Exciton-Plasmon Coupling Interactions: from Principle to Applications
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3.4 V-A Coupling of Leptons and Quarks 3.5 CKM Matrix to Describe the Quark Mixing
Advanced Particle Physics: VI. Probing the weak interaction 3.4 V-A coupling of leptons and quarks Reminder u γ µ (1− γ 5 )u = u γ µu L = (u L + u R )γ µu L = u Lγ µu L l ν l ν l l ν l ν In V-A theory the weak interaction couples left-handed lepton/quark currents (right-handed anti-lepton/quark currents) with an universal coupling strength: 2 GF gw = 2 2 8MW Weak transition appear only inside weak-isospin doublets: Not equal to the mass eigenstate Lepton currents: Quark currents: ⎛ν ⎞ ⎛ u ⎞ 1. ⎜ e ⎟ j µ = u γ µ (1− γ 5 )u 1. ⎜ ⎟ j µ = u γ µ (1− γ 5 )u ⎜ − ⎟ eν e ν ⎜ ⎟ du d u ⎝e ⎠ ⎝d′⎠ ⎛ν ⎞ ⎛ c ⎞ 5 2. ⎜ µ ⎟ j µ = u γ µ (1− γ 5 )u 2. ⎜ ⎟ j µ = u γ µ (1− γ )u ⎜ − ⎟ µν µ ν ⎜ ⎟ sc s c ⎝ µ ⎠ ⎝s′⎠ ⎛ν ⎞ ⎛ t ⎞ µ µ 5 3. ⎜ τ ⎟ j µ = u γ µ (1− γ 5 )u 3. ⎜ ⎟ j = u γ (1− γ )u ⎜ − ⎟ τν τ ν ⎜ ⎟ bt b t ⎝τ ⎠ ⎝b′⎠ 3.5 CKM matrix to describe the quark mixing One finds that the weak eigenstates of the down type quarks entering the weak isospin doublets are not equal to the their mass/flavor eigenstates: ⎛d′⎞ ⎛V V V ⎞ ⎛d ⎞ d V u ⎜ ⎟ ⎜ ud us ub ⎟ ⎜ ⎟ ud ⎜ s′⎟ = ⎜Vcd Vcs Vcb ⎟ ⋅ ⎜ s ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ W ⎝b′⎠ ⎝Vtd Vts Vtb ⎠ ⎝b⎠ Cabibbo-Kobayashi-Maskawa mixing matrix The quark mixing is the origin of the flavor number violation of the weak interaction. -
UNIVERSITY of CALIFORNIA, SAN DIEGO Exciton Transport
UNIVERSITY OF CALIFORNIA, SAN DIEGO Exciton Transport Phenomena in GaAs Coupled Quantum Wells A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Jason R. Leonard Committee in charge: Professor Leonid V. Butov, Chair Professor John M. Goodkind Professor Shayan Mookherjea Professor Charles W. Tu Professor Congjun Wu 2016 Copyright Jason R. Leonard, 2016 All rights reserved. The dissertation of Jason R. Leonard is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2016 iii TABLE OF CONTENTS Signature Page . iii Table of Contents . iv List of Figures . vi Acknowledgements . viii Vita........................................ x Abstract of the Dissertation . xii Chapter 1 Introduction . 1 1.1 Semiconductor introduction . 2 1.1.1 Bulk GaAs . 3 1.1.2 Single Quantum Well . 3 1.1.3 Coupled-Quantum Wells . 5 1.2 Transport Physics . 7 1.3 Spin Physics . 8 1.3.1 D'yakanov and Perel' spin relaxation . 10 1.3.2 Dresselhaus Interaction . 10 1.3.3 Electron-Hole Exchange Interaction . 11 1.4 Dissertation Overview . 11 Chapter 2 Controlled exciton transport via a ramp . 13 2.1 Introduction . 13 2.2 Experimental Methods . 14 2.3 Qualitative Results . 14 2.4 Quantitative Results . 16 2.5 Theoretical Model . 17 2.6 Summary . 19 2.7 Acknowledgments . 19 Chapter 3 Controlled exciton transport via an optically controlled exciton transistor . 22 3.1 Introduction . 22 3.2 Realization . 22 3.3 Experimental Methods . 23 3.4 Results . 25 3.5 Theoretical Model . -
Strong Coupling and Quantum Molecular Plasmonics
Strong coupling and molecular plasmonics Javier Aizpurua http://cfm.ehu.es/nanophotonics Center for Materials Physics, CSIC-UPV/EHU and Donostia International Physics Center - DIPC Donostia-San Sebastián, Basque Country AMOLF Nanophotonics School June 17-21, 2019, Science Park, Amsterdam, The Netherlands Organic molecules & light Excited molecule (=exciton on molecule) Photon Photon Adding mirrors to this interaction The photon can come back! Optical cavities to enhance light-matter interaction Optical mirrors Dielectric resonator Veff Q ∼ 1/κ Photonic crystals Plasmonic cavity Veff Q∼1/κ Coupling of plasmons and molecular excitations Plasmon-Exciton Coupling Plasmon-Vibration Coupling Absorption, Scattering, IR Absorption, Fluorescence Veff