DOCSLIB.ORG

The Higgs Particle in Condensed Matter

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Higgs Particle in Condensed Matter 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.
Load more

Recommended publications
  • Two-Plasmon Spontaneous Emission from a Nonlocal Epsilon-Near-Zero Material ✉ ✉ Futai Hu1, Liu Li1, Yuan Liu1, Yuan Meng 1, Mali Gong1,2 & Yuanmu Yang1
    ARTICLE https://doi.org/10.1038/s42005-021-00586-4 OPEN Two-plasmon spontaneous emission from a nonlocal epsilon-near-zero material ✉ ✉ Futai Hu1, Liu Li1, Yuan Liu1, Yuan Meng 1, Mali Gong1,2 & Yuanmu Yang1 Plasmonic cavities can provide deep subwavelength light confinement, opening up new avenues for enhancing the spontaneous emission process towards both classical and quantum optical applications. Conventionally, light cannot be directly emitted from the plasmonic metal itself. Here, we explore the large field confinement and slow-light effect near the epsilon-near-zero (ENZ) frequency of the light-emitting material itself, to greatly enhance the “forbidden” two-plasmon spontaneous emission (2PSE) process. Using degenerately- 1234567890():,; doped InSb as the plasmonic material and emitter simultaneously, we theoretically show that the 2PSE lifetime can be reduced from tens of milliseconds to several nanoseconds, com- parable to the one-photon emission rate. Furthermore, we show that the optical nonlocality may largely govern the optical response of the ultrathin ENZ film. Efficient 2PSE from a doped semiconductor film may provide a pathway towards on-chip entangled light sources, with an emission wavelength and bandwidth widely tunable in the mid-infrared. 1 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing, China. ✉ 2 State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing, China. email: [email protected]; [email protected] COMMUNICATIONS PHYSICS | (2021) 4:84 | https://doi.org/10.1038/s42005-021-00586-4 | www.nature.com/commsphys 1 ARTICLE COMMUNICATIONS PHYSICS | https://doi.org/10.1038/s42005-021-00586-4 lasmonics is a burgeoning field of research that exploits the correction of TPE near graphene using the zero-temperature Plight-matter interaction in metallic nanostructures1,2.
    [Show full text]
  • 7 Plasmonics
    7 Plasmonics Highlights of this chapter: In this chapter we introduce the concept of surface plasmon polaritons (SPP). We discuss various types of SPP and explain excitation methods. Finally, di®erent recent research topics and applications related to SPP are introduced. 7.1 Introduction Long before scientists have started to investigate the optical properties of metal nanostructures, they have been used by artists to generate brilliant colors in glass artefacts and artwork, where the inclusion of gold nanoparticles of di®erent size into the glass creates a multitude of colors. Famous examples are the Lycurgus cup (Roman empire, 4th century AD), which has a green color when observing in reflecting light, while it shines in red in transmitting light conditions, and church window glasses. Figure 172: Left: Lycurgus cup, right: color windows made by Marc Chagall, St. Stephans Church in Mainz Today, the electromagnetic properties of metal{dielectric interfaces undergo a steadily increasing interest in science, dating back in the works of Gustav Mie (1908) and Rufus Ritchie (1957) on small metal particles and flat surfaces. This is further moti- vated by the development of improved nano-fabrication techniques, such as electron beam lithographie or ion beam milling, and by modern characterization techniques, such as near ¯eld microscopy. Todays applications of surface plasmonics include the utilization of metal nanostructures used as nano-antennas for optical probes in biology and chemistry, the implementation of sub-wavelength waveguides, or the development of e±cient solar cells. 208 7.2 Electro-magnetics in metals and on metal surfaces 7.2.1 Basics The interaction of metals with electro-magnetic ¯elds can be completely described within the frame of classical Maxwell equations: r ¢ D = ½ (316) r ¢ B = 0 (317) r £ E = ¡@B=@t (318) r £ H = J + @D=@t; (319) which connects the macroscopic ¯elds (dielectric displacement D, electric ¯eld E, magnetic ¯eld H and magnetic induction B) with an external charge density ½ and current density J.
