Shot Noise and Multiple Andreev Reflections in $d$-Wave Superconductors

We present a theoretical analysis of the shot noise in $d\mathrm{\text{-wave}}/d\mathrm{\text{-wave}}$ contacts with arbitrary transparency, including the contribution of multiple Andreev reflections. The multiple charge quanta transferred in these processes are revealed as a huge enhancement of the noise-current ratio at low voltages, which survives for all crystal misorientations. We also show how different ingredients such as nonmagnetic impurities or a magnetic field produce very characteristic hallmarks in the shot noise, which can be used as a further test of the $d$-wave scenario in superconducting cuprates.

Figure 1

$d_0\mathrm{\text{−}}{d}_0$ contact in the clean case: (a) angle-resolved shot noise as a function of the voltage in units of the trajectory gap for different transmissions. $G_N$ is the normal state conductance. (b) Angle-resolved effective charge, $q=S/2I$. (c) Angle-averaged shot noise. The voltage is normalized by the maximum gap $\Delta$. (d) Angle-averaged effective charge.

Figure 2

$d_{\pi /4}\mathrm{\text{−}}{d}_{-\pi /4}$ contact in the clean case: (a) shot noise as a function of voltage for different transmissions. (b) Effective charge vs voltage. The curves were computed using a small inelastic broadening ($\sim 0.003\Delta$). Inset: local DOS at the interface for a $45°$ misorientation for different values of the bulk-impurity scattering rate $\Gamma$ (Born scatterers), measured in units of $2\pi T_C$, where $T_C$ is the critical temperature in the clean case. $\Delta$ is the maximum bulk gap for the clean superconductor.

Figure 3

Shot noise and effective charge as a function of voltage for a $d_{\pi /4}\mathrm{\text{−}}{d}_{-\pi /4}$ contact for two values of the bulk-impurity scattering rate $\Gamma$.

Figure 4

Differential shot noise of a clean $d_{\pi /4}\mathrm{\text{−}}{d}_{-\pi /4}$ junction with $D=0.2$ and different values of the magnetic field. The curves have been vertically displaced for clarity and dotted lines have been added to guide the eye.