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...
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.
This Letter examines the relation between the spin-wave instabilities of collinear magnetic phases and the resulting noncollinear phases for a geometrically frustrated triangular-lattice antiferromagnet in the high-spin limit. Using a combination of phenomenological and Monte Carlo techniques, we demonstrate that the instability wave vector with the strongest intensity in the collinear phase determines the wave vector of a cycloid or the dominant elastic peak of a more complex noncollinear phase. Our results are related to the observed multiferroic phase of Al-doped CuFeO2.
This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically frustrated triangular-lattice antiferromagnet ͑TLA͒. Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the one-, two-, three-, four-, and eight-sublattice ͑SL͒ ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The two-, four-, and eight-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the critical anisotropy is a continuous function everywhere except across the two-SL/three-SL and three-SL/four-SL phase boundaries, where the three-SL phase has the higher critical anisotropy.
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