The Higgs mode in disordered superconductors close to a quantum phase transition

Abstract

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...

Towards properties on demand in quantum materials

“…4d), including the recent observation of the Higgs mode 86 in a disordered superconductor and in NbN using time-resolved terarhertz spectroscopy 87 .…”

Higgs mode and its decay in a two-dimensional antiferromagnet

“…Therefore, its rapid decay in the longitudinal susceptibility measured by INS does not necessarily imply its instability in two dimensions. In fact, it has been shown in other two-dimensional systems, such as disordered superconductors 3 and superfluids of cold atoms 2 , that the Higgs mode is clearly visible in the scalar susceptibility with its characteristic ∼ω 3 onset in the energy spectrum. Indeed, theory predicts a contrasting behaviour of the Higgs mode in the scalar and longitudinal susceptibilities; in the latter, the Higgs mode quickly loses its coherence by decaying into a pair of Goldstone modes 25,26 .…”

“…Evidence for the Higgs mode has been reported in a number of di erent settings, including ultracold atomic gases 2 , disordered superconductors 3 , and dimerized quantum magnets 4 . However, decay processes of the Higgs mode (which are eminently important in particle physics ) have not yet been studied in condensed matter due to the lack of a suitable material system coupled to a direct experimental probe.…”

The Higgs mechanism and superconductivity: A case study of formal analogies

“…Perhaps surprisingly, it took even longer to obtain experimental verification of the Anderson-Bogoliubov mode corresponding to the Higgs boson in a superconductor than it did to obtain experimental evidence for the Higgs boson! (See Anderson (2015) and Sherman et al (2015).) Does the Anderson-Bogoliubov collective mode supply an analogical template for physically interpreting the Higgs boson?…”