INTRODUCTION À LA PHYSIQUE MÉSOSCOPIQUE: ÉLECTRONS ET PHOTONS INTRODUCTION TO MESOSCOPIC PHYSICS: ELECTRONS AND PHOTONS
|
|
- Geraldine Chapman
- 6 years ago
- Views:
Transcription
1 Chaire de Physique Mésoscopique Michel Devoret Année 2007, Cours des 7 et 14 juin INTRODUCTION À LA PHYSIQUE MÉSOSCOPIQUE: ÉLECTRONS ET PHOTONS INTRODUCTION TO MESOSCOPIC PHYSICS: ELECTRONS AND PHOTONS Première Leçon / First Lecture This College de France document is for consultation only. Reproduction rights are reserved. 07-I-1
2 AIM OF THESE TWO LECTURES Discuss a selection of basic concepts of mesoscopic physics and contrast their treatment with that of atomic physics OUTLINE 1. General remarks on mesoscopic physics a) fundamental constants b) survival of quantum effects in macrosystems 2. What are "electrons"? a) example of mesoscopic resistor b) screening c) finite lifetime 3. What are "photons"? a) example of transmission line b) longitudinal and transverse modes c) 1-D Planck's law 4. Conclusion: quantum transport v.s. quantum optics part 1 part 2 07-I-2
3 General remarks Purpose: explain the novelty of mesoscopic phenomena by discussing status of variables and parameters 07-I-3
4 MACRO versus micro MACRO SYSTEM classical mechanics many particles, strongly coupled to environment 2 2 pθ kθ H = M 2 can have engineered structural parameters micro system quantum mechanics few particles, almost isolated from environment 2 2 ˆ pˆ e H = m 4πε rˆ e 0 always "God-given" structural parameters 07-I-4
5 MESOSCOPIC PHENOMENA: Number of particles: macroscopic Collective degrees of freedom: quantum High-Q nanomechanical low temperatures: clearly mesoscopic Superconducting magnets for MRI: clearly not mesoscopic Characteristic energies in mesoscopic phenomena involve not only fundamental constants, but also geometric dimensions adjusted by design and fabrication 07-I-5
6 REVIEW OF UNIVERSAL CONSTANTS S. I. Units : s, m, kg, A, K Classical constants Quantum constants speed of light impedance of vacuum c Z vac 377Ω charge quantum action quantum e electrical permittivity of vacuum magnetic permeability of vacuum ε 0 1 = cz Z µ 0 = c vac vac flux quantum resistance quantum h Φ 0 = 2e R K h = 26kΩ 2 e Boltzmann's constant gravitational constant k B G fine structure cst. α = Zvac 1 2R 137 K 07-I-6
7 UNIVERSAL AND MICROSCOPIC QUANTUM CONSTANTS Universal constants Microscopic constants charge of electron: e mass of electron: m e Planck's constant: flux quantum: Φ = 0 h 2e magn. mt. of electron: mass of proton: mass of neutron µ B m p m n resistance quantum: fine structure cst.: R K α = h = 26kΩ 2 e Zvac 1 2R 137 K magn. mt. of proton µ p 07-I-7
8 FORMS OF CHARACTERISTIC ENERGIES ω 20 GHz ev 80 µv kbt 1K I-8
9 USUAL ENERGY SCALES OF MICROSCOPIC QUANTUM EFFECTS Atomic matter Bulk condensed matter E ~ ev Ry En = 2 n m c Ry 2 α 2 e 2 = = 13.6eV conduction band E gap ~ ev valence band E Debye ~ 10meV = sc E Debye e N 1 ( 0) V ~ mev IN MESOSCOPIC QUANTUM EFFECTS, NEW ENERGY SCALES EMERGE! 07-I-9
10 MESOSCOPIC PHYSICS CHALLENGES COMMON WISDOM ABOUT THE SUPPRESSION OF COLLECTIVE QUANTUM EFFECTS IN LARGE AND DIRTY SYSTEMS THERMAL ENERGY CAN BE BIGGER THAN SINGLE PARTICLE ENERGY LEVEL SPACINGS DISORDER DOES NOT FULLY SUPPRESS INTERFERENCES, IT IS DECOHERENCE WHICH IS IMPORTANT A SINGLE ELECTRON CAN COUNT LOCAL CIRCUIT THEORY WILL UNEXPECTEDLY FAIL 07-I-10
11 MESOSCOPIC PHYSICS CHALLENGES COMMON WISDOM ABOUT THE SUPPRESSION OF COLLECTIVE QUANTUM EFFECTS IN LARGE AND DIRTY SYSTEMS THERMAL ENERGY CAN BE BIGGER THAN SINGLE PARTICLE ENERGY LEVEL SPACINGS DISORDER DOES NOT FULLY SUPPRESS INTERFERENCES, IT IS DECOHERENCE WHICH IS IMPORTANT A SINGLE ELECTRON CAN COUNT LOCAL CIRCUIT THEORY WILL UNEXPECTEDLY FAIL 07-I-11
12 EXAMPLE OF COMMON WISDOM AT WORK: THE CROSSOVER TO DULONG-PETIT LAW C V Nk T 3 B 0 kt B ω Debye T quantum classical 07-I-12
13 2-DIMENSIONAL ELECTRON GAS SYSTEM contact electrode gate electrode z before charge transfer after charge transfer n-algaas i-gaas a 2DEG forms here! 07-I-13
14 PINCHING THE 2DEG INTO A SMALL WIRE source reservoir drain reservoir d small effective mass I V g V g v F ~ 1nm/ps V/2 V/2 Ballistic transport: L L what if F kt? e B v d 07-I-14