Raman Scattering Extreme plasmonic cavities Top-down Bottom-up STM ultra high-vacuum Wet Chemistry Low temperature Self-assembled monolayers (Hefei, China) (Cambridge, UK) “More interacting system” One cannot distinguish whether we have a photon or an excited molecule. The eigenstates are “hybrid” states, part molecule and part photon: “polaritons” Strong coupling! Experiments: organic molecules Organic molecules: Microcavity: D. G. Lidzey et al., Nature 395, 53 (1998) • Large dipole moments • High densities collective enhancement • Rabi splitting can be >1 eV (~30% of transition energy) • Room temperature! Surface plasmons: J. Bellessa et al., Single molecule with gap plasmon: Phys. Rev. Lett. 93, 036404 (2004) Chikkaraddy et al., Nature 535, 127 (2016) from lecture by V. Shalaev Plasmonic cavities -
Tip-Enhanced Strong Coupling Spectroscopy, Imaging, and Control of a Single Quantum Emitter
Tip-enhanced strong coupling spectroscopy, imaging, and control of a single quantum emitter Kyoung-Duck Park,1y;∗ Molly A. May,1y Haixu Leng,2 Jiarong Wang,1 Jaron A. Kropp,2 Theodosia Gougousi,2 Matthew Pelton,2∗ and Markus B. Raschke1∗ 1Department of Physics, Department of Chemistry, and JILA, University of Colorado, Boulder, CO 80309, USA 2Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA yThese authors contributed equally to this work. ∗To whom correspondence should be addressed; E-mail: [email protected] (M.B.R.), [email protected] (M.P.), [email protected] (K.-D.P.) Optical cavities can enhance and control light-matter interactions. This has re- cently been extended to the nanoscale, and with single emitter strong coupling regime even at room temperature using plasmonic nano-cavities with deep sub-diffraction-limited mode volumes. However, with emitters in static nano- cavities, this limits the ability to tune coupling strength or to couple different emitters to the same cavity. Here, we present tip-enhanced strong coupling arXiv:1902.10314v1 [physics.optics] 27 Feb 2019 (TESC) spectroscopy, imaging, and control. Based on a nano-cavity formed between a scanning plasmonic antenna-tip and the substrate, by reversibly and dynamically addressing single quantum dots (QDs) we observe mode splitting > 160 meV and anticrossing over a detuning range of ∼100 meV, and with 1 sub-nm precision control over the mode volume in the ∼103 nm3 regime. Our approach, as a new paradigm of nano-cavity quantum-electrodynamics near- field microscopy to induce, probe, and control single-emitter plasmon hybrid quantum states, opens new pathways from opto-electronics to quantum infor- mation science. -
The Electron-Phonon Coupling Constant
The electron-phonon coupling constant Philip B. Allen Department of Physics and Astronomy, State University of New York, Stony Brook, NY 11794-3800 March 17, 2000 Tables of values of the electron-phonon coupling constants and are given for selected tr elements and comp ounds. A brief summary of the theory is also given. I. THEORETICAL INTRODUCTION Grimvall [1] has written a review of electron-phonon e ects in metals. Prominent among these e ects is sup ercon- ductivity. The BCS theory gives a relation T exp1=N 0V for the sup erconducting transition temp erature c D T in terms of the Debye temp erature .Values of T are tabulated in various places, the most complete prior to c D c the high T era b eing ref. [2]. The electron-electron interaction V consists of the attractive electron-phonon-induced c interaction minus the repulsive Coulombinteraction. The notation is used = N 0V 1 eph and the Coulomb repulsion N 0V is called , so that N 0V = , where is a \renormalized" Coulomb c repulsion, reduced in value from to =[1 + ln! =! ]. This suppression of the Coulomb repulsion is a result P D of the fact that the electron-phonon attraction is retarded in time by an amountt 1=! whereas the repulsive D screened Coulombinteraction is retarded byamuch smaller time, t 1=! where ! is the electronic plasma P P frequency. Therefore, is b ounded ab oveby1= ln! =! which for conventional metals should b e 0:2. P D Values of are known to range from 0:10 to 2:0. -