    [Show full text]
  • Magnon-Drag Thermopower in Antiferromagnets Versus Ferromagnets
    Journal of Materials Chemistry C Magnon-drag thermopower in antiferromagnets versus ferromagnets Journal: Journal of Materials Chemistry C Manuscript ID TC-ART-11-2019-006330.R1 Article Type: Paper Date Submitted by the 06-Jan-2020 Author: Complete List of Authors: Polash, Md Mobarak Hossain; North Carolina State University, Department of Materials Science and Engineering Mohaddes, Farzad; North Carolina State University, Department of Electrical and Computer Engineering Rasoulianboroujeni, Morteza; Marquette University, School of Dentistry Vashaee, Daryoosh; North Carolina State University, Department of Electrical and Computer Engineering Page 1 of 17 Journal of Materials Chemistry C Magnon-drag thermopower in antiferromagnets versus ferromagnets Md Mobarak Hossain Polash1,2, Farzad Mohaddes2, Morteza Rasoulianboroujeni3, and Daryoosh Vashaee1,2 1Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27606, US 2Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27606, US 3School of Dentistry, Marquette University, Milwaukee, WI 53233, US Abstract The extension of magnon electron drag (MED) to the paramagnetic domain has recently shown that it can create a thermopower more significant than the classical diffusion thermopower resulting in a thermoelectric figure-of-merit greater than unity. Due to their distinct nature, ferromagnetic (FM) and antiferromagnetic (AFM) magnons interact differently with the carriers and generate different amounts of drag-thermopower. The question arises if the MED is stronger in FM or in AFM semiconductors. Two material systems, namely MnSb and CrSb, which are similar in many aspects except that the former is FM and the latter AFM, were studied in detail, and their MED properties were compared.
    [Show full text]
  • Plasmon‑Polaron Coupling in Conjugated Polymers on Infrared Metamaterials
    This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg) Nanyang Technological University, Singapore. Plasmon‑polaron coupling in conjugated polymers on infrared metamaterials Wang, Zilong 2015 Wang, Z. (2015). Plasmon‑polaron coupling in conjugated polymers on infrared metamaterials. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/65636 https://doi.org/10.32657/10356/65636 Downloaded on 04 Oct 2021 22:08:13 SGT PLASMON-POLARON COUPLING IN CONJUGATED POLYMERS ON INFRARED METAMATERIALS WANG ZILONG SCHOOL OF PHYSICAL & MATHEMATICAL SCIENCES 2015 Plasmon-Polaron Coupling in Conjugated Polymers on Infrared Metamaterials WANG ZILONG WANG WANG ZILONG School of Physical and Mathematical Sciences A thesis submitted to the Nanyang Technological University in partial fulfilment of the requirement for the degree of Doctor of Philosophy 2015 Acknowledgements First of all, I would like to express my deepest appreciation and gratitude to my supervisor, Asst. Prof. Cesare Soci, for his support, help, guidance and patience for my research work. His passion for sciences, motivation for research and knowledge of Physics always encourage me keep learning and perusing new knowledge. As one of his first batch of graduate students, I am always thankful to have the opportunity to join with him establishing the optical spectroscopy lab and setting up experiment procedures, through which I have gained invaluable and unique experiences comparing with many other students. My special thanks to our collaborators, Professor Dr. Harald Giessen and Dr. Jun Zhao, Ms. Bettina Frank from the University of Stuttgart, Germany. Without their supports, the major idea of this thesis cannot be experimentally realized.