15 CONDUCTANCE QUANTIZATION G 2 / e h 12 d kt B v d F 10 8 van Wees et al. 1988: G di = dv ev / k T 0 B V g waveguide effect! 07-I-15
16 UP TO WHAT SIZE CAN QUANTUM EFFECTS PERSIST IN PRESENCE OF DISORDER? weak disorder: 1/ e k F L e NON-TRIVIAL RESULT kt, B τ ϕ v L F e L Thouless energy Can be much larger than level spacing in box of size L! vk F F v ( Lk ) 2 L 2 F F e 07-I-16
17 BOOKS ON MESOSCOPIC PHYSICS S. Datta Y. Imry E. Akkermans and G. Montambaux H. Grabert and M. Devoret REQUISITES: Quantum mechanics Solid state physics Statistical mechanics Useful reference books on quantum statistical physics: Feynman; Schrieffer; Pines and Nozières 07-I-17
18 2. How mesoscopic physics models the "electron" Purpose: provide groundwork for Landauer's approach of transport phenomena 07-I-18
19 THE MESOSCOPIC RESISTOR + V _ quantum coherent wire I source reservoir L L ϕ drain reservoir Landauer reservoir: metallic electrode which injects into the quantum coherent region quasi-electron waves with well-defined chemical potential and temperature. It also accepts without reflection any quasi-electron waves and thoroughly recycles them. The Landauer reservoir is to Fermi waves what a black-body is to Bose waves. 07-I-19
20 Collection of independent channels t r t r µ + µ E ev f + f 07-I-19 bis
21 THE LANDAUER-BÜTTIKER FORMULA I = I I + e + I = f ( E) t ( E) 2 d E ± ± m h m f ± E ( ) = 1 E µ ± 1+ exp kt B µ µ = + ev schizophrenic! why does it work? 07-I-20
22 RESISTANCE DETERMINED BY ELASTIC TRANSMISSION COEFFICIENT! WHAT ABOUT JOULE HEATING? 07-I-21
23 QUESTION: What are the differences between a quasi-electron (a.k.a. dressed electron) and the usual (bare) electron? PARTICLE IDENTIFICATION CARD Last Name: Electron First First name: name: Bare Bare Address: Vacuum Genre: Genre: Fermion Fermion Occupation: Wave packet Lifetime: infinite Average energy: ω Average momentum: k Velocity: v=dω/dk Mass: dk/dv=m e Charge: -e Spin: S=1/2 Magnetic moment: µ g eb Sµ B ge α = O 2 π 2 ( α ) 07-I-22
24 An example of a Feynman diagram involving the usual electron and photon of atomic physics which propagate in vacuum γ γ e - e - 07-I-22bis
25 THE "ELECTRON" OF MESOSCOPICS PARTICLE IDENTIFICATION CARD Last Name: Electron First name: Quasi Address: Metal Genre: Fermion Occupation: Wave packet Lifetime: finite, k F Average energy: ω Average momentum: k Velocity: v=dω/dk Mass: dk/dv=m eff (k) Transverse charge: -e Longitudinal charge: 0 (q 0) Spin: S=1/2 Magnetic moment: g eff Sµ B 07-I-23
26 Definition of the longitudinal and transverse part of a field: F = F + F l F = 0 t F = 0 l t The longitudinal and transverse charges are the sources of the longitudinal and transverse parts of the electrical field, respectively. 07-I-23bis
27 SOLIDS van der Waals ionic insulators covalent metal I-24
28 REVIEW OF DRUDE MODEL E v x t τ v x e E ( ) = τ j = n( e) v x m j σ = = E ne m 2 τ 07-I-25
29 PROBLEM: ELECTRONS ARE FERMIONIC WAVES! 07-I-26
30 REVIEW OF FREE FERMI GAS MODEL Box volume V Nb of fermions N k y kf ( k ) a Total energy E K Length scale a 0 Energy scale Ry 2 4 me e = 4 πε ; Ry = 2 4πε me e N k a n r k V = = ( π ) = = a a = r a 3 1 r 2 4π F ; 2 s ; F 3 2 4π 3 0 s 0 F F g m E e C s 2 E K 3 F = = E F = 2 N 5 2m e 5 rs v = k = v E N = Ry F Ry 0 k x 07-I-27
31 OTHER PROBLEM: ELECTRONS INTERACT STRONGLY! BUT TOO STRONG INTERACTION KILLS INTERACTION.. 07-I-28
32 Acknowledgements : D. Esteve, H. Pothier, D. Stone and C. Urbina
INTRODUCTION À LA PHYSIQUE MÉSOSCOPIQUE: ÉLECTRONS ET PHOTONS INTRODUCTION TO MESOSCOPIC PHYSICS: ELECTRONS AND PHOTONS
Chaire de Physique Mésoscopique Michel Devoret Année 2007, Cours des 7 et 14 juin INTRODUCTION À LA PHYSIQUE MÉSOSCOPIQUE: ÉLECTRONS ET PHOTONS INTRODUCTION TO MESOSCOPIC PHYSICS: ELECTRONS AND PHOTONS
More informationQuantum transport in nanoscale solids
Quantum transport in nanoscale solids The Landauer approach Dietmar Weinmann Institut de Physique et Chimie des Matériaux de Strasbourg Strasbourg, ESC 2012 p. 1 Quantum effects in electron transport R.
