Supercurrent in nodal superconductors

In recent years, a number of nodal superconductors have been identified; $d$-wave superconductors in high $T_c$ cuprates, ${\mathrm{CeCoIn}}_5$ and $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}\left(\mathrm{NCS}\right)}_2$, two-dimensional (2D) $f$-wave superconductor in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, and hybrid $s+g$-wave superconductor in ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$. In this work we conduct a theoretical study of nodal superconductors in the presence of supercurrent. For simplicity, we limit ourselves to $d$-wave and 2D $f$-wave superconductors. We compute the quasiparticle density of states and the temperature dependence of the depairing critical current in nodal superconductors, both of which are accessible experimentally.

Figure 1

Quasiparticle DOS $g(E,s)$ given in Eq. (7).

Figure 2

Quasiparticle DOS $g(E,s)$ given in Eq. (9).

Figure 3

Quasiparticle DOS $g(E,s)$ given in Eq. (10).

Figure 4

Quasiparticle DOS $g(E,s)$ given in Eq. (12).

Figure 5

Zero temperature order parameter as a function of $s$, as defined by Eq. (15).

Figure 6

Zero temperature supercurrent as a function of $s$, given in Eq. (18). Note that the $J_0$ differs by a factor of $v_{Fc}∕v_F$ between the in-plane and $c$-axis cases.

Figure 7

Depairing critical current as a function of temperature, defined by the maximum value of $j_s$ [Eq. (19)] for given $T$.