Présentation

Electrons and phonons dans les nanostructures (3ECTS)

Professeurs :
Christophe Voisin (PR UP, LPENS)
Emmanuelle Deleporte (PR ENS Cachan, LPQM)
Francesca Carosella (MCF UP, LPENS)

Part 1

• Fundamentals of solid state physics:
• Band structure and Bloch theorem
• Density of states
• Effective mass
• Overview of phonons
• Envelope function approximation
• Electron – phonon interaction: weak coupling regime
• Fermi golden rule
• Rabi oscillations
• Importance of energy loss in opto-electronic devices
• Electron – phonon interaction: strong coupling regime
• Polarons in quantum dots
• Energy relaxation within polaron framework

Part 2

• Optical absorption in a bulk material
• Direct absorption, indirect absorption, selection rules
• Excitons
• Optical absorption in a quantum well
• Interband and intraband transitions
• Type I and type II quantum wells, superlattice
• Excitonic effects
• Optical emission in bulk materials and quantum wells
• Einstein coefficients
• Luminescence
• Different kinds of experience: electroluminescence, photoluminescence, excitation spectroscopy, time-resolved photoluminescence
• Effect of an external electric field on heterostructure electronic states and optical properties
• Effect of an external magnetic field on heterostructure electronic states and optical properties

Examples of problem class:

• Density of states and energy states calculation in various kind of heterostructures
• Determination of electrons lifetime in presence of phonons
• Calculation of absorption coefficient in a bulk material
• Optical absorption in a quantum well
• Landau levels and magnetoabsorption

Theorie Quantique du rayonnement (3ECTS)

Professeurs :
Edouard Boulat (MCF UP, LMPQ)
Loic Lanco (MCF UP, C2N)

SEMI-CLASSICAL THEORY OF LIGHT MATTER INTERACTION

• Free particle of Spin 1/2
• Jauge invariance of Schroedinger equation ; Pauli Hamiltonian
• Semiclassical theory of light – matter interaction
• Electron-field interaction and Fermi golden rule ; transition rate

QUANTUM NATURE OF LIGHT : PHOTONS

• Fock space
• Operators : electric field, momentum, photon number
• The Casimir effect
• Special states of the electromagnetic field : coherent states, squeezed states

PHOTON EMISSION AND ABSORPTION

• Hamiltonian electron-photon; revisiting the Fermi golden rule
• Spontaneous and stimulated emission
• Natural linewidth
• Dipolar electric emission
• Diffusion of a photon from an atom

Physique de l’etat solide avancée (3ECTS)

Professeurs :
A. Sacuto (PR, LMPQ)
F. Sirotti (DR CNRS, LPMC Ecole Polytechnique)
F. Sottile (DR CNRS, LSI Ecole Polytechnique)

1. Reminder of Solid State Physics and Introduction to the course

• Electrons and nuclei
• Born-Oppenheimer approximation
• Bloch theorem
• spin and k-points
• magnetism (diamagnetic, paramagnetic, ferromagnetic, anti-ferromagnetic, etc.)

2-4. Superconductivity
Scope:

• An introduction to Superconductivity
◦ Introduction to a short story of superconductivity and its fascinating properties
◦ The quest of very low temperature
◦ The discovery of superconductivity
◦ The high-Tc superconductors
◦ Their properties with experiments performed during the lecture
• The Cooper’s model :
◦ bound electrons in a degenerate Fermi gaz
◦ the superconducting gap
• A first approach to the microscopic theory of Bardeen Cooper Schrieffer (BCS)
◦ description of the ground state
◦ the BCS Hamiltonian
◦ the energy of the ground state and the superconducting gap
• Signatures of the superconductivity in some spectroscopy probes
◦ Tunnelling and ARPES
◦ Infrared and Raman
◦ NMR

5. Electronic structure: the ground-state

• Ground-state quantities (lattice parameters, phonons, Bulk modulus, phase transitions)
• The many-body problem: independent particles
• Hartree and Hartree-Fock approaches
• Koopmans’s theorem and self-interaction concerns
• Density Functional Theory
◦ Theory
◦ Approximations and examples
• Band-structure and Density of States
• Absorption in DFT ?