More informationChapter 3 Properties of Nanostructures
Chapter 3 Properties of Nanostructures In Chapter 2, the reduction of the extent of a solid in one or more dimensions was shown to lead to a dramatic alteration of the overall behavior of the solids. Generally,
More informationQUANTUM ELECTRONICS ON THE TRAY* *Sur le plateau (de Saclay)
QUANTUM ELECTRONIC ON THE TRAY* *ur le plateau (de aclay) Goal: Reveal the quantum behavior of electrons everal ways of revealing the quantum behavior of electrons 1 Interference experiments of coherent
More informationAppendix 1: List of symbols
Appendix 1: List of symbols Symbol Description MKS Units a Acceleration m/s 2 a 0 Bohr radius m A Area m 2 A* Richardson constant m/s A C Collector area m 2 A E Emitter area m 2 b Bimolecular recombination
More informationFundamental Constants
Fundamental Constants Atomic Mass Unit u 1.660 540 2 10 10 27 kg 931.434 32 28 MeV c 2 Avogadro s number N A 6.022 136 7 36 10 23 (g mol) 1 Bohr magneton μ B 9.274 015 4(31) 10-24 J/T Bohr radius a 0 0.529
More informationNanoscience, MCC026 2nd quarter, fall Quantum Transport, Lecture 1/2. Tomas Löfwander Applied Quantum Physics Lab
Nanoscience, MCC026 2nd quarter, fall 2012 Quantum Transport, Lecture 1/2 Tomas Löfwander Applied Quantum Physics Lab Quantum Transport Nanoscience: Quantum transport: control and making of useful things
More informationSingle Electron Tunneling Examples
Single Electron Tunneling Examples Danny Porath 2002 (Schönenberger et. al.) It has long been an axiom of mine that the little things are infinitely the most important Sir Arthur Conan Doyle Books and
More informationFUNDAMENTALS OF PHYSICS Vol. II - Quantum Phenpmena In Low-Dimensional Systems- Michael R. Geller QUANTUM PHENOMENA IN LOW-DIMENSIONAL SYSTEMS
QUANTUM PHENOMENA IN LOW-DIMENSIONAL SYSTEMS Michael R. Geller Department of Physics and Astronomy, University of Georgia, USA Keywords: Aharonov-Bohm effect, Bucky balls, composite fermions, coulomb blockade,
More informationNon-Continuum Energy Transfer: Phonons
Non-Continuum Energy Transfer: Phonons D. B. Go Slide 1 The Crystal Lattice The crystal lattice is the organization of atoms and/or molecules in a solid simple cubic body-centered cubic hexagonal a NaCl
More informationElectrical Transport in Nanoscale Systems
Electrical Transport in Nanoscale Systems Description This book provides an in-depth description of transport phenomena relevant to systems of nanoscale dimensions. The different viewpoints and theoretical
More informationIntroduction to Molecular Electronics. Lecture 1: Basic concepts
Introduction to Molecular Electronics Lecture 1: Basic concepts Conductive organic molecules Plastic can indeed, under certain circumstances, be made to behave very like a metal - a discovery for which
More informationOlivier Bourgeois Institut Néel
Olivier Bourgeois Institut Néel Outline Introduction: necessary concepts: phonons in low dimension, characteristic length Part 1: Transport and heat storage via phonons Specific heat and kinetic equation
More informationPhysics of Semiconductors
Physics of Semiconductors 13 th 2016.7.11 Shingo Katsumoto Department of Physics and Institute for Solid State Physics University of Tokyo Outline today Laughlin s justification Spintronics Two current
More informationThe Physics of Nanoelectronics
The Physics of Nanoelectronics Transport and Fluctuation Phenomena at Low Temperatures Tero T. Heikkilä Low Temperature Laboratory, Aalto University, Finland OXFORD UNIVERSITY PRESS Contents List of symbols
More informationOptical Properties of Lattice Vibrations
Optical Properties of Lattice Vibrations For a collection of classical charged Simple Harmonic Oscillators, the dielectric function is given by: Where N i is the number of oscillators with frequency ω
More informationPhonon II Thermal Properties
Phonon II Thermal Properties Physics, UCF OUTLINES Phonon heat capacity Planck distribution Normal mode enumeration Density of states in one dimension Density of states in three dimension Debye Model for
More informationSemiconductor Physics and Devices Chapter 3.
