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Condensed Matter Theory
Antoine Georges Collège de France and Ecole Polytechnique
Master CFP October 2012
Condensed Matter Physics:
- Understand structure and physical properties of « organised forms » of matter
- Relate their MACROSCOPIC properties to their MICROSCOPIC constituents
- Collective phenomena
What is this all about ...? De quoi s’agit il…?
Our playground… an atomic-scale « LEGO »
Diamond
« Buckminsterfullerènes »
Lonsdaléite Graphite
Carbon nanotubes Amorphous (glass) Image : wikipedia
Organised forms of CARBON
The Nobel prize for Physics 2010
The Nobel Prize in Physics 2010 was awarded jointly to Andre Geim and Konstantin Novoselov
"for groundbreaking experiments regarding the two-dimensional material graphene"
Folding graphene onto itself: carbon nanotubes
Diamètre: quelques nanomètres 1 nanomètre= 10-9 mètres
= 1 millionième de millimètre
Oxides…
La2-xSrxCuO4: a superconducting oxide with « high » critical temperature
CuO2 plane
LiCoO2: an intercalation compound key to « Lithium – ion » batteries
Li ou Sr
Other architectures …
GEL
MOUSSE
Solide cristallin
Cristal liquide
Liquide
”Soft” Matter
« Artificial » Materials
Molecular Beam Epitaxy Building a solid
atomic layer by atomic layer
Iron/Chromium multilayers: The discovery of Giant Magnetoresistance (A.Fert, P.Grünberg, Nobel prize 2007)
Image: A.Fert
Structuration… Towards the nanometer
Images: Groupe Quantronique CEA-SPEC-Saclay
An Aluminium wire 50 nm in diameter !
A very small bridge
New Frontier: Ultra-cold atoms and Condensed Matter Physics
Optical lattices: « Crystals of Light and Atoms »
Imaging atoms with single-site resolution…
Bakr et coll. Nature, 2009 Group of M.Greiner, Harvard
The 3 « driving forces » :
• Synthesis and elaboration of new materials • Experimental investigation of their
properties and instrumentation • New fundamental questions and theories
Fundamental motivations
Application-driven Enjeux appliqués
Condensed Matter Physics
cf: Donald E. Stokes « Pasteur’s Quadrant » Brookings Inst. Press
Emergence o collective phenomena at large length-scales: a fundamental challenge
10-10 10-9 10-6 10-3 (meters)
Å nm µm mm
Atomic Mesoscopic # Macroscopic#
Distances:
10 1 10-3 10-6 (electronvolts) Energy / Temperature:
(Degrees Kelvin)
105 104 10 10-2=10mK
7 orders of magnitude !
Paul Dirac, 1929 ``Quantum Mechanics of Many-Electron Systems’’
P. A. M. Dirac, "Quantum Mechanics of Many-Electron Systems“, Proceedings of the Royal Society of London, Series A, Vol.123, April 1929, pp 714.
``The general theory of quantum mechanics is now almost complete (…).
The underlying physical laws necessary for the mathematical theory of a large part of physics
and the whole of chemistry are thus completely known, and the difficulty is only that
the exact application of these laws leads to equations much too complicated to be soluble.''
La « grande équation universelle » ? Fonction d’onde: {ri} positions des électrons, {Rp} des noyaux
Interaction électrostatique de Coulomb (1785)
1ère ligne: énergie cinétique des électrons et des noyaux 2nde ligne: interaction entre noyaux, entre noyaux et électrons,
et des électrons entre eux (c’est le terme difficile à traiter !)
(Schrödinger, 1926)
Two classes of theoretical approaches…
I. Directly at large scale « Low energy » theories of emerging collective
phenomena II. « Bottom-up »: from atomic scale upwards
Effective theory of low-energy excitations in graphene: Dirca fermions!
Study of relativistic Phenomena in the solid-state context
Quasi one-dimensional conductors: « Bechgaard salts » Field theories in in 1+1 dimensions,
conformal field theories
TMTSF (tetramethyl-
tetraselenafulvalene)
Conducteurs organiques (TMTSF)2X
X=PF6, ClO4,…
Théories des champs effectives en 1+1 dimension (Liquides de Luttinger) Théories des champs conformes
« Bottom-up » Microscopic Theories
Start from the atomic scale To understand the physical
properties of a material
Dircet numerical simulation of fermionic systems faces two dramatic diificulties:
• Huge size of the Hilbert spce, which grows exponentially with particle number.
• In Quantum Monte-Carlo methods: random sign of amplitudes to be summed up.
Need novel theoretical and algorithmic methods
Materials with « strong electronic correlations »: a challenge to physical understanding
A « Mott insulator »: LaTiO3
Transition Metals
Rare earths and Actinides
The Mott phenomenon: repulsive interactions block
electronic motion
Animation: par permission de Hidetoshi Fukuyama
1986 : A revolution in Superconductivity
Température de L’Hélium liquide (4 degrés K)
K.A. Müller J.G. Bednorz
RFeAsO (2008)
Température de L’Azote liquide (77 degrés K)
Copper-oxide superconductors: a rich phase diagram with mysterious
electronic phases !
Mott Insulator Hole injection Electron injection
Tem
pera
ture
(Kel
vin)
Superconducting state
Magnetic State (AF)
« Strange » Metal (not a conventional Fermi liquid)
Selective destruction of « quasi-particle » excitations and « pseudo-gap »
Photoémission - A.Kaminski et al. Phys Rev B 71 (2005) 014517
Pic de quasiparticule sur la diagonale de la zone de Brillouin
Absence de pic de quasiparticule loin de la diagonale
DE NOMBREUSES QUESTIONS OUVERTES:
- Pourquoi ces matériaux sont ils supraconducteurs ? (Qu’est ce qui apparie les électrons ?)
- Comment expliquer les étranges propriétés de l’etat metallique juste au dessus de Tc ?
The quest for new superconductors: new discoveries, new questions…
MgB2 (Tc ~ 40 K) Akimitsu et al., 2001
Les nouveaux pnictures de Fer (Tc ~ 55 K) Hosono et al., 2008
Challenges and Frontiers…
• New Materials (« somputer-assisted » discoveries ?)
• New experimental probes • Challenges for Theory • Algorithmic challenges • Nouveaux domaines frontières atomes froids, …
A non-exhaustive list of research teams in the Paris/Saclay area
• LPS-Orsay nombreux domaines
• LPTMS-Orsay atomes froids, effet Hall, mésoscopiques • CEA-Saclay: IPhT et SPEC systèmes fortement
corrélés, mésoscopiques, spins frustres • Ecole Polytechnique: CPHT: systèmes fortement corrélés, atomes froids, structure
électronique ab-initio
LSI: structure électronique ab-initio • Institut d’Optique (IOGS) atomes froids
Paris-centre…
- ENS (semiconducteurs, mésoscopiques, atomes froids…)
- Université Pierre et Marie Curie: LPTMC – nombreux sujets
LPTHE - Université Denis Diderot Paris 7 – LMPQ
