Field-angle resolved flux-flow resistivity as a phase-sensitive probe of unconventional Cooper pairing

We theoretically investigate the applied magnetic field-angle dependence of the flux-flow resistivity ${\rho }_{\mathrm{f}}\left({\alpha }_{\mathrm{M}}\right)$ for a uniaxially anisotropic Fermi surface. ${\rho }_{\mathrm{f}}$ is related to the quasiparticle scattering rate inside a vortex core, which reflects the sign change in the superconducting pair potential. We find that ${\rho }_{\mathrm{f}}\left({\alpha }_{\mathrm{M}}\right)$ is sensitive to the sign change in the pair potential and has its maximum when the magnetic field is parallel to the gap-node direction. We propose the measurement of the field-angle dependent oscillation of ${\rho }_{\mathrm{f}}\left({\alpha }_{\mathrm{M}}\right)$ as a phase-sensitive field-angle resolved experiment.

Figure 1

The schematic figures of (a) the forward scattering and (b) the backward scattering in the vicinity of a vortex. $s$ and $s^{\prime }$ indicate the QP trajectory before and after scattering, respectively.

Figure 2

Field-angle (${\alpha }_{\mathrm{M}}$) dependence of the flux-flow resistivity ${\rho }_{\mathrm{f}}$ in the case of (a) a line-node $s$ wave and (b) a $d$-wave pair for a spheroidal FS ($\gamma =3$). Each curve indicates a different temperature. The vertical axis is normalized by the minimum value of ${\rho }_{\mathrm{f}\min }$ for each plot.

Figure 3

${\mathit{k}}_{\mathrm{F}}$ dependence of $\Gamma$ in the case of (a) the line-node $s$-wave pair when $\mathit{H}$ is parallel to the gap-node direction, (b) the $d$-wave pair when $\mathit{H}$ is parallel to the gap-node direction, (c) the line-node $s$-wave pair when $\mathit{H}$ is parallel to the antinode direction, and (d) the $d$-wave pair when $\mathit{H}$ is parallel to the antinode direction on a spheroidal FS ($\gamma =3$). The quasiparticle energy $\varepsilon$ is set to $0.2{\Delta }_0$ in each plot. The vertical and horizontal axes denote the polar angle ${\theta }_k$ and the azimuthal angle ${\varphi }_k$, respectively. The dotted lines indicate the antinode directions. The field directions are indicated by arrows.

Figure 4

Field-angle (${\alpha }_{\mathrm{M}}$) dependences of the part of $\Gamma$ containing the coherence factor and the other part of it for the $d$-wave pair with the spheroidal FS. The vertical axis is normalized by the minimum value.

Figure 5

Schematic figure of the forward QP scattering, which is characterized by the angle between the projections of the Fermi velocities onto the plane perpendicular to an in-plane magnetic field $\mathit{H}$.