Dynamical conductivity across the disorder-tuned superconductor-insulator transition

We study the superconductor-insulator transition (SIT) in both clean and disordered systems by calculating the dynamical conductivity $\sigma (\omega )$ and the bosonic (pair) spectral function $P(\omega )$ using quantum Monte Carlo simulations. We identify characteristic energy scales in the superconducting and insulating phases that vanish at the transition due to enhanced quantum fluctuations, despite the persistence of a robust fermionic gap across the SIT [1]. While $\sigma (\omega )$ shows a energy scale for absorption associated with a Higgs (amplitude) mode in the clean superconductor, disorder leads to enhanced low frequency absorption in $\sigma (\omega )$ on both the superconducting and insulating side of the transition. Disorder also expands the quantum critical region, due to a change in the universality class, with an underlying $T =$ 0 critical point with a universal low-frequency conductivity $\sigma $* $\cong $ 0.5 (4e$^{2}$/h) [2]. \\[4pt] [1] K. Bouadim, Y.L. Loh, M. Randeria, and N. Trivedi, \textit{Nat. Phys.} 7 884 (2011)\\[0pt] [2] M. Swanson, Y.L. Loh, M. Randeria, and N. Trivedi\textit{, arXiv} 1310.1073 (2013)