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The Higgs Particle in Condensed Matter

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The Higgs particle in condensed matter Assa Auerbach, Technion N. H. Lindner and A. A, Phys. Rev. B 81, 054512 (2010) D. Podolsky, A. A, and D. P. Arovas, Phys. Rev. B 84, 174522 (2011)S. Gazit, D. Podolsky, A.A, Phys. Rev. Lett. 110, 140401 (2013); S. Gazit, D. Podolsky, A.A., D. Arovas, Phys. Rev. Lett. 117, (2016). D. Sherman et. al., Nature Physics (2015) S. Poran, et al., Nature Comm. (2017) Outline _ Brief history of the Anderson-Higgs mechanism _ The vacuum is a condensate _ Emergent relativity in condensed matter _ Is the Higgs mode overdamped in d=2? _ Higgs near quantum criticality Experimental detection: Charge density waves Cold atoms in an optical lattice Quantum Antiferromagnets Superconducting films 1955: T.D. Lee and C.N. Yang - massless gauge bosons 1960-61 Nambu, Goldstone: massless bosons in spontaneously broken symmetry Where are the massless particles? 1962 1963 The vacuum is not empty: it is stiff. like a metal or a charged Bose condensate! Rewind t 1911 Kamerlingh Onnes Discovery of Superconductivity 1911 R Lord Kelvin Mathiessen R=0 ! mercury Tc = 4.2K T Meissner Effect, 1933 Metal Superconductor persistent currents Phil Anderson Meissner effect -> 1. Wave fncton rigidit 2. Photns get massive Symmetry breaking in O(N) theory N−component real scalar field : “Mexican hat” potential : Spontaneous symmetry breaking ORDERED GROUND STATE Dan Arovas, Princeton 1981 N-1 Goldstone modes (spin waves) 1 Higgs (amplitude) mode Relativistic Dynamics in Lattice bosons Bose Hubbard Model Large t/U : system is a superfluid, (Bose condensate). Small t/U : system is a Mott insulator, (gap for charge fluctuations). ZimanyiQuantum et. criticalal (1994) Mott insulators Quantum critical incompressible † =0 h i Quantum critical superfluid n2 ( n )2 h j i⇡ h ii Galilean regime Galilean Relativistic Gross Pitaevskii Relativistic Dynamics O(2) model Relativistic Gross Pitaevskii =0 ψ = ∆eiφ h i h i charge excitation gap Higgs-Amplitude mode phase mode (plasmon) strong interactions weak interactions collective excitations Boson t/U “Relativistic Superfluid” Mott insulator 3D O(2) Quantum critical point! classical d+1 model at “temperature” U/t Higgs - Goldstones coupling Fluctuations in the ordered state: (N−1 directions) (1 direction) Harmonic theory Interactions Higgs coupling to 2 Goldstones Is te Higgs mode over damped in d=2? Quantum Critical point Landau theory Symmetric phase Sponateously broken symmetry Quantum Critical point (quantum disordered) order parameter g<gc g = gc g>gc The Higgs decay The Higgs mode can decay into a pair of Goldstone bosons : ! Higgs mode In neutral systems, and for 2D superconductors, Goldstone modes the Goldstones are massless. charged, d=3 d=3 Higgs decay rate is bounded even at strong k coupling d=2 self-energy diverges at low frequency, even at weak coupling : k k + p σ p σ 1 2 ImΣ(!) infrared (Nepomnyaschii) (1978) ∝ ! divergent! Sachdev (1999), Zwerger (2004) | | Behavior of different dynamical correlation functions (Nepomnyaschii)2 (1978) order parameter susceptibility Sachdev (1999), Zwerger (2004) 1 χ11(!)= 1(!) 1( !) !− h − i ⇠ infrared divergent in d=2 scalar susceptibility D. Podolsky, A. A, and D. P. Arovas, PRB (2011) ~ 2 ~ 2 3 χ⇢⇢(!)