Introduction to the Quantum Theory of Solids We applied quantum mechanics and Schrödinger s equation to determine the behavior of electrons in a potential. Important findings Semiconductor Physics and
More informationCorrelated 2D Electron Aspects of the Quantum Hall Effect
Correlated 2D Electron Aspects of the Quantum Hall Effect Outline: I. Introduction: materials, transport, Hall effects II. III. IV. Composite particles FQHE, statistical transformations Quasiparticle charge
More informationwire z axis Under these assumptions, if we model the electrons by plane waves in the z direction we get n E, n, 1,2,
Part 4. Two Terminal Quantum Wire Devices Part 4. Two Terminal Quantum Wire Devices Let s consider a quantum wire between two contacts. As we saw in Part, a quantum wire is a one-dimensional conductor.
More informationCIRCUIT QUANTUM ELECTRODYNAMICS WITH ELECTRONS ON HELIUM
CIRCUIT QUANTUM ELECTRODYNAMICS WITH ELECTRONS ON HELIUM David Schuster Assistant Professor University of Chicago Chicago Ge Yang Bing Li Michael Geracie Yale Andreas Fragner Rob Schoelkopf Useful cryogenics
More informationQuantum physics in quantum dots
Quantum physics in quantum dots Klaus Ensslin Solid State Physics Zürich AFM nanolithography Multi-terminal tunneling Rings and dots Time-resolved charge detection Moore s Law Transistors per chip 10 9
More informationPhysics of Semiconductors (Problems for report)
Physics of Semiconductors (Problems for report) Shingo Katsumoto Institute for Solid State Physics, University of Tokyo July, 0 Choose two from the following eight problems and solve them. I. Fundamentals
More informationIntroduction to Quantum Mechanics of Superconducting Electrical Circuits
Introduction to Quantum Mechanics of Superconducting lectrical Circuits What is superconductivity? What is a osephson junction? What is a Cooper Pair Box Qubit? Quantum Modes of Superconducting Transmission
More informationQUANTUM- CLASSICAL ANALOGIES
D. Dragoman M. Dragoman QUANTUM- CLASSICAL ANALOGIES With 78 Figures ^Ü Springer 1 Introduction 1 2 Analogies Between Ballistic Electrons and Electromagnetic Waves 9 2.1 Analog Parameters for Ballistic
More informationLessons from Nanoscience: A Lecture Note Series
Lessons from Nanoscience: A Lecture Note Series http://nanohub.org/topics/lessonsfromnanoscience Volume 1: Lessons from Nanoelectronics: A New Perspective on Transport Supriyo Datta Purdue University datta@purdue.edu
More informationCharge carrier statistics/shot Noise
Charge carrier statistics/shot Noise Sebastian Waltz Department of Physics 16. Juni 2010 S.Waltz (Biomolecular Dynamics) Charge carrier statistics/shot Noise 16. Juni 2010 1 / 36 Outline 1 Charge carrier
More informationUNIVERSITY OF LONDON. BSc and MSci EXAMINATION 2005 DO NOT TURN OVER UNTIL TOLD TO BEGIN
UNIVERSITY OF LONDON BSc and MSci EXAMINATION 005 For Internal Students of Royal Holloway DO NOT UNTIL TOLD TO BEGIN PH610B: CLASSICAL AND STATISTICAL THERMODYNAMICS PH610B: CLASSICAL AND STATISTICAL THERMODYNAMICS
More informationIntroduction to semiconductor nanostructures. Peter Kratzer Modern Concepts in Theoretical Physics: Part II Lecture Notes
Introduction to semiconductor nanostructures Peter Kratzer Modern Concepts in Theoretical Physics: Part II Lecture Notes What is a semiconductor? The Fermi level (chemical potential of the electrons) falls
More informationSemiclassical formulation
The story so far: Transport coefficients relate current densities and electric fields (currents and voltages). Can define differential transport coefficients + mobility. Drude picture: treat electrons
More informationMaterial Properties & Characterization - Surfaces
1) XPS Spectrum analysis: The figure below shows an XPS spectrum measured on the surface of a clean insoluble homo-polyether. Using the formulas and tables in this document, answer the following questions:
More informationModern Physics for Scientists and Engineers International Edition, 4th Edition
Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL BASIS
More informationQuantized Electrical Conductance of Carbon nanotubes(cnts)
Quantized Electrical Conductance of Carbon nanotubes(cnts) By Boxiao Chen PH 464: Applied Optics Instructor: Andres L arosa Abstract One of the main factors that impacts the efficiency of solar cells is
More informationThe statistical theory of quantum dots
The statistical theory of quantum dots Y. Alhassid Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520 A quantum dot is a sub-micron-scale conducting
More information7. FREE ELECTRON THEORY.
