DOCSLIB.ORG

List of Symbols

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
List of Symbols APPENDIX LIST OF SYMBOLS n the following table of symbols, the many transitory symbols that I have no application beyond their immediate relevance to the deri­ vation involved have not been included for the sake of clarity. Even so, many symbols have had to be used for more than one purpose. Where possible I have kept to the standard usage, but many of the symbols still need to be taken in the context of the equation. For example, Z is used for both the ionic charge number and the renormalization constant, but since the former always appears with the electronic charge e, the danger of confusion is small. As an indication the chapter number has been given if a symbol has a definition restricted to that chapter. Throughout, the following standard notation has been used to indicate the possible meanings of a symbol (0). o An operator. o The matrix form of a function. o A vector. 0+ The Hermitian conjugate. 0-1 The inverse. 6 The time derivative. (0) The expectation value. °lm The matrix element (1101 m). Heisenberg to Schrodinger representation transformation operator. A(k,w) Spectral weight function. A(1,2) The two-particle propagator [G(1,2)G(1,2)]. An(x) A known function of x (Chap. 5). Ax(t) Fourier coefficient of the electromagnetic potential for the wave vector kx and polarization A. A(r,t) Electromagnetic vector potential. a Interatomic separation of atoms on the linear chain. 311 APPENDIX lth components of the expansion of the Landau parameters in Legendre polynomials. Creation and annihilation (boson) operators for the normal mode k. Creation and annihilation operators in the "thermal" Heisenberg representation. Annihilation and creation operators corresponding to the condensate state. Coefficient of the quasiparticle state of wave vector k, band index n. Landau interaction parameters. Spectral weight function. Annihilation and creation operators for the state j. Annihilation and creation operators for the plasmon excitation of wave vector k. Velocity of light. Fermion annihilation and creation operators for the state m. D(rl ,tl ,r2,t2) Phonon Green's function (propagator). Do(rv t 1,r2, t2) Bare phonon Green's function. E Energy of a system. Ek Energy of the jth state of the M-particle system (j = 0 corresponds to the ground state). Energy of the state n. Eigenvalue of the particle i in the state ~~(r) (Chap. 1). Real and imaginary parts of the energy (Chap. 5). Et/> Energy of the N-particle system for a given external potential ¢(r). (Chap. 12). Ground-state energy of the interacting system (Chap. 5). E(k) Energy of the isolated Landau quasiparticle state k in the presence of other quasiparticle (Chap. 5). E(k) Energy of the state k. 312 LIST OF SYMBOLS E(k) Energy eigenvalue for the state corresponding to the transformed operators &jJk (Chap. 13). Energy of the isolated Landau quasiparticle state k (Chaps. 5 and 9). E(v) Energy of the N-particle system as a function of the velocity of the observer (Chap. 5). E(r,t) Electric field. E[n] The energy as a functional of the electron density. ExJn] The exchange and correlation energy functional. e Electronic charge. e Polarization vector. F Number of closed fermion loops in a diagram (Chap. 8). F Free energy (Chaps. 10, 12). F(rI1Tl1r 2,T2) Anomalous Green's function (Chap. 13). f(k,k') Landau quasiparticle interaction function. r(kF,8),f(kF,8) The direct and exchange parts of the quasiparticle interaction. f(r) Arbitrary function (Chap. 2). G Reciprocal lattice vector (Chap. 9). Expansion coefficients for the Green's function (Chap. 2). Anomalous Green's functions. The normal (Le., nonpairing) part of the two- particle Green's function (Chap. 13). G(k,w) Momentum-energy dependent Green's function. G(r,r',t,t') Time-dependent Green's function (Chap. 2). G(r,r',E) Energy-dependent Green's function (Chap. 2). G(x,x',w) Energy-dependent Green's function. G[n] The functional which contains the kinetic, exchange, and correlation contributions to the total energy (Chap. 12). Gc(X l1 t 1,X2l t2) Condensate part of the Green's function. Gix1,tI1 X2,t2) Real-time thermal Green's function. G:(X1,tI1 X2l t2) Advanced real-time thermal Green's function. G:(Xl1 t 1,X2,t2) Retarded real-time thermal Green's function. GO(Xl,tI1X2,t2) Noninteracting Green's function. 