    [Show full text]
  • 2 Quantum Theory of Spin Waves
    2 Quantum Theory of Spin Waves In Chapter 1, we discussed the angular momenta and magnetic moments of individual atoms and ions. When these atoms or ions are constituents of a solid, it is important to take into consideration the ways in which the angular momenta on different sites interact with one another. For simplicity, we will restrict our attention to the case when the angular momentum on each site is entirely due to spin. The elementary excitations of coupled spin systems in solids are called spin waves. In this chapter, we will introduce the quantum theory of these excita- tions at low temperatures. The two primary interaction mechanisms for spins are magnetic dipole–dipole coupling and a mechanism of quantum mechanical origin referred to as the exchange interaction. The dipolar interactions are of importance when the spin wavelength is very long compared to the spacing between spins, and the exchange interaction dominates when the spacing be- tween spins becomes significant on the scale of a wavelength. In this chapter, we focus on exchange-dominated spin waves, while dipolar spin waves are the primary topic of subsequent chapters. We begin this chapter with a quantum mechanical treatment of a sin- gle electron in a uniform field and follow it with the derivations of Zeeman energy and Larmor precession. We then consider one of the simplest exchange- coupled spin systems, molecular hydrogen. Exchange plays a crucial role in the existence of ordered spin systems. The ground state of H2 is a two-electron exchange-coupled system in an embryonic antiferromagnetic state.
    [Show full text]
  • Quasiparticle Scattering, Lifetimes, and Spectra Using the GW Approximation
    Quasiparticle scattering, lifetimes, and spectra using the GW approximation by Derek Wayne Vigil-Fowler A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Steven G. Louie, Chair Professor Feng Wang Professor Mark D. Asta Summer 2015 Quasiparticle scattering, lifetimes, and spectra using the GW approximation c 2015 by Derek Wayne Vigil-Fowler 1 Abstract Quasiparticle scattering, lifetimes, and spectra using the GW approximation by Derek Wayne Vigil-Fowler Doctor of Philosophy in Physics University of California, Berkeley Professor Steven G. Louie, Chair Computer simulations are an increasingly important pillar of science, along with exper- iment and traditional pencil and paper theoretical work. Indeed, the development of the needed approximations and methods needed to accurately calculate the properties of the range of materials from molecules to nanostructures to bulk materials has been a great tri- umph of the last 50 years and has led to an increased role for computation in science. The need for quantitatively accurate predictions of material properties has never been greater, as technology such as computer chips and photovoltaics require rapid advancement in the control and understanding of the materials that underly these devices. As more accuracy is needed to adequately characterize, e.g. the energy conversion processes, in these materials, improvements on old approximations continually need to be made. Additionally, in order to be able to perform calculations on bigger and more complex systems, algorithmic devel- opment needs to be carried out so that newer, bigger computers can be maximally utilized to move science forward.
    [Show full text]
  • Room Temperature and Low-Field Resonant Enhancement of Spin
    ARTICLE https://doi.org/10.1038/s41467-019-13121-5 OPEN Room temperature and low-field resonant enhancement of spin Seebeck effect in partially compensated magnets R. Ramos 1*, T. Hioki 2, Y. Hashimoto1, T. Kikkawa 1,2, P. Frey3, A.J.E. Kreil 3, V.I. Vasyuchka3, A.A. Serga 3, B. Hillebrands 3 & E. Saitoh1,2,4,5,6 1234567890():,; Resonant enhancement of spin Seebeck effect (SSE) due to phonons was recently discovered in Y3Fe5O12 (YIG). This effect is explained by hybridization between the magnon and phonon dispersions. However, this effect was observed at low temperatures and high magnetic fields, limiting the scope for applications. Here we report observation of phonon-resonant enhancement of SSE at room temperature and low magnetic field. We observe in fi Lu2BiFe4GaO12 an enhancement 700% greater than that in a YIG lm and at very low magnetic fields around 10À1 T, almost one order of magnitude lower than that of YIG. The result can be explained by the change in the magnon dispersion induced by magnetic compensation due to the presence of non-magnetic ion substitutions. Our study provides a way to tune the magnon response in a crystal by chemical doping, with potential applications for spintronic devices. 1 WPI Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. 2 Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. 3 Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany. 4 Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan. 5 Center for Spintronics Research Network, Tohoku University, Sendai 980-8577, Japan.
