The concept of mass-generation via the Higgs mechanism was strongly inspired by earlier works on the Meissner-Ochsenfeld effect in superconductors. In quantum field theory, the excitations of longitudinal components of the Higgs field manifest as massive Higgs bosons. The analogous Higgs mode in superconductors has not yet been observed due to its rapid decay into particle-hole pairs. Following recent theories, however, the Higgs mode should decrease below the pairing gap 2∆ and become visible in two-dimensional systems close to the superconductor-insulator transition (SIT). For experimental verification, we measured the complex terahertz transmission and tunneling density of states (DOS) of various thin films of superconducting NbN and InO close to criticality. Comparing both techniques reveals a growing discrepancy between the finite 2∆ and the threshold energy for electromagnetic absorption which vanishes critically towards the SIT. We identify the excess absorption below 2∆ as a strong evidence of the Higgs mode in two dimensional quantum critical superconductors.The Higgs mechanism, which has great implications to recent developments in particle physics [1], originates in Anderson's pioneering work on symmetry breaking with gauge fields in superconductors [2]. A superconductor spontaneously breaks continuous U (1) symmetry and acquires the well-known Mexican hat potential with a degenerate circle of minima described by the order parameter Ψ = Ae iϕ , see Fig. 1a. Excitations from the ground state can be classified as transverse Nambu-Goldstone (phase) modes and massive longitudinal Higgs (amplitude) modes (see blue and red lines in Fig. 1a). In particle physics, the latter manifest themselves as the Higgs boson which was recently discovered at CERN [3]. Indications of a Higgs mode in correlated many-body systems have been found in one-dimensional charge-densitywave systems [4], quantum antiferromagnets [5] and twodimensional superfluid to Mott transition in cold atoms [6]. An amplitude mode, also named Higgs mode, was theoretically predicted for superconductors [7] and recently reported to be measured by pump-probe spectroscopy [8]. This amplitude mode describes pairing fluctuations, which are qualitatively distinct from the purely bosonic mode expected from the O(2) field theory. The Higgs-amplitude mode analogous to the highenergy Higgs Boson has not yet been observed in superconductors. A partial reason is that in homogeneous, BCS superconductors the Higgs mode is short-lived and decays to particle hole (Bogoliubov) pairs [9,10]. Nevertheless, collective modes were recently predicted to be significant in strongly disordered superconductors [11], and, in particular it was shown [12][13][14] that the Higgs mode softens but remains sufficiently sharp near a quantum critical point (QCP) in two dimensions since it is found to be a critical energy scale of the quantum phase transition. Hence, the Higgs mass can be reduced below twice the pairing gap, 2∆, making this mode experimentally visible. Such a critical...

Deterministic enhancement of the superconducting (SC) critical temperature T c is a longstanding goal in material science. One strategy is engineering a material at the nanometer scale such that quantum confinement strengthens the electron pairing, thus increasing the superconducting energy gap ∆ [1-6], as was observed for individual nanoparticles [7]. A true phasecoherent SC condensate, however, can exist only on larger scales and requires a finite phase stiffness J [13]. In the case of coupled aluminium (Al) nanograins [8][9][10], T c can exceed that of bulk Al by a factor of three, but despite several proposals the relevant mechanism at play is not yet understood. Here we use optical spectroscopy on granular Al to disentangle the evolution of the fundamental SC energy scales, ∆ and J, as a function of grain coupling. Starting from wellcoupled arrays, ∆ grows with progressive grain decoupling, causing the increasing of T c . As the grain-coupling is further suppressed, ∆ saturates while T c decreases, concomitantly with a sharp decline of J. This crossover to a phase-driven SC transition is accompanied by an optical gap persisting above T c . These findings identify granular Al as an ideal playground to test the basic mechanisms that enhance superconductivity by nanoinhomogeneity.Bulk samples of pure Al represent a prototypical BCS superconductor (SC) with relatively low T c0 ≈ 1.2 K. Several studies since the late 1960s [8][9][10] have shown a quite different situation for granular Al, i.e. thin films composed of 2 nm grains separated by thin insulating barriers, where a superconducting condensate is established via Josephson-coupling across the grain array. The coupling between the grains can be controlled during film growth, leading to samples with strong coupling and low resistivity (LR) in electrical transport compared to high resistivity (HR) samples with weak intergrain coupling. In LR samples T c can be enhanced up to several times T c0 , whereas it is suppressed to zero in HR samples, shaping a superconducting dome in the phase diagram, see Fig. 1(a).To understand the behavior of T c it is crucial to access the underlying SC energy scales associated with the amplitude and phase of the complex order parameter ψ = ∆e iφ . Indeed, while the SC energy gap ∆ measures the pairing strength between the electrons, the true superfluid behavior can only be established if the Cooper pairs acquire the same macroscopic SC phase φ. The energy scale controlling the rigidity of the condensate with respect to a deformation of this collective phase-coherent state is the so-called superfluid stiffness J. In ordinary BCS superconductors J exceeds ∆ by orders of magnitudes, and the SC transition at T c is amplitude-driven. However, in the unconventional situation where ∆ exceeds J the transition is expected to be phase-driven, due to the loss of phase coherence at a temperature scale of order of J. Consequently, even though several finite-size effects have been proposed to explain the enhancement of ∆ in isolated nano-grai...