313 APPENDIX Green's function corresponding to the single­ particle Hamiltonian without the Hartree potential (Chap. 7). nth order approximation to the single-particle Green's function. G2( xI,t I,X2f t2,X3, t 3,X4, t4) Two-particle Green's function. G±(r,r,t - t') Advanced (+) and retarded (-) Green's function (Chap. 2). Noncondensate part of the Green's function (Chap. 11). G-I(Xl1tl,X2ft2) Inverse of the single-particle Green's function. G'(XI,tl,X2,t2) The matrix Green's function for a system with a condensate (Chap. 11). G(k,w n) Momentum-energy dependent thermal Green's function. g (X, r ,x',r') Thermal Green's function. go(x,r,x',T') Noninteracting thermal Green's function. go(XI ,X2fWn) Noninteracting energy-dependent thermal Green's function. The spin-up electron propagator (Chap. 13). g The strength of the effective electron-electron interaction (Chap. 13). Energy functions (not functionals) of the electron density. The energy density functional. Hamiltonian. Hamiltonian describing the background neutralizing charge (Chap. 11). Hamiltonian containing the coulomb repulsion (Chap. 12). Hel Electron Hamiltonian (Chaps. 11 and 12). Hel-ion Electron-ion interaction Hamiltonian (Chap. 11). HINT Hamiltonian describing the interaction between the N-particle system and the added electron (Chap. 11). Electron-phonon interaction Hamiltonian (Chap. 12). Ion Hamiltonian. 314 LIST OF SYMBOLS Coupling Hamiltonian between localized and de localized states (Chap. 12). Hamiltonian for the N-particle system (Chap. 11). Hamiltonian for the delocalized states (Chap. 12). HPh Phonon Hamiltonian (Chap. 12). Ho Single-particle Hamiltonian. HI Hamiltonian for one particle (Chap. 11). Ho(xl) Single-particle Hamiltonian. H(r,t) Magnetic field (Chap. 3). H[n1 Hamiltonian as a functional of the electron density. H[cf>1 Hamiltonian as a function of the external potential. 71 Hamiltonian density. 71 Magnetic field (Chap. 12). 71/ An effective internal magnetic field (Chap. 12). 71 0 External magnetic field (Chap. 12). h Plank's constant. 1(1,2,3,4) T-matrix for electron-electron scattering. i(x) Single-particle operator. Jo(r) Zero-order Bessel function (Chap. 9). d(x) Operator density. K Effective Spring constant for internuclear forces (Chap. 3). Grand canonical Hamiltonian. Soluble part of the grand canonical hamiltonian. Eigenvalue of the grand canonical hamiltonian for the state n. The normal (i.e., nonpairing) part of the grand canonical Hamiltonian (Chap. 13). Variable conjugate to x [= (k, spin)]. Boltzmann constant. Fermi wave vector, i.e., wave vector of state at the Fermi level. k Wave vector of a plane-wave state. L Lagrangian. .L Lagrangian denSity. 315 APPENDIX M Atomic mass. M Occupation number of the q = 2kF phonon in the one-dimensional solid (Chap. 12). M(k,j,q) Matrix element appearing in the response function of an insulator. m Electron mass. m* Effective m'ass of an electron. N Number of atoms in the linear chain (Chap. 3). N Electron density (Chap. 11). N(E) Density of states at energy E. N. Number eigenvalue of the state I n) (Chap. 10). n Number of particles not in the condensate (Chap. 11). n Order number of a diagram (Chap. 8). n(k) Number of particles in the eigenstate k. n(r) Density of electrons. fl(r) Density operator. n[¢] The electron density as a functional of the external potential. Number operator for the normal mode of wave vector k. Number operator for the state 1,0". no(k) Ground-state occupation factor (Chap. 5). o General operator. OH(q,t) Heisenberg representation operator. O[(q,t) Interaction representation operator. OK(q,T) Operator in the "thermal" Heisenberg representation. Os(q,t) Schrodinger representation operator. P(q,w) Energy-momentum dependent polarization propagator. P( X II t I1X21 t2) Polarization propagator. P(Xl1TllX21T2) Thermal response function. P{} Permutation operator which produces all possible permutation of the labels; thus, P{1/Ia1/l~1/I.,} = 1/Ia1/l~1/I., + 1/Ia1/l.,1/I~ + 1/I.,1/Ia1/l~ + t/;'Yt/;~t/;a + t/;~t/;'Yt/;a + t/;~t/;at/;'Y' Probability of finding a system in the state In} (Chap. 10). 316 LIST OF SYMBOLS PO(X1,t1,X2,t2) First-order polarization propagator. p Momentum operator. P Momentum operator (single-particle). Momentum of ith atom (Chap. 3). Fourier transform of Pi and momentum coordinate of the normal mode of wave vector k (Chap. 3). Particle momentum. Momentum of the ith atom (Chap. 11). Momentum coordinate for the normal mode (k,A). Q(k,k') The transformed interaction matrix element in a paired electron system (Chap. 13). q Generalized position variable. qi Shift of ith atom from its equilibrium position (Chap. 3). Position variable of the normal mode of wave vector k. The Fourier transform of qi (Chap. 3). Position coordinate for the normal mode (k,A) (Chap. 11). q Wave vector variable. R(k,k') As Q(k,k') (Chap. 13). R(r1,t1,r2,t2) The plasmon Green's function (or propagator). RA Operator occurring in the electron electromagnetic field interaction (Chap. 4). Atomic position vector. Position vector describing the equilibrium position of the ith atom in a lattice. Electron position vector for the nth electron. 5 Entropy of a system (Chap.