7. FREE ELECTRON THEORY. Aim: To introduce the free electron model for the physical properties of metals. It is the simplest theory for these materials, but still gives a very good description of many
More informationFinal Exam Practice Solutions
Physics 390 Final Exam Practice Solutions These are a few problems comparable to those you will see on the exam. They were picked from previous exams. I will provide a sheet with useful constants and equations
More informationQuantum Noise Measurement of a Carbon Nanotube Quantum dot in the Kondo Regime
Quantum Noise Measurement of a Carbon Nanotube Quantum dot in the Kondo Regime J. Basset, 1 A.Yu. Kasumov, 1 C.P. Moca, G. Zarand,, 3 P. Simon, 1 H. Bouchiat, 1 and R. Deblock 1 1 Laboratoire de Physique
More informationScattering theory of thermoelectric transport. Markus Büttiker University of Geneva
Scattering theory of thermoelectric transport Markus Büttiker University of Geneva Summer School "Energy harvesting at micro and nanoscales, Workshop "Energy harvesting: models and applications, Erice,
More informationThe phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other
1 The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other phases of matter that have been experimentally observed,
More informationSupercondcting Qubits
Supercondcting Qubits Patricia Thrasher University of Washington, Seattle, Washington 98195 Superconducting qubits are electrical circuits based on the Josephson tunnel junctions and have the ability to
More informationQuantum Conductance. John Carroll. March 22, 2009
Quantum Conductance John Carroll March 22, 2009 Introduction The concept of conductance is used to explain the manner in which electrical current flows though a material. The original theory of conductance
More informationCandidacy Exam Department of Physics February 6, 2010 Part I
Candidacy Exam Department of Physics February 6, 2010 Part I Instructions: ˆ The following problems are intended to probe your understanding of basic physical principles. When answering each question,
More informationVISIT THE WEBSITE OF THE CHAIR OF MESOSCOPIC PHYSICS
Chaire de Physique Mésoscopique Michel Devoret Année 00, mai - juin INTRODUCTION AU CALCUL QUANTIQUE INTRODUCTION TO QUANTUM COMPUTATION Quatrième Leçon / Fourth Lecture This College de France document
More informationsin[( t 2 Home Problem Set #1 Due : September 10 (Wed), 2008
Home Problem Set #1 Due : September 10 (Wed), 008 1. Answer the following questions related to the wave-particle duality. (a) When an electron (mass m) is moving with the velocity of υ, what is the wave
More informationWeakly-coupled quasi-1d helical modes in disordered 3D topological insulator quantum wires
Weakly-coupled quasi-1d helical modes in disordered 3D topological insulator quantum wires J. Dufouleur, 1 L. Veyrat, 1 B. Dassonneville, 1 E. Xypakis, 2 J. H. Bardarson, 2 C. Nowka, 1 S. Hampel, 1 J.