How the Electron-Phonon Coupling Mechanism Work in Metal Superconductor
How the electron-phonon coupling mechanism work in metal superconductor Qiankai Yao1,2 1College of Science, Henan University of Technology, Zhengzhou450001, China 2School of physics and Engineering, Zhengzhou University, Zhengzhou450001, China Abstract Superconductivity in some metals at low temperature is known to arise from an electron-phonon coupling mechanism. Such the mechanism enables an effective attraction to bind two mobile electrons together, and even form a kind of pairing system(called Cooper pair) to be physically responsible for superconductivity. But, is it possible by an analogy with the electrodynamics to describe the electron-phonon coupling as a resistivity-dependent attraction? Actually so, it will help us to explore a more operational quantum model for the formation of Cooper pair. In particularly, by the calculation of quantum state of Cooper pair, the explored model can provide a more explicit explanation for the fundamental properties of metal superconductor, and answer: 1) How the transition temperature of metal superconductor is determined? 2) Which metals can realize the superconducting transition at low temperature? PACS numbers: 74.20.Fg; 74.20.-z; 74.25.-q; 74.20.De ne is the mobile electron density, η the damping coefficient 1. Introduction that is determined by the collision time τ . In the BCS theory[1], superconductivity is attributed to a In metal environment, mobile electrons are usually phonon-mediated attraction between mobile electrons near modeled to be a kind of classical particles like gas molecules, Fermi surface(called Fermi electrons). The attraction is each of which performs a Brown-like motion and satisfies the sometimes referred to as a residual Coulomb interaction[2] that Langevin equation can glue Cooper pair together to cause superconductivity. -
Chapter 09584
Author's personal copy Excitons in Magnetic Fields Kankan Cong, G Timothy Noe II, and Junichiro Kono, Rice University, Houston, TX, United States r 2018 Elsevier Ltd. All rights reserved. Introduction When a photon of energy greater than the band gap is absorbed by a semiconductor, a negatively charged electron is excited from the valence band into the conduction band, leaving behind a positively charged hole. The electron can be attracted to the hole via the Coulomb interaction, lowering the energy of the electron-hole (e-h) pair by a characteristic binding energy, Eb. The bound e-h pair is referred to as an exciton, and it is analogous to the hydrogen atom, but with a larger Bohr radius and a smaller binding energy, ranging from 1 to 100 meV, due to the small reduced mass of the exciton and screening of the Coulomb interaction by the dielectric environment. Like the hydrogen atom, there exists a series of excitonic bound states, which modify the near-band-edge optical response of semiconductors, especially when the binding energy is greater than the thermal energy and any relevant scattering rates. When the e-h pair has an energy greater than the binding energy, the electron and hole are no longer bound to one another (ionized), although they are still correlated. The nature of the optical transitions for both excitons and unbound e-h pairs depends on the dimensionality of the e-h system. Furthermore, an exciton is a composite boson having integer spin that obeys Bose-Einstein statistics rather than fermions that obey Fermi-Dirac statistics as in the case of either the electrons or holes by themselves. -