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]
  • 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]
  • 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]
  • 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).
    [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]
  • 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]
  • Plasmon-Enhanced Solar Energy Harvesting by Scott K
    Plasmon-Enhanced Solar Energy Harvesting by Scott K. Cushing and Nianqiang Wu olar energy can be directly converted strength up to ~103 times the incident field Plasmonic Enhancement of to electrical energy via photovoltaics. and greatly increase far-field scattering. Light Absorption and Scattering S Alternatively, solar energy can be In a plasmonic heterostructure the energy converted and stored in chemical fuels stored in the LSPR can (1.) be converted through photoelectrochemical cells and to heat in the metal lattice, (2.) re-emit as The first enhancement mechanism, photocatalysis (see front cover image), scattered photons, or (3.) transfer to the referred to as photonic enhancement, allowing continued power production when semiconductor. requires engineering the metal nanostructure the sky is cloudy or dark. The conversion of Plasmonic nanostructures improve or pattern to direct and concentrate light at solar energy is regulated by four processes: solar energy conversion efficiency via the the interface or bulk of the semiconductor. light absorption, charge separation, charge following mechanisms: (a) enhancing the This is possible because the LSPR causes migration, and charge recombination. An light absorption in the semiconductor by both absorption and scattering with strengths individual material cannot be optimized photonic enhancement through increasing dependent on the size of the nanoparticle. A 15 nm sized gold nanoparticle (Fig. 1a), for all four processes. For example, TiO2 the optical path length and concentrating has excellent charge migration qualities. the incident field;6 (b) directly transferring primarily localizes the EM field as depicted However, the ultraviolet (UV) band gap the plasmonic energy from the metal to in Fig.
    [Show full text]
  • Infrared Absorption and Raman Scattering on Coupled Plasmon-Phonon Modes in Superlattices
    University of Utah Institutional Repository Author Manuscript Infrared absorption and Raman scattering on coupled plasmon-phonon modes in superlattices L. A. Falkovskyl, E. G. Mishchenko1,2 1 Landau Institute for Theoretical Physics) 119337 Moscow) Russia 2 Department of Physics) University of Utah) Salt Lake City) UT 84112 Abstract We consider theoretically a superlattice formed by thin conducting layers separated spatially between insulating layers. The dispersion of two coupled phonon-plasmon modes of the system 1 University of Utah Institutional Repository Author Manuscript I. INTRODUCTION Coupling of collective electron oscillations (plasmons) to optical phonons in polar semi­ c conductors was predicted more than four decades ago [1], experimentally observed using c Raman spectroscopy in n-doped GaAs [2] and extensively investigated since then (see, e.g. , [3]). Contrary, the interaction of optical phonons with plasmons in the semiconductor super­ lattices is much less studied. A two-dimensional electron gas (2DEG) created at the interface of two semiconductors has properties which differ drastically from the properties of its three­ dimensional counterpart. In particular, the plasmon spectrum of the 2DEG is gapless [4] owing to the long-range nature of the Coulomb interaction of carriers, w 2 (k) = v~K,ok/2 , where Vp is the Fermi velocity and K,o is the inverse static screening length in the 2DEG. Coupling of two-dimensional plasmons to optical phonons has been considered in Refs. [5 , 6] for a single 2DEG layer. The resulting coupling is usually non-resonant since characteristic phonon energies r-v 30 - 50 meV are several times larger than typical plasmon energies.