    [Show full text]
  • My Life As a Boson: the Story of "The Higgs"
    International Journal of Modern Physics A Vol. 17, Suppl. (2002) 86-88 © World Scientific Publishing Company MY LIFE AS A BOSON: THE STORY OF "THE HIGGS" PETER HIGGS Department of Physics and Astronomy University of Edinburgh, Scotland The story begins in 1960, when Nambu, inspired by the BCS theory of superconductivity, formulated chirally invariant relativistic models of inter­ acting massless fermions in which spontaneous symmetry breaking generates fermionic masses (the analogue of the BCS gap). Around the same time Jeffrey Goldstone discussed spontaneous symmetry breaking in models con­ taining elementary scalar fields (as in Ginzburg-Landau theory). I became interested in the problem of how to avoid a feature of both kinds of model, which seemed to preclude their relevance to the real world, namely the exis­ tence in the spectrum of massless spin-zero bosons (Goldstone bosons). By 1962 this feature of relativistic field theories had become the subject of the Goldstone theorem. In 1963 Philip Anderson pointed out that in a superconductor the elec­ tromagnetic interaction of the Goldstone mode turns it into a "plasmon". He conjectured that in relativistic models "the Goldstone zero-mass difficulty is not a serious one, because one can probably cancel it off against an equal Yang-Mills zero-mass problem." However, since he did not discuss how the theorem could fail or give an explicit counter example, his contribution had by Dr. Horst Wahl on 08/28/12. For personal use only. little impact on particle theorists. If was not until July 1964 that, follow­ ing a disagreement in the pages of Physics Review Letters between, on the one hand, Abraham Klein and Ben Lee and, on the other, Walter Gilbert Int.
    [Show full text]
  • Introducing Coherent Time Control to Cavity Magnon-Polariton Modes
    ARTICLE https://doi.org/10.1038/s42005-019-0266-x OPEN Introducing coherent time control to cavity magnon-polariton modes Tim Wolz 1*, Alexander Stehli1, Andre Schneider 1, Isabella Boventer1,2, Rair Macêdo 3, Alexey V. Ustinov1,4, Mathias Kläui 2 & Martin Weides 1,3* 1234567890():,; By connecting light to magnetism, cavity magnon-polaritons (CMPs) can link quantum computation to spintronics. Consequently, CMP-based information processing devices have emerged over the last years, but have almost exclusively been investigated with single-tone spectroscopy. However, universal computing applications will require a dynamic and on- demand control of the CMP within nanoseconds. Here, we perform fast manipulations of the different CMP modes with independent but coherent pulses to the cavity and magnon sys- tem. We change the state of the CMP from the energy exchanging beat mode to its normal modes and further demonstrate two fundamental examples of coherent manipulation. We first evidence dynamic control over the appearance of magnon-Rabi oscillations, i.e., energy exchange, and second, energy extraction by applying an anti-phase drive to the magnon. Our results show a promising approach to control building blocks valuable for a quantum internet and pave the way for future magnon-based quantum computing research. 1 Institute of Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany. 2 Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany. 3 James Watt School of Engineering, Electronics & Nanoscale Engineering
    [Show full text]
  • Amplitude Modes in Cold Atoms
    T01 Amplitude modes in cold atoms S.D. Huber, Institute for Theoretical Physics, ETH Zurich E-mail address: [email protected] The Bose Hubbard model exhibits a quantum phase transition between an insulating Mott state and a superfluid. We aim at the determination of the excitation spectrum of the superfluid phase, in particular its evolution from the vicinity of the Mott phase towards the weakly interacting regime. Furthermore, we discuss a method allowing to observe our findings in an experiment. We make the link between our microscopic findings and the notion of a “Higgs” mode. Specifically, we highlight the role of emergent symmetries. Recent developments in the description of amplitude modes in exotic chiral Mott insulators will be mentioned. [1] S.D. Huber, E. Altman, H.P. Buchler,¨ and G. Blatter, Phys. Rev. B, 75 085106 (2007) [2] S.D. Huber, B. Theiler, E. Altman, G. Blatter, Phys. Rev. Lett., 100 050404 (2008) [3] S.D. Huber and N.H. Lindner, Proc. Natl. Acad. Sci. USA, 108 19925 (2011) T02 Higgs mode and universal dynamics near quantum criticality D. Podolsky Department of Physics, Technion – Israel Institute of Technology, Haifa 32000, Israel E-mail address: [email protected] The Higgs mode is a ubiquitous collective excitation in condensed matter systems with broken continuous symmetry. Its detection is a valuable test of the corresponding field theory, and its mass gap measures the proximity to a quantum critical point. However, since the Higgs mode can decay into low energy Goldstone modes, its experimental visibility has been questioned. In this talk, I will show that the visibility of the Higgs mode depends on the symmetry of the measured susceptibility.