Amplitude/Higgs Modes in Condensed Matter Physics
Amplitude / Higgs Modes in Condensed Matter Physics David Pekker1 and C. M. Varma2 1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15217 and 2Department of Physics and Astronomy, University of California, Riverside, CA 92521 (Dated: February 10, 2015) 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 Ψ(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 Ψ(r; t). The phase oscillations are the 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 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. -
Exciton Binding Energy in Small Organic Conjugated Molecule
1 Exciton Binding Energy in small organic conjugated molecule. Pabitra K. Nayak* Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot, 76100, Israel Email: [email protected] Abstract: For small organic conjugated molecules the exciton binding energy can be calculated treating molecules as conductor, and is given by a simple relation BE ≈ 2 e /(4πε0εR), where ε is the dielectric constant and R is the equivalent radius of the molecule. However, if the molecule deviates from spherical shape, a minor correction factor should be added. 1. Introduction An understanding of the energy levels in organic semiconductors is important for designing electronic devices and for understanding their function and performance. The absolute hole transport level and electron transport level can be obtained from theoretical calculations and also from photoemission experiments [1][2][3]. The difference between the two transport levels is referred to as the transport gap (Et). The transport gap is different from the optical gap (Eopt) in organic semiconductors. This is because optical excitation gives rise to excitons rather than free carriers. These excitons are Frenkel excitons and localized to the molecule, hence an extra amount of energy, termed as exciton binding energy (Eb) is needed to produce free charge carriers. What is the magnitude of Eb in organic semiconductors? Answer to this question is more relevant in emerging field of Organic Photovoltaic cells (OPV), due to their impact in determining the output voltage of the solar cells. A lot of efforts are also going on to develop new absorbing material for OPV. It is also important to guess the magnitude of exciton binding energy before the actual synthesis of materials. -
Pion-Induced Transport of Π Mesons in Nuclei
Central Washington University ScholarWorks@CWU All Faculty Scholarship for the College of the Sciences College of the Sciences 2-8-2000 Pion-induced transport of π mesons in nuclei S. G. Mashnik R. J. Peterson A. J. Sierk Michael R. Braunstein Follow this and additional works at: https://digitalcommons.cwu.edu/cotsfac Part of the Atomic, Molecular and Optical Physics Commons, and the Nuclear Commons PHYSICAL REVIEW C, VOLUME 61, 034601 Pion-induced transport of mesons in nuclei S. G. Mashnik,1,* R. J. Peterson,2 A. J. Sierk,1 and M. R. Braunstein3 1T-2, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 2Nuclear Physics Laboratory, University of Colorado, Boulder, Colorado 80309 3Physics Department, Central Washington University, Ellensburg, Washington 98926 ͑Received 28 May 1999; published 8 February 2000͒ A large body of data for pion-induced neutral pion continuum spectra spanning outgoing energies near 180 MeV shows no dip there that might be ascribed to internal strong absorption processes involving the formation of ⌬’s. This is the same observation previously made for the charged pion continuum spectra. Calculations in an intranuclear cascade model or a cascade exciton model with free-space parameters predict such a dip for both neutral and charged pions. We explore several medium modifications to the interactions of pions with internal nucleons that are able to reproduce the data for nuclei from 7Li through Bi. PACS number͑s͒: 25.80.Hp, 25.80.Gn, 25.80.Ls, 21.60.Ka I. INTRODUCTION the NCX data at angles forward of 90° by a factor of 2 ͓3͔. -
