Calculated positions of point nodes in the gap structure of the borocarbide superconductor $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$

To determine the superconducting gap function of $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$, we calculate the local density of states around a single vortex core with the use of Eilenberger theory and the band structure calculated by local density approximation, assuming various gap structures with point nodes at different positions. We also calculate the angular-dependent heat capacity in the vortex state on the basis of the Doppler-shift method. Comparing our results with the scanning tunneling microscopy and spectroscopy experiment, the angular-dependent heat capacity and thermal conductivity, we propose the gap structure of $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$, which has the point nodes and gap minima along ⟨110⟩. Our gap structure is consistent with all results of angular-resolved experiments.

Figure 1

(Color) Tunneling conductance images observed by Nishimori et al. at $0.46\mathrm{K}$ in $0.07\mathrm{T}$ $(72\times 72\mathrm{nm})$ for the bias voltage (a) $0\mathrm{meV}$, (b) $-1.5\mathrm{meV}$, (c) $-2.2\mathrm{meV}$. In this figure, we quoted from Figs. 5(a), 5(c), and 5(e) in Ref. 11. The LDOS images calculated for (d) $ϵ∕{\Delta }_{\infty }=0$, (e) 0.15, (f) 0.3, where $4\sqrt{2}{\xi }_0\times 4\sqrt{2}{\xi }_0$ is shown. Here, ${\Delta }_{\infty }$ denotes a pair potential in the bulk region averaged on the Fermi surface and ${\xi }_0$ denotes a coherent length. The smearing factor is $\delta =0.05{\Delta }_{\infty }$

Figure 2

Cross section including the $\Gamma$ point of FS with the bct Brillouin zone for the 17th band. A solid circle ● and an open circle ○ indicate the positions of point-node and the local minima, respectively. An open triangle ▵, box ◻, and diamond ◇ indicate the $\Gamma$ point, $Z$ point, $X$ point, respectively.

Figure 3

(Color online) Distribution of the pair amplitude on the cross section including the $\Gamma$ point of FS with the bct Brillouin zone for the 17th band.

Figure 4

Angular dependence of specific heat $C_s\propto \nu (ϵ=0,\varphi )$ with use of the band structure of $\mathrm{Y}{\mathrm{Ni}}_2{\mathrm{B}}_2\mathrm{C}$. $\varphi$ is the angle between magnetic field direction and the $a$ axis.

Figure 5

Quasiparticle density of states without magnetic fields. the smearing factor $\delta =0.05{\Delta }_{\infty }$.

Figure 6

(Color online) Distributions of the local density of states for the vortex tilting from the $c$ axis by angle $\theta$ and the $a$ axis by angle $\varphi$. (a) $(\varphi ,\theta )=(0,\pi ∕4)$, (b) $(\varphi ,\theta )=(\pi ∕4,\pi ∕4)$. The smearing factor is $\delta =0.05{\Delta }_{\infty }$ and the energy is $ϵ=0.3{\Delta }_{\infty }$. These LDOS patterns will be observed by the STM/STS experiments from the $c$ axis.