    [Show full text]
  • High-Q Surface Plasmon-Polariton Microcavity
    Chapter 5 High-Q surface plasmon-polariton microcavity 5.1 Introduction As the research presented in this thesis has shown, microcavities are ideal vehicles for studying light and matter interaction due to their resonant property, which allows individual photons to sample their environment thousands of times. Accurate loss characterization is possible through Q factor measurements, which can elucidate origins of loss if the measurements are performed while varying factors under study (e.g., presence of water). This chapter explores the interaction of light and metal in surface plasmon polariton (SPP) mi- crocavity resonators. The aim of this research effort is to accurately quantify metal loss for SPP waves traveling at the interface between glass and silver. The electric field components of SPP modes in the resonator are calculated by FEM simulation. Two types of plasmonic microcavity resonators are built and tested based on the microtoroid, and microdisk. Only dielectric resonances are observed in the microtoroid resonator, where the optical radiation is attenuated by a metal coating at the surface. However, a silver coated silica microdisk resonator is demonstrated with surface plasmon resonances. In fact, the plasmonic microdisk resonator has record Q for any plas- monic microresonator. Potential applications of a high quality plasmonic waveguide include on-chip, high-frequency communication and sensing. 5.1.1 Plasmonics A plasmon is an oscillation of the free electron gas that resides in metals. Plasmons are easy to excite in metals because of the abundance of loosely bound, or free, electrons in the highest valence shell. These electrons physically respond to electric fields, either present in a crystal or from an external source.
    [Show full text]
  • Observation of Surface Plasmon Polaritons in 2D Electron Gas of Surface Electron Accumulation in Inn Nanostructures
    Observation of surface plasmon polaritons in 2D electron gas of surface electron accumulation in InN nanostructures Kishore K. Madapu,*,† A. K. Sivadasan,†,# Madhusmita Baral,‡ Sandip Dhara*,† †Nanomaterials Characterization and Sensors Section, Surface and Nanoscience Division, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institute, Kalpakkam- 603102, India ‡Synchrotron Utilization Section, Raja Ramanna Centre for Advanced technology, Homi Bhabha National Institute, Indore-452013, India Real space imaging of propagating surface plasmon polaritons having the wavelength in the 500 nm, for the first time, indicating InN as a promising alternate for the 2D low loss plasmonic material in the THz region. Abstract Recently, heavily doped semiconductors are emerging as an alternate for low loss plasmonic materials. InN, belonging to the group III nitrides, possesses the unique property of surface electron accumulation (SEA) which provides two dimensional electron gas (2DEG) system. In this report, we demonstrated the surface plasmon properties of InN nanoparticles originating from SEA using the real space mapping of the surface plasmon fields for the first time. The SEA is confirmed by Raman studies which are further corroborated by photoluminescence and photoemission spectroscopic studies. The frequency of 2DEG corresponding to SEA is found to be in the THz region. The periodic fringes are observed in the nearfield scanning optical microscopic images of InN nanostructures. The observed fringes are attributed to the interference of propagated and back reflected surface plasmon polaritons (SPPs). The observation of SPPs is solely attributed to the 2DEG corresponding to the SEA of InN. In addition, resonance kind of behavior with the enhancement of the near- field intensity is observed in the near-field images of InN nanostructures.
    [Show full text]