Amplitude / Higgs Modes in Condensed Matter Physics

Abstract

The order parameter and its variations in space and time in many different states in condensed matter physics at low temperatures are described by the complex function $\Psi (\mathbf{r},t)$. These states include superfluids, superconductors, and a subclass of antiferromagnets and charge-density waves. The collective fluctuations in the ordered state may then be categorized as oscillations of phase and amplitude of $\Psi (\mathbf{r},t)$. The phase oscillations are the {\it Goldstone} modes of the broken continuous symmetry. The amplitude modes, even at long wavelengths, are well defined and decoupled from the phase oscillations only near particle-hole symmetry, where the equations of motion have an effective Lorentz symmetry as in particle physics, and if there are no significant avenues for decay into other excitations. They bear close correspondence with the so-called {\it Higgs} modes in particle physics, whose prediction and discovery is very important for the standard model of particle physics. In this review, we discuss the theory and the possible observation of the amplitude or Higgs modes in condensed matter physics -- in superconductors, cold-atoms in periodic lattices, and in uniaxial antiferromagnets. We discuss the necessity for at least approximate particle-hole symmetry as well as the special conditions required to couple to such modes because, being scalars, they do not couple linearly to the usual condensed matter probes.

39 pages, 12 figures. Replaced with published version; Annual Reviews of Condensed Matter Physics Volume 6 (2015)

References in corpus (10)

• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• Synchronization in the BCS Pairing Dynamics as a Critical Phenomenon
• Dynamical properties of ultracold bosons in an optical lattice
• Collective coherence in planar semiconductor microcavities
• Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering
• The Higgs mode in a two-dimensional superfluid
• The Amplitude Mode in the Quantum Phase Model

Cited by in corpus (35)

• Quantum Nanophotonics in Two-Dimensional Materials
• Goldstone mode and pair-breaking excitations in atomic Fermi superfluids
• Quantum quench phase diagrams of an s-wave BCS-BEC condensate
• Higgs mode in a strongly interacting fermionic superfluid
• Nonlinear electromagnetic response and Higgs mode excitation in BCS superconductors with impurities
• Nonlinear optical response of collective modes in multiband superconductors assisted by nonmagnetic impurities
• Nonlocal Andreev Entanglements and Triplet Correlations in Graphene with Spin Orbit Coupling
• Twisting Anderson pseudospins with light: Quench dynamics in THz-pumped BCS superconductors
• Direct observation of the Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point
• Higgs criticality in a two-dimensional metal
• Spinon Confinement and a Sharp Longitudinal Mode in Yb${}_2$Pt${}_2$Pb in Magnetic Fields
• Correlation-induced superconductivity dynamically stabilized and enhanced by laser irradiation
• Lightwave Terahertz Quantum Manipulation of Non-equilibrium Superconductor Phases and their Collective Modes
• Spectral function of the Higgs mode in 4-\varepsilon dimensions
• Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems
• Collective dynamics and the Anderson-Higgs mechanism in a bona fide holographic superconductor
• Dynamical structure factors of a two-dimensional Fermi superfluid within random phase approximation
• Pure Goldstone mode in the quench dynamics of a confined ultracold Fermi gas in the BCS-BEC crossover regime
• Quasi-two-dimensional Bose-Einstein condensation of spin triplets in dimerized quantum magnet Ba${}_2$CuSi${}_2$O${}_6$Cl${}_2$
• Order parameter fluctuation and ordering competition in $\mathrm{B}{\mathrm{a}}_{1-\mathrm{x}}{\mathrm{K}}_{\mathrm{x}}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Anomalous Magnetoresistance due to Longitudinal Spin Fluctuations in a Jeff = 1/2 Mott Semiconductor
• Van Vleck excitons in Ca${}_2$RuO${}_4$
• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$
• Dark matter candidate with well-defined mass and couplings
• Electron-momentum dependence of electron-phonon coupling underlies dramatic phonon renormalization in YNi${}_2$B${}_2$C
• Goldstone and Higgs Hydrodynamics in the BCS-BEC Crossover
• Higgs and Nambu-Goldstone modes in condensed matter physics
• Localized Higgs modes of superfluid Bose gases in optical lattices: A Guzwiller mean-field study
• Topological Higgs Amplitude Modes in Strongly Interacting Superfluids
• Total Moment Sum Rule for Magnets in the Vicinity of Quantum Critical Point
• Signatures of Bardasis-Schrieffer mode excitation in Third-Harmonic generated currents
• Collective terahertz fluctuation modes in a polariton laser
• Linear response of a superfluid Fermi gas inside its pair-breaking continuum
• Gauge couplings in a multicomponent dark matter scenario