More informationSuperconductivity at nanoscale
Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and
More informationMIDSUMMER EXAMINATIONS 2001 PHYSICS, PHYSICS WITH ASTROPHYSICS PHYSICS WITH SPACE SCIENCE & TECHNOLOGY PHYSICS WITH MEDICAL PHYSICS
No. of Pages: 6 No. of Questions: 10 MIDSUMMER EXAMINATIONS 2001 Subject PHYSICS, PHYSICS WITH ASTROPHYSICS PHYSICS WITH SPACE SCIENCE & TECHNOLOGY PHYSICS WITH MEDICAL PHYSICS Title of Paper MODULE PA266
More informationPH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5
PH575 Spring 2014 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 POP QUIZ Phonon dispersion relation:
More informationMesoscopic Nano-Electro-Mechanics of Shuttle Systems
* Mesoscopic Nano-Electro-Mechanics of Shuttle Systems Robert Shekhter University of Gothenburg, Sweden Lecture1: Mechanically assisted single-electronics Lecture2: Quantum coherent nano-electro-mechanics
More informationSolution: An electron with charge e (e > 0) experiences the Lorentz force due to the perpendicular magnetic field and the electric force
Question 1 The fractional quantum Hall effect (FQHE) was discovered by D. C. Tsui and H. Stormer at Bell Labs in 1981. In the experiment electrons were confined in two dimensions on the GaAs side by the
More informationPHYSICS-PH (PH) Courses. Physics-PH (PH) 1
Physics-PH (PH) 1 PHYSICS-PH (PH) Courses PH 110 Physics of Everyday Phenomena (GT-SC2) Credits: 3 (3-0-0) Fundamental concepts of physics and elementary quantitative reasoning applied to phenomena in
More informationElectronic transport in low dimensional systems
Electronic transport in low dimensional systems For example: 2D system l
More informationRÉSONATEURS NANOMÉCANIQUES DANS LE RÉGIME QUANTIQUE NANOMECHANICAL RESONATORS IN QUANTUM REGIME
Chaire de Physique Mésoscopique Michel Devoret Année 1, 15 mai - 19 juin RÉSONATEURS NANOMÉCANIQUES DANS LE RÉGIME QUANTIQUE NANOMECHANICAL RESONATORS IN QUANTUM REGIME Troisième leçon / Third lecture
More informationPreliminary Examination - Day 1 Thursday, August 10, 2017
UNL - Department of Physics and Astronomy Preliminary Examination - Day Thursday, August, 7 This test covers the topics of Quantum Mechanics (Topic ) and Electrodynamics (Topic ). Each topic has 4 A questions
More informationThermal and Statistical Physics Department Exam Last updated November 4, L π
Thermal and Statistical Physics Department Exam Last updated November 4, 013 1. a. Define the chemical potential µ. Show that two systems are in diffusive equilibrium if µ 1 =µ. You may start with F =
More information2.57/2.570 Midterm Exam No. 1 April 4, :00 am -12:30 pm
Name:.57/.570 Midterm Exam No. April 4, 0 :00 am -:30 pm Instructions: ().57 students: try all problems ().570 students: Problem plus one of two long problems. You can also do both long problems, and one
More informationCambridge International Examinations Cambridge International Advanced Level
Cambridge International Examinations Cambridge International Advanced Level *2203241344* PHYSICS 9702/42 Paper 4 A2 Structured Questions May/June 2015 2 hours Candidates answer on the Question Paper. No
More informationElectrical and Optical Properties. H.Hofmann
Introduction to Nanomaterials Electrical and Optical Properties H.Hofmann Electrical Properties Ohm: G= σw/l where is the length of the conductor, measured in meters [m], A is the cross-section area of
More informationTunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime
Tunneling Spectroscopy of Disordered Two-Dimensional Electron Gas in the Quantum Hall Regime The Harvard community has made this article openly available. Please share how this access benefits you. Your
More informationPhysics 607 Final Exam
Physics 67 Final Exam Please be well-organized, and show all significant steps clearly in all problems. You are graded on your work, so please do not just write down answers with no explanation! Do all
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationA. F. J. Levi 1 EE539: Engineering Quantum Mechanics. Fall 2017.