Abstract-We report on terahertz frequency-domain spectroscopy (THz-FDS) experiments in which we measure charge carrier dynamics and excitations of thin-film superconducting systems at low temperatures in the THz spectral range. The characteristics of the set-up and the experimental procedures are described comprehensively. We discuss the single-particle density of states and a theory of electrodynamic absorption and optical conductivity of conventional superconductors. We present the experimental performance of the setup at low temperatures for a broad spectral range from 3 to 38 cm -1 (0.1 -1.1 THz) by the example of ultra-thin films of weakly disordered superconductors niobium nitride (NbN) and tantalum nitride (TaN) with different values of critical temperatures Tc. Furthermore, we analyze and interpret our experimental data within the framework of conventional Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. By and large, we find the properties of our NbN and TaN thin films to be well described by the theory. Our results on NbN resemble tendencies towards anomalous behavior of the ratio 2∆(0)/kBTc as a function of Tc.Index Terms-Frequency-domain THz spectroscopy, superconducting thin films, BCS theory, density of states of a superconductor, optical conductivity of superconductors, superconductorinsulator transition, TaN, NbN.

We have prepared high-quality epitaxial thin films of CaRuO 3 with residual resistivity ratios up to 55. Shubnikov-de Haas oscillations in the magnetoresistance and a T 2 temperature dependence in the electrical resistivity only below 1.5 K, whose coefficient is substantially suppressed in large magnetic fields, establish CaRuO 3 as a Fermi liquid (FL) with anomalously low coherence scale. Non-Fermi liquid (NFL) T 3/2 dependence is found between 2 and 25 K. The high sample quality allows access to the intrinsic electronic properties via THz spectroscopy. For frequencies below 0.6 THz, the conductivity is Drude-like and can be modeled by FL concepts, while for higher frequencies non-Drude behavior, inconsistent with FL predictions, is found. This establishes CaRuO 3 as a prime example of optical NFL behavior in the THz range.PACS numbers:

We report on the charge carrier dynamics of superconducting titanium nitride (TiN) in the frequency range 90 -510 GHz (3 -17 cm −1 ). The experiments were perfomed on a 18 nm thick TiN film with a critical temperature of Tc = 3.4 K. Measurements were carried out from room temperature down to 2 K, and in magnetic fields up to B = 7 T. We extract the real and imaginary parts of the complex conductivityσ as a function of frequency and temperature, directly providing the superconducting energy gap 2∆. Further analysis yields the superconducting London penetration depth λL. The findings as well as the normal state properties strongly suggest conventional BCS superconductivity, underlined by the ratio 2∆(0)/kB Tc = 3.44. Detailed analysis of the charge carrier dynamics of the silicon substrate is also discussed.