6. Photoemission spectroscopy

• Energy and momentum conservation
• ARPES, XPS, Spin-resolution
• Bulk surfaces and interfaces, Cross sections,
• Experimental issues: Ultra High Vacuum, X-rays sources, Electron energy analyzers,
• Examples

7. Green’s Functions theory I

• the need for the Green’s function
• Spectral representation
• The self-energy
• Hedin’s equations
• The GW approximations
• Quasiparticle and satellites
• Results and examples

8. X-ray Absorption and Ellipsometry

• Valence spectroscopy and ellipsometry
• Core electrons: XAS, XANES, EXAFS,
• Magnetic systems: Linear and circular Dichroism
• Applications

9. Green’s Functions theory II

• the need for the two-particle Green’s function
• the Bethe-Salpeter equation
• 4 points quantities
• results and examples

10. Scattering spectroscopies and TDDFT

• scattering process and the inverse dielectric function
• electron energy loss
• electron microscope
• inelastic x-ray scattering
• experimental resolution: energy, momentum, space, time
• Time Dependent Density Functional Theory
◦ theory
◦ linear response and polarizability
◦ approximations and applications

Dispositifs électroniques quantiques (3ECTS)

Professeurs :
P. Joyez (DR CEA Saclay, Lab SPEC)
P. Lafarge (PR UP, Lab MPQ)

• Basics of Solid State Physics : band structure, metals, semiconductors, phonons, balistic and diffusive electronic transport,…
• Second quantization
• Quantum transport : characteristic lenght scales, conductance quentum, Landauer formula, current nois in quantum conductors, localization, …
• Electrons in magnetic field : Landau levels, integer and fractionary quantum Hall effect, edge states, …
• Superconductivity : BCS theory, Josephson effect, mesoscopic superconductivity, Andreev reflexions.
• Electronic transport in carbon nanotubes.

Matériaux bidimensionnels (3ECTS)

Professeurs :
Y. Gallais (Prof UP, LMPQ)
J. Lagoute (CR CNRS, LMPQ)

Since the discovery of graphene, with its remarkable transport and optical properties, the field of two-dimensional crystals has flourished and many materials can now be studied down to single atomic layers. Compared to bulk materials, two-dimensional materials provide highly adjustable platforms for new functionality, which can be the source of exotic optoelectronic phenomena. The objective of this course is to give an overview of this highly dynamic research field by providing some basic concepts of two-dimensional materials (device fabrication, electronic and optical properties) and by focusing on a selection of recent developments in the field (van der Waals heterostructures, defects engineering, transition metal dichalcogenides, topological insulators, etc.).

We will first review the physical properties of graphene with an emphasis on the properties of graphene-based devices and the ways to characterize them. We will then introduce the physics of other two-dimensional materials such as transition metal dichalcogenides and black phosphorus, which have been discovered more recently and whose optical and electrical properties differ from graphene. The course will end with an introduction to the unusual two-dimensional electronic states formed on the surface of topological insulators.

I. The physics of graphene and its devices

– Introduction: graphene and its band structure
– Transport properties of graphene devices
– Optical properties and application to optoelectronic devices
– Local spectroscopies and defects engineering
-Graphene-based heterostructures and van der Waals engineering: concept and manufacturing

II. Beyond graphene: transition metal dichalcogenides (TMDs), black phosphorus (BP) and topological insulators (TI)

– Introduction to transition metal dichalcogenides and their band structure in the 2D limit: the case of semiconductor MoS2
– Degrees of freedom of spin and valley in semiconductor dichalcogenide and proximity effect
– Correlated states in transition metal dichalcogenides: density wave and superconductivity
– Black-phosphorus
– Introduction to topological isolators

Experimental projects in nanosciences (6ECTS)

Professeurs :
ML Della Rocca (MCF UP, LMPQ)
F. Raineri (MCF UP, C2N)
R. Braive (MCF UP, C2N)

In this original course, students will get trained with experimental techniques used in nanosciences. During the first three weeks of the formation, students will realize in complete autonomy an experimental project in the field of nanosciences, on hot-topics such as electronic transport or optical properties of graphene and carbon nanotubes, molecular electronics, nanoplasmonics, photonic crystals, organic electronics, quantum transport in tunnel diodes,…
A specific nanoscience platform equipped with advanced facilities (AFM – atomic force microscopes and STM- tunneling effect microscopes, TEM – transmission electron microscope, SEM – scanning electron microscope, spectrometers, cryogenics, electronic transport measurements, etc.) will be available with free use of these instruments. All students will also be initiated to clean room techniques and activity by practicing the realization of their own device.

