k

2 days of practicals in laboratories of Paris-Saclay University

→ Experimental techniques that are relevant for condensed matter research → Direct interaction with researchers in a broad range of subjects

7 practicals:

→ Suspensions of gold nanoparticles → Charge density wave in chromium → Silver nanoparticles deposited on polymers → Low energy electron diffraction (LEED)

→ Electronic structure of graphene → Quantum oscillations

→ Spin and phonon waves in a Fe-Ni alloy

M2 « Condensed Matter Physics »

Structural and Electronic Properties of Solids

Atomic structure (Å- and nm- scales)

Electronic structure

Elementary excitations in solids

Charge density waves in chromium

T = 120 K

CDW state: Modulation of the electron density Coupled structural modulation

Cryostat and 4-circle diffractometer at LPS

Experimental technique: X-ray diffraction

(from N. P. Ong)

Atomic structure

𝑻 > 𝑻𝒄 𝑻 < 𝑻𝒄

Experimental technique: X-ray diffraction

Suspensions of gold nanoparticles

“MAR” diffractometer at LPS

40% mass concentration

1% mass concentration

Low concentration High concentration

Atomic structure

{211} reflection of tungsten in the multilayer system [3 nm W / 1 nm Cu] ×37 / 125 µm Kapton

Diffraction image Monitoring of a Bragg peak profile as a function of the applied force

Flexible microelectronics

Flexibles screens Solar cells

Mechanical response of a thin film deposited on a flexible substrate Atomic structure

X-ray diffraction + Numerical image correlation

6-circle diffractometer + biaxial tensile tests (SOLEIL synchrotron)

Practical @ SOLEIL - LEED

LEED: The technique stands for « Low Energy Electron Diffraction » Goal: Determining reconstruction of solid crystal surfaces Topics: Diffraction and physics of 2 dimensional electronic systems Surface science techniques: surface preparation and characterization Ultra High Vacuum (UHV) technology and methods

Low-energy electron-diffraction pattern

for 1T-TaS2

In the Ta-plane, charge density wave (CDW)

reconstructions may occur (that is a star-like clustering

of atoms also known as “stars of David”)

Atomic structure

The electronic structure of graphene exhibits so-called Dirac cones at the K points of reciprocal space.

k

Energy and wave-vector of photoelectrons…

☞ Band structure

kx=0 section of cones around point K. Each cone corresponds to a single graphene sheet.

Graphene

Graphene: formed by carbon atoms distributed in a hexagonal lattice.

Electronic structure of graphene

CASSIOPEE beamline - SOLEIL

Angle-resolved photoemission spectroscopy

Electronic structure

PPMS installed at LPS

1/B (G-1)

Measurement of the Fermi surface of bismuth

In a metal subjected to a magnetic field along 𝑧 -axis, the 𝑘𝑥 and 𝑘𝑦 components of the electron wave-vectors are quantized…

Magnetization and resistivity measurements T down to 2 K / B up to 9 T

Quantum oscillations of resistivity

… As a consequence, the density of states at the fermi level depends on the value of the applied magnetic field, and so the physical properties determined by the electrons at the Fermi level: resistivity, magnetic susceptibility...

Electronic structure

Ni40Fe60: ferromagnetic alloy → Lattice excitations (phonons) → Magnetic excitations (spin waves)

Ni40Fe60 : crystal structure

Triple-axis spectrometer at LLB

Spin waves and phonons in a nickel alloy

Inelastic neutron scattering

Classical description of a spin wave:

Precession about the magnetization direction

Elementary excitations in solids

∆𝐸 = -11 meV

Inte

nsi

ty

𝑙 in 00𝑙 direction

𝑙 in 00𝑙 direction

Ener

gy ℏ𝜔

(m

eV)

Practicals - Structural and Electronic Properties of Solids

Final mark = 0.1 x [report 1] + 0.1 x [report 2] + 0.2 x oral exam + 0.6 x written exam

1) Practical 1

2) 1 week after practical 1: report sent to the teacher and to Claire Laulhé

3) 2 weeks after practical 1: oral examination

4) Practical 2

5) 1 week after practical 2: report sent to the teacher and to Claire Laulhé

E. Papalazarou V. Balédent S. Petit P. Lefèvre V. Jacques D. Thiaudière

Practical work teachers:

M. Monteverde

Practicals - General schedule

Questions ?

Website

--> claire.laulhe@synchrotron-soleil.fr

--> https://www.equipes.lps.u-psud.fr/m2structure/