A. F. J. Levi 1 Engineering Quantum Mechanics. Fall 2017. TTh 9.00 a.m. 10.50 a.m., VHE 210. Web site: http://alevi.usc.edu Web site: http://classes.usc.edu/term-20173/classes/ee EE539: Abstract and Prerequisites
More informationQuantum Theory of Matter
Quantum Theory of Matter Overview Lecture Derek Lee Imperial College London January 2007 Outline 1 Course content Introduction Superfluids Superconductors 2 Course Plan Resources Outline 1 Course content
More informationPart II - Electronic Properties of Solids Lecture 12: The Electron Gas (Kittel Ch. 6) Physics 460 F 2006 Lect 12 1
Part II - Electronic Properties of Solids Lecture 12: The Electron Gas (Kittel Ch. 6) Physics 460 F 2006 Lect 12 1 Outline Overview - role of electrons in solids The starting point for understanding electrons
More informationMany-Body Problems and Quantum Field Theory
Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and
More information2.4 GaAs Heterostructures and 2D electron gas
Semiconductor Surfaces and Interfaces 8 2.4 GaAs Heterostructures and 2D electron gas - To determine the band structure of the heterostructure, a self consistent solution of Poisson and Schrödinger equation
More informationLecture 6 Photons, electrons and other quanta. EECS Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku
Lecture 6 Photons, electrons and other quanta EECS 598-002 Winter 2006 Nanophotonics and Nano-scale Fabrication P.C.Ku From classical to quantum theory In the beginning of the 20 th century, experiments
More informationSpins and spin-orbit coupling in semiconductors, metals, and nanostructures
B. Halperin Spin lecture 1 Spins and spin-orbit coupling in semiconductors, metals, and nanostructures Behavior of non-equilibrium spin populations. Spin relaxation and spin transport. How does one produce
More informationINTRODUCTION TO SUPERCONDUCTING QUBITS AND QUANTUM EXPERIENCE: A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUD
INTRODUCTION TO SUPERCONDUCTING QUBITS AND QUANTUM EXPERIENCE: A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUD Hanhee Paik IBM Quantum Computing Group IBM T. J. Watson Research Center, Yorktown Heights, NY USA
More informationMartes Cuánticos. Quantum Capacitors. (Quantum RC-circuits) Victor A. Gopar
Martes Cuánticos Quantum Capacitors (Quantum RC-circuits) Victor A. Gopar -Universal resistances of the quantum resistance-capacitance circuit. Nature Physics, 6, 697, 2010. C. Mora y K. Le Hur -Violation
More informationPhysics 607 Exam 2. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2
Physics 607 Exam Please be well-organized, and show all significant steps clearly in all problems. You are graded on your work, so please do not just write down answers with no explanation! Do all your
More informationThe Oxford Solid State Basics
The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS Contents 1 About Condensed Matter Physics 1 1.1 What Is Condensed Matter Physics 1 1.2 Why Do We Study Condensed
More informationFYS Vår 2015 (Kondenserte fasers fysikk)
FYS410 - Vår 015 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/fys410/v15/index.html Pensum: Introduction to Solid State Physics by Charles Kittel (Chapters 1-9 and 17, 18, 0)
More informationElectronic Quantum Transport in Mesoscopic Semiconductor Structures
Thomas Ihn Electronic Quantum Transport in Mesoscopic Semiconductor Structures With 90 Illustrations, S in Full Color Springer Contents Part I Introduction to Electron Transport l Electrical conductance
More information+ - Indirect excitons. Exciton: bound pair of an electron and a hole.
Control of excitons in multi-layer van der Waals heterostructures E. V. Calman, C. J. Dorow, M. M. Fogler, L. V. Butov University of California at San Diego, S. Hu, A. Mishchenko, A. K. Geim University
More informationCHAPTER 2: ENERGY BANDS & CARRIER CONCENTRATION IN THERMAL EQUILIBRIUM. M.N.A. Halif & S.N. Sabki
CHAPTER 2: ENERGY BANDS & CARRIER CONCENTRATION IN THERMAL EQUILIBRIUM OUTLINE 2.1 INTRODUCTION: 2.1.1 Semiconductor Materials 2.1.2 Basic Crystal Structure 2.1.3 Basic Crystal Growth technique 2.1.4 Valence
More informationMath Questions for the 2011 PhD Qualifier Exam 1. Evaluate the following definite integral 3" 4 where! ( x) is the Dirac! - function. # " 4 [ ( )] dx x 2! cos x 2. Consider the differential equation dx
More informationLecture 3: Optical Properties of Insulators, Semiconductors, and Metals. 5 nm
Metals Lecture 3: Optical Properties of Insulators, Semiconductors, and Metals 5 nm Course Info Next Week (Sept. 5 and 7) no classes First H/W is due Sept. 1 The Previous Lecture Origin frequency dependence
More informationVICTORIA JUNIOR COLLEGE 2014 JC2 PRELIMINARY EXAMINATION. 23/9/ h 1600h
Name: Class: 13S VICTORIA JUNIOR COLLEGE 2014 JC2 PRELIMINARY EXAMINATION PHYSICS 9646/3 Higher 2 Paper 3 23/9/2014 1400h 1600h TUESDAY (2 Hours) This paper consists of two sections: Section A (40 marks)
More informationPH575 Spring Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5
PH575 Spring 2009 Lecture #26 & 27 Phonons: Kittel Ch. 4 & 5 PH575 Spring 2009 POP QUIZ Phonons are: A. Fermions B. Bosons C. Lattice vibrations D. Light/matter interactions PH575 Spring 2009 POP QUIZ
More informationUnderstanding. Solid State Physics. Sharon Ann Holgate. CRC Press Taylor & Francis Group Boca Raton London NewYork
Understanding Solid State Physics Sharon Ann Holgate (И CRC Press Taylor & Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa business A TAYLORS FRANCIS
More informationNanoelectronics 14. [( ) k B T ] 1. Atsufumi Hirohata Department of Electronics. Quick Review over the Last Lecture.