Calcul Quantique (3ECTS)

Professeurs :
P. Millmann (DR CNRS, LMPQ)
H. Perrin (DR CNRS, LPL)

-Introduction au calcul quantique : classes de complexité, communication, portes universelles, variables discrètes et continues, coder un qubit…
-Les ions piégés pour le calcul quantique : méthodes de piégeage, refroidissement, interrogation, réalisation des portes élémentaires
-Pprésentation en détail de deux algorithmes : algorithmes de Shor et algorithmes de Grover, présentation du projet sur les qbits IBM
-Réalisation de l’algorithme de Shor avec des ions, les qbits supra
-Les codes correcteurs d’erreur
-Calcul quantique avec des qbits supra utilisant des codes correcteurs d’erreur (réalisation expérimentale), les autres plateformes pour le calcul quantique (Si, RMN, photons…)
-Une autre approche : la simulation quantique (discrète et continue)
-Les plateformes de simulation quantique : gaz quantiques (bulk ou réseaux), atomes froids de Rydberg dans des pinces optiques, ions, supra, micro-ondes, polaritons…

Communication Quantique (3ECTS)

Professeurs :
E. Diamanti (DR CNRS, LIP6 )
S. Ducci (PR UP, LMPQ)

Theoretical quantum information

1. The qubit and its states
* quick review of the basic quantum formalism (kets, bras and
density matrices)
* No cloning theorem and Wiesner’s unforgeable banknotes
* Quantum Key Distribution and BB84 protocol

2. Quantum Entanglement 1 : Definition and some Properties
* Formal definition (as non separable state)
* Apparent Heisenberg inequality violation
* Link with partial trace
* Entanglement detection for pure and mixed states
* Entanglement monogamy and application to QKD
* Partial transpose and its physical meaning

3. Quantum Entanglement 2: Bell inequalities and Application
* Entanglement is not a limitation of quantum formalism
* Bell inequalities (mainly CHSH)
* GHZ Paradox
* Some Entanglement application
* The 4 Bell States
* Quantum Dense Coding
* Quantum Teleportation

4. Introduction to Quantum Computation
* Grover’s Algorithm
* Quantum Error Correcting Codes

Devices for quantum information

5. Introduction :
Experimental implementation of quantum information : challenges and some famous experiments.

6. Photon sources :
Single photon sources and their characterization : Hanbury Brown and Twiss interferometry, colloidal and grown quantum dots, colored centers in diamonds,..
Entangled photon sources and their characterization : Bell inequality test, density matrix reconstruction, nonlinear dielectric crystals and fibers, quantum dots, semiconductor waveguides,…

7. Single photon detectors :
Photomultipliers, single photons avanlanche photodiodes, supraconducting detectors

8. Quantum metrology :
absolute detector calibration, absolute radiance measurement, polarization mode dispersion, quantum ellipsometry …

9. Physical implementations of quantum computation : General overview, exemple of trapped ions.

Nanomagnetism and spintronics (3ECTS)

Professeurs :
H. Jaffres (PR Ecole Plytechnique
UMR CNRS -Thales)
P. Seneor (PR Paris Saclay, UMR CNRS -Thales)

The ‘NanoMagnetism and Spintronics’ course targets the physics of Magnetism, of Magnetism at the nanometer scale (NanoMagnetism) and the spin-dependant transport in magnetic Nanostructures, scientific discipline designated today as Spin Electronics. After having introduced the fundamentals of orbital and spin localized magnetism in ionic systems, the course will tackle the important notions of paramagnetic, ferromagnetic and antiferromagnetic order. An important effort will be brought on the understanding of the establishment of band-ferromagnetism of 3d transition metals taking into account atomic exchange interactions. The second part of this course will be devoted some more actual problems of spin-dependent transport in Magnetic nanostructures (magnetic multilayers, nanowires, Magnetic tunnel junctions). The concepts of spin-dependent conduction in the diffusive regime, spin diffusion length and spin accumulation will be clearly emphasized to explain Giant MagnetoResistance (GMR) and Tunnel Magnetoresistance (TMR) effects. An opening will be done on the Magneto-Coulomb effects obtained with nanoparticules dispersed between ferromagnetic reservoirs and on spin transfer effects observed on metallic nanopillars and magnetic tunnel junctions.

Fonctionnals Materials (3ECTS)

Professeurs :
S. Biermann (PR Ecole Polytechnique, LPMC)

Ce cours est à l’interface entre applications et science fondamentale (recherche industrielle et académique). Il se tient complètement à l’Ecole Polytechnique.
Il consiste en une série de séminaires sur une démi-journée tenus par des chercheurs invités à la pointe des thematiques à l’interface entre la physique fondamentale et applique et la science des matériaux (material design, meta-materials, 2D material for valleytronics, 2D oxide heterostructures, …) .
Un cours d’introduction est initiallement donne par le Prof. Biermann avec remise à niveau des connaissances nécessaires à suivre les séminaires.

