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Kumpula 18.10.2010
Quantum mechanics makes nano differentRisto Nieminen
COMP/Applied PhysicsAalto University School of Science and Technology
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The basic ideas of quantum physics
1. Matter has both wave- and particle-like properties.
- WavelengthmEh
2=λ
Jsh 341062607540.6 −⋅=Planck´s constant
=m =Emass of the particle its kinetic energy
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In thermal equilibrium, TkE B23
=
Quantum mechanics is important when a≈λ=a interparticle spacing or device size.
For electrons, nearly always.For protons, sometimes (especially at low temperatures).For He atoms, at very low temperaturesFor other atoms, at even lower temperatures
(e.g. cold atomic gases, BEC)
Inside nuclei and nucleons: different length and energy scales!
1231038065812.1 −−⋅= JKk BBoltzmann’s constant
eVJ 1910624.0 ⋅= 300 K = 25,8 meV
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Experimental EVIDENCEWhether it is light, orelectrons, the Double SlitDiffraction experiment showsthat in BOTH casesinterference effects occur!
What about in the oppositecase? Is light made up of
particles ?
The experimental evidencesays YES!
This is Einstein’s
photoelectric effect.
Electron Wave Interference
φ−= hfmv max2 )
21(
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Wave-like properties:
• Diffraction• Scattering• ”Uncertainty principle”• Coherence• Quantum confinement, zero-point energy
Particle-like properties:
• Single-particle counting• Scattering• Ballistic transport
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The Bizarre World of Quantum
UNCERTAINTY
The quantum world is probabilistic.This is decribed by Heisenberg’s
Uncertainty Principle.The uncertainty relations are:
Notice that the uncertainty principle is unimportant to macroscopic objects since Planck's constant, h, is so small (of order 10-34). For example, the uncertainty in position of a thrown baseball is 10-30 millimeters!
2h
≥px ΔΔ2h
≥tE ΔΔ
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QUANTUM WORLD
• “weird” = counterintuitive : wave-particle dualism
• inherently “parallel” → quantum computing
• phase information
• many-particle symmetry/antisymmetry →mathematical description of electrons very complex(“fermion sign problem”)
• coupling to (classical) environments → decoherencedissipation
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Quantum confinement
22
2
min 8 mLhE
π=
L
Energy
Emin
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2. More quantum properties
• Many physical properties are quantized, i.e. onlydiscrete values are possible, e.g.
- Energy levels → spectra(transitions between energy levels)
- Angular momentum- Conductivity- Magnetic flux- Vorticity (in quantum liquids)- etc.
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• Particles (e.g. electrons) have ”internal”degrees of freedom : Spin → Magnetism
•The properties of of the quantum particlesare described by the Schrödinger equation(”wave equation”) → the wave function
•The wave function describing several particlesis either symmetric or antisymmetric with respectto particle exchange → “quantum statistics”,fermions (such as electrons) and bosons(such as photons (light quanta) or some light atoms)
),( trrψ
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The wave function can be interpreted as the probabilityof finding the system (or an observable) in a given state.
For example, the electron density
2),(),( trtrn rr ψ=
),(),(),( trtrHdt
trdi rrr
h ψψ=
Time evolution:
Hamilton operator: ),(2 2
22
trVrm
H rh+
∂∂
−=
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Schrödinger wave equation + boundary conditions
→ Stationary ”eigenstates” )(rnrψ
General state is a superposition of theeigenstates
)()(),( rtctr nn
nrr ψψ ∑=
→ Quantum information and computing
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Quantum physics can be completely married withspecial relativity: ”quantum electrodynamics” (QED).
Not with general relativity (gravity), butthe energy scale is larger by a factor of 1040.
”Standard model”: QED + quantum chromodynamics (QCD).
Challenge: many interacting particles- collective properties (e.g. ferromagnetism)- emergent phenomena (e.g. superconductivity)- macroscopic quantum effects (e.g. superfluidity)
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Coulomb interaction
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Playing Playing withwith AtomicAtomic LegoLego
But I am not afraid to consider But I am not afraid to consider the final question as to the final question as to
whether, ultimatelywhether, ultimately------in the in the great futuregreat future------we can we can
arrange the atoms the arrange the atoms the way we want;way we want;
the very the very atomsatoms, all the way , all the way down!down!
RICHARD FEYNMAN
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“All things are made of atoms.“
- Richard P. Feynman, 1963
”Electrons are the glue”.
- Linus Pauling, 1962
CONDENSED MATTER PHYSICS AND CHEMISTRY
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“There Is Plenty of Roomat the Bottom”
Richard P. FeynmanDecember 1959
• How do we write small?• Information on a small scale• Better electron microscopes• The marvellous biological system• Miniaturizing the computer• Miniaturization by evaporation• Problems of lubrication• A hundred tiny hands• Rearranging the atoms• Atoms in a small world
10-9 m
NANOSCIENCE:
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Central paradigms for Condensed Matter Physics
Weakly interacting electrons Strongly interacting electrons
Fermi-Landau theory Spin fluctuations
Quasiparticles Mixed-valence behavior
Band theory Anderson and Kondo resonances
BCS superconductivity Exotic superconductivity
Disorder-induced localization Wigner crystallization
Integer QHE Fractional QHE
Fantastic testbed for many-body phenomena: cold atoms in optical lattices.
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Central paradigms for CMP (contd.)
Interacting atoms Elementary excitations
”Reductionist” approach: Emergence: phonons, plasmons,magnons, spinons etc.
Quantum mechanics and electromagnetic interactions Response functions
From chemical bonds to bands Collective phenomena
Density-functional theories
These two paradigms can be linked.