Phonon-Exciton Interactions in Wse2 Under a Quantizing Magnetic Field
ARTICLE https://doi.org/10.1038/s41467-020-16934-x OPEN Phonon-exciton Interactions in WSe2 under a quantizing magnetic field Zhipeng Li1,10, Tianmeng Wang 1,10, Shengnan Miao1,10, Yunmei Li2,10, Zhenguang Lu3,4, Chenhao Jin 5, Zhen Lian1, Yuze Meng1, Mark Blei6, Takashi Taniguchi7, Kenji Watanabe 7, Sefaattin Tongay6, Wang Yao 8, ✉ Dmitry Smirnov 3, Chuanwei Zhang2 & Su-Fei Shi 1,9 Strong many-body interaction in two-dimensional transitional metal dichalcogenides provides 1234567890():,; a unique platform to study the interplay between different quasiparticles, such as prominent phonon replica emission and modified valley-selection rules. A large out-of-plane magnetic field is expected to modify the exciton-phonon interactions by quantizing excitons into dis- crete Landau levels, which is largely unexplored. Here, we observe the Landau levels origi- nating from phonon-exciton complexes and directly probe exciton-phonon interaction under a quantizing magnetic field. Phonon-exciton interaction lifts the inter-Landau-level transition selection rules for dark trions, manifested by a distinctively different Landau fan pattern compared to bright trions. This allows us to experimentally extract the effective mass of both holes and electrons. The onset of Landau quantization coincides with a significant increase of the valley-Zeeman shift, suggesting strong many-body effects on the phonon-exciton inter- action. Our work demonstrates monolayer WSe2 as an intriguing playground to study phonon-exciton interactions and their interplay with charge, spin, and valley. 1 Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. 2 Department of Physics, The University of Texas at Dallas, Richardson, TX 75080, USA. -
Lattice-QCD Determinations of Quark Masses and the Strong Coupling Αs
Lattice-QCD Determinations of Quark Masses and the Strong Coupling αs Fermilab Lattice, MILC, and TUMQCD Collaborations September 1, 2020 EF Topical Groups: (check all that apply /) (EF01) EW Physics: Higgs Boson Properties and Couplings (EF02) EW Physics: Higgs Boson as a Portal to New Physics (EF03) EW Physics: Heavy Flavor and Top-quark Physics (EF04) EW Physics: Electroweak Precision Physics and Constraining New Physics (EF05) QCD and Strong Interactions: Precision QCD (EF06) QCD and Strong Interactions: Hadronic Structure and Forward QCD (EF07) QCD and Strong Interactions: Heavy Ions (EF08) BSM: Model-specific Explorations (EF09) BSM: More General Explorations (EF10) BSM: Dark Matter at Colliders Other Topical Groups: (RF01) Weak Decays of b and c Quarks (TF02) Effective Field Theory Techniques (TF05) Lattice Gauge Theory (CompF2) Theoretical Calculations and Simulation Contact Information: Andreas S. Kronfeld (Theoretical Physics Department, Fermilab) [email]: [email protected] on behalf of the Fermilab Lattice, MILC, and TUMQCD Collaborations Fermilab Lattice, MILC, and TUMQCD Collaborations: A. Bazavov, C. Bernard, N. Brambilla, C. DeTar, A.X. El-Khadra, E. Gamiz,´ Steven Gottlieb, U.M. Heller, W.I. Jay, J. Komijani, A.S. Kronfeld, J. Laiho, P.B. Mackenzie, E.T. Neil, P. Petreczky, J.N. Simone, R.L. Sugar, D. Toussaint, A. Vairo, A. Vaquero Aviles-Casco,´ J.H. Weber, R.S. Van de Water Lattice-QCD Determinations of Quark Masses and the Strong Coupling αs Quantum chromdynamics (QCD) as a stand-alone theory has 1 + nf + 1 free parameters that must be set from experimental measurements, complemented with theoretical calculations connecting the measurements to the QCD Lagrangian.