    [Show full text]
  • Strong Plasmon-Phonon Splitting and Hybridization in 2D Materials Revealed Through a Self-Energy Approach Mikkel Settnes,†,‡,§ J
    Article Cite This: ACS Photonics 2017, 4, 2908-2915 pubs.acs.org/journal/apchd5 Strong Plasmon-Phonon Splitting and Hybridization in 2D Materials Revealed through a Self-Energy Approach Mikkel Settnes,†,‡,§ J. R. M. Saavedra,∥ Kristian S. Thygesen,§,⊥ Antti-Pekka Jauho,‡,§ F. Javier García de Abajo,∥,# and N. Asger Mortensen*,§,○,△ †Department of Photonics Engineering, ‡Department of Micro and Nanotechnology, §Center for Nanostructured Graphene, and ⊥Center for Atomic-Scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark ∥ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain # ICREA-Institució Catalana de Recerca i Estudis Avancats,̧ Passeig Lluıś Companys, 23, 08010 Barcelona, Spain ○Center for Nano Optics and △Danish Institute for Advanced Study, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark *S Supporting Information ABSTRACT: We reveal new aspects of the interaction between plasmons and phonons in 2D materials that go beyond a mere shift and increase in plasmon width due to coupling to either intrinsic vibrational modes of the material or phonons in a supporting substrate. More precisely, we predict strong plasmon splitting due to this coupling, resulting in a characteristic avoided crossing scheme. We base our results on a computationally efficient approach consisting in including many-body interactions through the electron self-energy. We specify this formalism for a description of plasmons based upon a tight-binding electron Hamiltonian combined with the random-phase approximation. This approach is valid provided vertex corrections can be neglected, as is the case in conventional plasmon-supporting metals and Dirac-Fermion systems.
    [Show full text]
  • Plasmon Lasers
    Plasmon Lasers Wenqi Zhu1,2, Shawn Divitt1,2, Matthew S. Davis1, 2, 3, Cheng Zhang1,2, Ting Xu4,5, Henri J. Lezec1 and Amit Agrawal1, 2* 1Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899 USA 2Maryland NanoCenter, University of Maryland, College Park, MD 20742 USA 3Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 USA 4National Laboratory of Solid-State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University, Nanjing, China 5Collaborative Innovation Center of Advanced Microstructures, Nanjing, China Corresponding*: [email protected] Recent advancements in the ability to design, fabricate and characterize optical and optoelectronic devices at the nanometer scale have led to tremendous developments in the miniaturization of optical systems and circuits. Development of wavelength-scale optical elements that are able to efficiently generate, manipulate and detect light, along with their subsequent integration on functional devices and systems, have been one of the main focuses of ongoing research in nanophotonics. To achieve coherent light generation at the nanoscale, much of the research over the last few decades has focused on achieving lasing using high- index dielectric resonators in the form of photonic crystals or whispering gallery mode resonators. More recently, nano-lasers based on metallic resonators that sustain surface plasmons – collective electron oscillations at the interface between a metal and a dielectric – have emerged as a promising candidate. This article discusses the fundamentals of surface plasmons and the various embodiments of plasmonic resonators that serve as the building block for plasmon lasers.
    [Show full text]