Superconductivity in disordered systems close to an incipient localization transition has been an area of investigation for many years. It has been noted that in such highly disordered superconductors, anomalous spectral weight develops in their conductivity near and below the superconducting gap energy. In this work we investigate the low frequency conductivity in disordered superconducting NbN thin films close to the localization transition with time-domain terahertz spectroscopy. In the normal state, strong deviations from the Drude form due to incipient localization are found. In the superconducting state we find substantial spectral weight at frequencies well below the superconducting gap scale derived from tunneling. We analyze this spectral weight in the context of a model of disorder induced broadening of the quasiparticle density of states and effective pair-breaking. We find that although aspects of the optical and tunneling data can be consistently modeled in terms of this effect of mesoscopic disorder, the optical conductivity returns to the normal state value much faster than any model predicts. This points to the non-trivial interplay of superconductivity and disorder close to localization.The manifestation of superconductivity in systems close to a disorder-driven localization transition has been an area of investigation for many years, yet many even central topics are not understood. The electrodynamic response of such systems is a fundamental probe of their low-energy physics but wide-open issues exist here as well. The optical conductivity corresponding to the mean-field Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity was worked out in the context of the celebrated Matthis-Bardeen (MB) theory [1]. A central prediction of the MB theory is the presence of a zero-frequency delta function and a gap 2∆ of a form that depends non-trivially on the BCS coherence factors in the real part of optical conductivity (σ 1 ). This theory works exceptionally well for many superconductors in the "dirty" limit, where the normal state scattering rate (1/τ ) is much larger than the gap, but which are still far from a localization transition [2][3][4]. The MB theory predicts that in the limit of zero temperature, e.g. the gap is clean, there is no spectral weight in σ 1 for frequencies below 2∆. However, it has been noticed for many years that in highly disordered superconductors, for instance in thin-film systems near the superconductor-insulator transition, anomalous spectral weight develops near and below the expected gap edge. This has been observed in many different systems including granular superconductors [5][6][7][8][9], amorphous thin films [10][11][12], and high-temperature superconductors with intrinsic disorder [13,14].In this work we studied the low-frequency conductivity of strongly disordered superconducting NbN thin films close to the localization transition. In the normal state, strong deviations from the Drude form are found, which are indicative of incipient localization in these film...

Correspondence to: matsunaga@issp.u-tokyo.ac.jp †The authors contributed equally.High harmonic generation (HHG), the frequency conversion of an ac electric field, plays a key role in high-speed electronics at terahertz (THz) frequencies as well as in ultrafast photonics. Recent discoveries of material-based HHG have facilitated the search of the best system for high conversion efficiency. Here we report the appearance of strong THz range third harmonics in thin films of Cd3As2, a three-dimensional Dirac semimetal with linearly dispersing electronic states. THz pump-THz probe spectroscopy gives evidence for the microscopic mechanism originating in the coherent acceleration of Dirac electrons in momentum space as theoretically anticipated. The extreme conversion efficiency, which is detectable using only a tabletop THz source and exceeds that of graphene by over a factor of 100 times, paves the way toward novel devices for ultrafast THz electronics and photonics based on topological semimetals.

Dirac and Weyl semimetals with linearly crossing bands are the focus of much recent interest in condensed matter physics. Although they host fascinating phenomena, their physics can be understood in terms of weakly interacting electrons. In contrast, more than 40 years ago, Abrikosov pointed out that quadratic band touchings are generically strongly interacting. We have performed terahertz spectroscopy on the films of the conducting pyrochlore Pr2Ir2O7, which has been shown to host a quadratic band touching. A dielectric constant as large as is observed at low temperatures. In such systems, the dielectric constant is a measure of the relative scale of interactions, which are therefore in our material almost two orders of magnitude larger than the kinetic energy. Despite this, the scattering rate exhibits a T 2 dependence, which shows that for finite doping a Fermi liquid state survives—however, with a scattering rate close to the maximal value allowed.