Nanoelectronics 14 Atsufumi Hirohata Department of Electronics 09:00 Tuesday, 27/February/2018 (P/T 005) Quick Review over the Last Lecture Function Fermi-Dirac distribution f ( E) = 1 exp E µ [( ) k B
More informationConductance quantization and quantum Hall effect
UNIVERSITY OF LJUBLJANA FACULTY OF MATHEMATICS AND PHYSICS DEPARTMENT FOR PHYSICS Miha Nemevšek Conductance quantization and quantum Hall effect Seminar ADVISER: Professor Anton Ramšak Ljubljana, 2004
More informationQuantum Noise of a Carbon Nanotube Quantum Dot in the Kondo Regime
Quantum Noise of a Carbon Nanotube Quantum Dot in the Kondo Regime Exp : J. Basset, A.Yu. Kasumov, H. Bouchiat, and R. Deblock Laboratoire de Physique des Solides Orsay (France) Theory : P. Simon (LPS),
More informationPHYSICS OF NANOSTRUCTURES
PHYSICS OF NANOSTRUCTURES Proceedings of the Thirty-Eighth Scottish Universities Summer School in Physics, St Andrews, July-August 1991. A NATO Advanced Study Institute. Edited by J H Davies Glasgow University
More informationUGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM PHYSICAL SCIENCE TEST SERIES # 4. Atomic, Solid State & Nuclear + Particle
UGC ACADEMY LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM BOOKLET CODE PH PHYSICAL SCIENCE TEST SERIES # 4 Atomic, Solid State & Nuclear + Particle SUBJECT CODE 05 Timing: 3: H M.M: 200 Instructions 1.
More informationAtoms, Molecules and Solids (selected topics)
Atoms, Molecules and Solids (selected topics) Part I: Electronic configurations and transitions Transitions between atomic states (Hydrogen atom) Transition probabilities are different depending on the
More informationPersistent spin helix in spin-orbit coupled system. Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab
Persistent spin helix in spin-orbit coupled system Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab Persistent spin helix in spin-orbit coupled system Jake Koralek, Chris Weber, Joe Orenstein
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *3781213391* PHYSICS 9702/43 Paper 4 A Level Structured Questions May/June 2017 2 hours Candidates answer
More informationCondensed matter theory Lecture notes and problem sets 2012/2013
Condensed matter theory Lecture notes and problem sets 2012/2013 Dmitri Ivanov Recommended books and lecture notes: [AM] N. W. Ashcroft and N. D. Mermin, Solid State Physics. [Mar] M. P. Marder, Condensed
More informationHigh School Curriculum Standards: Physics
High School Curriculum Standards: Physics Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical
More informationWhat is Quantum Transport?
What is Quantum Transport? Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. http://www.physics.udel.edu/~bnikolic Semiclassical Transport (is boring!) Bloch-Boltzmann
More informationCan superconductivity emerge out of a non Fermi liquid.
Can superconductivity emerge out of a non Fermi liquid. Andrey Chubukov University of Wisconsin Washington University, January 29, 2003 Superconductivity Kamerling Onnes, 1911 Ideal diamagnetism High Tc
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 2 Course Objectives
correlated to the College Board AP Physics 2 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring Understanding 1.A:
More information6.730 Physics for Solid State Applications
6.730 Physics for Solid State Applications Lecture 25: Chemical Potential and Equilibrium Outline Microstates and Counting System and Reservoir Microstates Constants in Equilibrium Temperature & Chemical
More informationSpin Transport in III-V Semiconductor Structures
Spin Transport in III-V Semiconductor Structures Ki Wook Kim, A. A. Kiselev, and P. H. Song Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695-7911 We
More informationStrong back-action of a linear circuit on a single electronic quantum channel F. PIERRE
Strong back-action of a linear circuit on a single electronic quantum channel F. PIERRE F. Parmentier, A. Anthore, S. Jézouin, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly Laboratory for Photonics &
More informationReview of Optical Properties of Materials
Review of Optical Properties of Materials Review of optics Absorption in semiconductors: qualitative discussion Derivation of Optical Absorption Coefficient in Direct Semiconductors Photons When dealing
More informationLecture 2: Quantum Mechanics and Relativity
Lecture 2: Quantum Mechanics and Relativity Atom Atomic number A Number of protons Z Number of neutrons A-Z Number of electrons Z Charge of electron = charge of proton ~1.6 10-19 C Size of the atom ~10-10
More informationMetals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p.
Metals: the Drude and Sommerfeld models p. 1 Introduction p. 1 What do we know about metals? p. 1 The Drude model p. 2 Assumptions p. 2 The relaxation-time approximation p. 3 The failure of the Drude model
More information