Infinite Randomness Fixed Point of the Superconductor-Metal Quantum Phase Transition

We examine the influence of quenched disorder on the superconductor-metal transition, as described by a theory of overdamped Cooper pairs which repel each other. The self-consistent pairing eigenmodes of a quasi-one-dimensional wire are determined numerically. Our results support the recent proposal by Hoyos et al. [Phys. Rev. Lett. 99, 230601 (2007)] that the transition is characterized by the same strong-disorder fixed point describing the onset of ferromagnetism in the random quantum Ising chain in a transverse field.

Figure 1

The equal-time disorder averaged correlation functions for $L=64$ and five values of the mean of ${\alpha }_j$, $\overline{\alpha }$. The solid lines are fits to Eq. (4) via $\xi$ and an overall scale parameter. The inset displays a fit to the power law form of the finite size scaled correlation length, providing an estimate for the location of the critical point ${\overline{\alpha }}_c=-0.93(3)$ and the correlation length exponent $\nu =1.9(2)$.

Figure 2

The finite size scaled value of the disorder averaged logarithm of the minimum excitation energy plotted against the distance from the critical point $\delta$. We observe divergence consistent with the scaling form $|\overline{\ln \Omega }|\sim {\delta }^{-\nu \psi }$, and using the value of ${\overline{\alpha }}_c$ and $\nu$ found above, we determine $\psi =0.53(6)$ from a log-log linear fit (inset).

Figure 3

The real frequency dependence of the finite size scaled value of the disorder averaged susceptibility ratio defined in Eq. (7) for three values of the $\delta =\overline{\alpha }-{\overline{\alpha }}_c$. We observe the predicted $|\ln \omega |$ behavior. After a suitable rescaling described in the text, we find that $\tilde{R}$ does not depend on frequency as $\omega \to 0$ (inset), and a log-log linear fit gives the value of the cluster exponent to be $\varphi =1.6(2)$.