Dispositifs Photoniques Quantiques (3ECTS)

Professeurs :
A. Vasanelli (PR, LPENS)
C. Sirtori (PR ENS, LPENS)

OPTOELECTRONICS AND SEMICONDUCTOR PHOTONIC DEVICES

1 – Basics of semiconductor physics

Electrons in solids: wavefunctions, band structures, effective mass
Statistics of semiconductors: Fermi-Dirac, semi-classical approximation, free-carrier density

Semiconductor doping: donors and acceptors, temperature regimes

Optical absorption: matrix element and absorption coefficient in direct-bandgap semiconductors, joint density of states, phonons and absorption in indirect-bandgap semiconductors

Non-radiative recombination

2 – Basics of semiconductor devices

Transport in semiconductors: diffusion and conductivity, Drude and Boltzmann

Quasi-neutral approximation: rate equations in doped semiconductors, minority-carrier evolution, application to photocarrier injection and surface recombination

p-n junctions: space charge and band profile, I-V characteristics and Shockley approximation, quasi Fermi levels

Photovoltaic detectors

3 – When electric fields come into play

Perturbation of electronic states: enveloppe function approximation, Franz-Keldysh effect

Application to heterostructures: quantum wells, intersubband transitions, QWIPs

Modulators: Quantum Confined Stark effect, QCSE vs. FK, designs

Introduction to non-linear optics: coupled-wave equations, slowly-varying-amplitude approximation, second-order processes and wave-vector mismatch

Second-order non-linear optics in semiconductors: susceptibility enhancement, phase-matching schemes

4 – Light emission in semiconductors

Radiative recombination and photoluminescence spectrum

Light-Emitting Diodes: carrier lifetime, internal quantum yield, light extraction
Stimulated emission: absorption, optical gain and Bernard-Duraffourg inversion condition

Double-heterostructure laser: electron and photon confinement, threshold, processing

Quantum-well laser: separate confinement, interband absorption and gain in quantum wells, threshold, comparison with DH, structures

Introduction to quantum-cascade laser: unipolar scheme, active part, superlattices and injector design

5 – From optoelectronics to photonic devices

Distributed-feedback lasers: principle, mode coupling, DFB operation

Vertical-cavity surface-emitting lasers: principle, Bragg mirrors, cavity design, electrical injection

Introduction to photonic crystals: DBR as 1D photonic crystals, modes and band structures, 2D and 3D generalisation, application to integrated optics, analogy with electron states and limits

Application to light extraction: emission from a cavity, light extraction and refractive-index engineering

Nano-objets à l’échelle atomique

Professeurs :
D. Alloyeau (CR CNRS, LMPQ)
Vincent Repain (PR UP, LMPQ)
H. Amara (CR ONERA)

1-Electronic, magnetic and optical properties down to the molecular scale

a- Microscopes history and state-of-the-art optical microscopes
• Diffraction principle, optical resolution
• Beyond diffraction

b-Near field microscopy
• A brief history
• General principle of working
• Scanning Tunneling Microscope and Atomic Force Microscope: signal to noise and resolution

c-Electronic properties
• Local Density of States
• Quantized levels and wavefunctions mapping
• Superconductivity at the nanoscale

d-Magnetic properties
• Local Tunnel Magneto-Resistance
• Single atom magnetism, superparamagnetism and non-collinear magnetism

e-Optical properties
• Optical Luminescence from a nanometer scale junction
• Tip Enhanced Raman Scattering

2-Structure-related properties of nanomaterials

a- The atomic structure of nanomaterials: a key to understand and optimize their properties

b- Revealing the atomic structure and the electronic properties of nanomaterials with a transmission electron microscope
• Image and diffraction
• Phase-contrast microscopy at the atomic scale (high-resolution TEM)
• Electron and X-ray spectroscopies
• Plasmon mapping at the nanoscale

c- Studying the dynamics of nanomaterials in realistic environments
• In situ electron microscopy and X-ray scattering methods
• Nucleation and growth phenomena
• Life cycle of nanomaterials in biological media

3-Modlisation of structural and electronic properties of nanomaterials

a-Different approaches at atomic scale
• DFT calculations
• Tight-binding formalism (diagonalization scheme, order N method, Green function, second moment approximation …)
• Empirical potentials (Lennard Jones, EAM, MEAM, Brenner, Tersoff, …)
• Different types of atomic calculations (static, Molecular Dynamics, Monte Carlo, energy landscape exploration methods, …)

b-Electronic properties of nano-objects
• Carbon nanomaterials : nanotube, graphene
• Green functions formalism
• Carbon nanotubes : imaging molecular orbitals
• Doped Graphene : DFT vs Tight-binding

c-Structural properties of nano-objects
• Thermodynamic of nanoalloys (driving forces : size, surface energy, ordering tendency, …) : empirical and semi-empirical approaches
• Growth mechanisms (nanorod, carbon nanotube, graphene)