= (!) ( !) ! infrared regular ⇥| | | | − ⇤ ⇠ in d=2 large N results Higgs peak in scalar response is well defined! vector vs scalar dynamical correlations Longitudinal versus radial perturbations : σ ⇢ Radial motion is less damped, since it is not effected by azimuthal meandering. σ ⇢ What happens to the spectral function near the quantum critical point? Numerical simulations Gazit Podolsky Auerbach PRL (2013), Gazit, Podolsky, AA, Arovas (in preparation) Higgs mass charge gap universal Higgs spectral function Conclusion: Higgs peak is visible close to criticality in d=2 Apr 26, 2013 Birth of a Higgs boson Results from ATLAS and CMS now provide enough evidence to identify the new particle of 2012 as ‘a Higgs mass Narrow Higgs peak —> vacuum is far from criticality Experimental detection: Charge density waves (coupled 1 dimensions) Quantum Antiferromagnets (3 dimensions) Cold atoms in an optical lattice (2 dimensions) Superconducting films (2 dimensions) CDW systems (TbTe3 , DyTe3 , 2H-TaSe2) : R. Yusupov et al., Nature Phys. 6, 681 (2010) QP peak pump t2 probe t3 destruction t1 Higgs phason Fourier transform Magnetic systems in 3 dimensions Heisenberg antiferromagnet O(3) Relativistic H = S S non linear sigma model i · j ij hXii neutron scattering, Headings 2010 Raman scattering Lyons, 1988 Neutrons, Ruegg, 2008 La2CuO4 TlCuCl3 spin waves Higgs Γ k Spin waves = Goldstone modes 2 Magnon = Higgs mode Cold atoms in optical lattices Greiner et. al. NatureI. Bloch 2001 velocity distribution Sponateously broken symmetry superfluid quantum phase transition g<gc Symmetric Mott insulator g>gc g>gc Relativistic Gross Pitaevskii a 1 V j/jc 1 Nambu- Anderson- Goldstone Higgs Mode Mode Im( Re( 2 j/jc 1 Higgs near criticality: 3 j/jc 1 87Rb M. Endres et al., Nature 487, 454 (2012) b lattice loading modulation hold time ramp to temperature atomic measurement 20 limit ) r E ( - Energy absorption rate of periodically 15 modulated lattice Ttot=200 ms 10 Lattice depth A=0.03 V0 5 V0 Tmod=20 0 0 100 200 300 400 Time (ms) V Ψ Critical gaps j = J/U jc Ψ =0 charge gap Higgs mass j Relativistic Gross Pitaevskii Superconductor to Insulator transition in thin films Partial list: Haviland et. al. PRL (1989) Hebard Palaanen PRL (1990) Insulator Yazdani & Kapitulnik (PRL (1995) MoGe Sambandamurthy et. al. PRL (2004) InO Baturina et. al. PRL 99 (2007) M. Chand et. Al, PRB (2009) Theory: Rc Finkelstein, Feigelman, Vinokur, Larkin, Ioffe, Trivedi, Randeria, Ghosal, Shimshoni, AA, Meir, Dubi, Michaeli Josephson coupling Josephson Superconductor O(2) Quantum phase tansiton at T=0 Colectve modes would prove quantum critcalit We find with The finite frequency part is computed from We evaluate this perturbatively in the coupling g. Conductivity diagrams : To lowest order, This yields a threshold at the Higgs mass, with d=3 d=2 Does this change qualitatively at higher orders? D. Sherman et. al., Nature Physics (2015) tunneling gap tunneling gap Higgs mass Higgs gap Rc Rc O(N) model Cartesian vs. polar long range ordered quantum disordered ➙ ! Higgs mode Higgs decays into Summary Goldstone modes scalar is sharper Goldstone bosons than longitudinal k conductivity pseudogap Summary A Higgs (amplitude) mode in condensed matter appears when 1. The dynamics are relativistic. (granular superconductors, cold atoms on optical lattices, antiferromagnets). 2. Near a quantum critical point, when the Higgs mass is low. In two dimensional superconductors, the Higgs mode is visible as a threshold for the AC conductivity. At criticality, the Higgs spectral function scales as a universal peak.
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