Dynamical Conductivity across the Disorder-Tuned Superconductor-Insulator Transition

Abstract

We calculate the dynamical conductivity σðωÞ and the bosonic (pair) spectral function PðωÞ from quantum Monte Carlo simulations across clean and disorder-driven superconductor-insulator transitions (SITs). 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. Disorder leads to enhanced absorption in σðωÞ at low frequencies compared to the SIT in a clean system. Disorder also expands the quantum critical region, due to a change in the universality class, with an underlying T ¼ 0 critical point with a universal low-frequency conductivity σ Ã ≃ 0.5ð4e 2 =hÞ.

Amplitude Mode in Three-Dimensional Dimerized Antiferromagnets

“…4(c). At the mean-field level, we estimate the constant ratios σ S /∆ H = 0.15(4) and σ D /∆ H = 0.43 (6). The log dependence on |g − g c | is too weak to discern given the quality of the present data and the separation from the critical point.…”

“…In loose analogy with the Standard Model, the latter is often called a Higgs mode. A strongly damped amplitude mode has been reported in two dimensions (2D) at the Mott transition of ultracold bosons [5] and at the disorder-driven superconductorinsulator transition [6,7]. In 3D, the amplitude mode is expected on theoretical grounds to be more robust, and indeed the cleanest observation to date of a "Higgs boson" in condensed matter is at the pressure-induced magnetic quantum phase transition (QPT) in the dimerized quantum antiferromagnet TlCuCl 3 [8][9][10].…”

Quantum critical response: from conformal perturbation theory to holography

“…We expect this randomness to modify the form of the asymptotic expansion (1.3); such an analysis could be performed in large-N vector models or in holography. This generalization would be relevant for recent numerical simulations that yielded the dynamical conductivity across the disorder-tuned superconductor-insulator transition [9].…”

“…Because interesting quantum critical theories are strongly coupled and lack long-lived quasiparticle excitations, obtaining quantitative predictions for critical dynamical response functions, where both quantum and thermal fluctuations must be accounted for, has proven to be challenging. In this respect, quantum Monte Carlo studies have proven useful to obtain the response functions in imaginary time [5][6][7][8][9]. The precise analytic continuation to real frequencies of such data constitutes a difficult open problem.…”

Superconductor-Insulator Transition and Fermi-Bose Crossovers

“…In the disordered case, ω pair was obtained [21] only after considerable numerical effort by analytically continuing imaginary-time DQMC data to real frequencies. In addition, Griffiths effects due to rare regions give rise to spectral weight at arbitrarily low energies in the two-particle spectral function [21,38]. Thus, the ω pair is a well-defined scale, but not a hard gap in the disordered case.…”