_{-}$-wave one.

Figure 3

The LDOS at the vortex center for (a) the antiparallel and (b) the parallel vortex. The dashed and solid lines are plots for $\Gamma =0.1{\Delta }_0$ and $0.3{\Delta }_0$, respectively.

Figure 4

Schematic illustration of STS/STM measurements to detect the odd-$\omega$ pair amplitude for (a) the antiparallel and (b) the parallel vortex in chiral $p$-wave SCs. The arrows represent the phase rotations.

Figure 5

The ZEP in the LDOS at the vortex center as a function of $\Gamma$. The lines are guides for the eye. Inset: the odd-$\omega$ pair amplitudes (${\omega }_{n=0}=\pi T$) at the vortex center as functions of $\Gamma$. The $s$-wave (circle) and $d_{-}$-wave (triangle) pair amplitudes are plotted for the antiparallel and parallel vortices, respectively (see also Fig. 2). Each pair amplitude is normalized by its value at $\Gamma =0$. The solid curve represents the Abrikosov-Gorkov law [20].