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Central paradigms for CMP (contd.)
Ground state Dynamics and excitations
Structure-property relationships Spectroscopy
Phase stability and transitions Reactions
Equilbrium transport Non-equilibrium and dissipation
Multiscale models Entanglement and decoherence
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DesigningDesigning withwithConventionalConventional ATOMSATOMS
Atomic clusters havesurprising properties at the nanoscale!
Single phosphorus atomsimplanted into a siliconsubstrate.
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To understand the chemical bond, we need themachinery of quantum physics.
Electrons are the glue. They behave quantum-mechanicallyand give rise to the variety of chemical bonds:
- The ionic bond- The covalent bond- The metallic bond- The hydrogen bond- The van der Waals bond
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Small is different:
the nanoscale materials and structures havenew, functional properties
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“Non-scalable” size region
no. of atoms/molecules N
Property
∼ Nα
1 10 100 1000 10000
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NANOSCIENCE AND –TECHNOLOGY: HANDSHAKING OF
• quantum and classical phenomena
• equilibrium and non-equilibrium phenomena
• top-down and bottom-up approaches
• reductionist and emergent viewpoints (“more is different”)
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The three pillars of nanoscience and -technology
Manufacture and manipulation
“top-down”: lithography
“bottom-up”: self-assembly
Characterisation,imaging andprobing
SPMTEMPES…
Theory, modelling andsimulation
• Predictive computation of physical, chemical and biologicalfunctions• Process design• Interpretation of probe data
Computational nanoscience
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makro - mm
mikro - μm
nano - nm
“TOP-DOWN”
• tarkkuusmanipulointi• mikroelektroniikka• litografia• etsaus• kasvatus
“BOTTOM-UP”
•itseorganisoituvuus•kemiallinen synteesi•molekyylisuunnittelu•SPM-manipulointi
poikkitieteellinenja -teknologinennanotutkimus
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NovelNovel NanosystemsNanosystems
Magnetic multilayers : Giant Magnetoresistance
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ExoticExotic QuantumQuantum SystemsSystems
WELCOME TO THEWORLD OF ARTIFICIAL ATOMS!
QUANTUM DOTS!FULLY TUNABLE SOLID
STATE DEVICESElectrons confined in a very small space
by an electrostatic potential.
CONFINEMENT = ATOM-LIKE PROPERTIES
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QuantumQuantum RingsRingsand and thingsthings......
Have very strangequantum properties,
such as persistentcurrents, when a
magnetic field is applied.Also interesting
magnetism which may beapplied in computing.
B
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AtomsAtoms trappedtrapped ininOpticalOptical LatticesLattices
Atoms trapped in optical potentials.
The optical potentials can be changedand therefore the artificial atomic
structure can also be changed.
This gives us greater design freedom to create new nanoscale devices, beyond
that which we could get from the periodictable elements.
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Atomic Force Microscopy: Tip ChangeAtomic Force Microscopy: Tip Change
Tip Change
Imaging Ca2+
Imaging F-
t
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Lipid membranes
Electrophoresis of nanocolloids
Bioworld is also a nanoworld.
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Quantum dots in biology: changing colours
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Quantum physics in biology: olfaction
The biggest thing we can smell is 40-50 atoms large.
Shape does not solve it: ”lock and key” not enough.
Ferrocene vs. nickeloscene: exactly the same structure,smell very different!
Explanation: inelastic electron tunnelling from the molecules.
Other examples: proton transfer – concentration gradientof protons across cell membranes
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Quantum wires: the quantization of conductivity
G. Rubio, N. Agraït, and S. Vieira,Phys. Rev. Lett. 76, 2302 (1996)
Quantum of conductance:G0 = 2e2/h = 1/12.9 kW, elongation force oscillations
M.R. Sorensen et al., Phys. Rev. B. 57, 3283 (1998)
Au quantum wire, STM
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C60 (fullerene)on a metal surface
The morphology of Pt surface
Graphite surface Triblock-copolymer
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Gordon MooreFounder of Intel Inc.
Electronics Magazine, 1965
The number of switches on a silicon chipswill double every 12 months (later revised to
18 months)
“Moore´s Law”
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Nanoelectronics and spintronicsas a new platform for information
technology:
a possibility to extend Moore’s Lawinto the future.
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The shrinking feature size
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One needs new insulator materials…
90 nm processcapacitance 1leakage current 1
HfO2
capacitance 1.6leakage current < 0.01
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Etching of silicon surfaces(Miguel Gosalvez)
Single-electron transistor
Carbon nanotube as a quantum wire
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Nanoscale Au clusters are reactive!
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Mono-layer Protected Gold Nanoclusters
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elektronimikroskopia
Rautaoksidi-nanopartikkeliUniv. California Berkeley
PbSe-kvanttipiste
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Kaksosraja <110>-suunnassaSrTiO3 -perovskiitissa
ultramikroskopia :- alle 0.1 nanometrin
tarkkuus
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d = 2.07 nm
α = 17.02˚
( ( m, n m, n ) = (21, 9) ) = (21, 9)
dd(21,9)(21,9) = 2.09= 2.09 nmnmαα(21,9)(21,9) = 17.0= 17.0˚
Metallinen, yksiseinäinen hiilinanoputki (SWNCT)
a) elektronidiffraktiokuva → kierteisyysb) transmissioelektronimikroskopiaAalto/Uusien Materiaalien Keskus
(Esko Kauppinen)
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Nobel 2010: Graphene
One atomic layer of hexagonal carbon
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Samsung Electronics