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The Joint Institute for Advanced Materials
Condensed Matter Physics: From Stone Age Pottery to Topological Quantum Computing
Hanno Weitering
Department of Physics and
Astronomy
Stone age (until ~ 5000 BC)
Bronze age (3300 – 1200 BC)alloy of copper and tin
Iron age (1200 BC – middle ages)Archimedes
Venus of Dolni Vestonice
A physicist’s view of the time line of human history
Silicon/digital age (1945 - )
Quantum age ( history in the making )
Roman Nanotechnology
Roman Lycurgus cup around 400 AD
but what about chromium?we mustn’t forget chromium
Early Periodic Table of the Elements
Building block of solid matter: the ATOM
Bohr’s (somewhat incorrect) model of the atom (1913)
• Electrons orbit the nucleus as in a planetary system
• Each orbit was given a number, called the quantum number.
• Bohr orbits are like steps of a ladder, each at a specific distance from the nucleus and each at a specific energy.
• Each shell can accommodate 2n2 electrons• Electrons can jump between orbits through
absorption or emission of light• Complete description requires solving the
Schrödinger equation (1926).
Atomic and molecular fingerprinting
Carbon
Oxygen
Nitrogen
wavelength
Pauli’s Exclusion Principle
Electrons are constantly spinning, either clockwiseor counter-clockwise. As such they behave as tiny magnets.A Bohr (sub)orbit can accommodate two electrons only if theyhave opposite spins
Quantum mechanics of molecules
H2 or H ─ H C6H6 (benzene)
A moment of reflection
Without Pauli’s Principle:
All electrons would condense into the lowest energy level
There would be no Periodic Table
There would be no Chemistry or Biology. No humans, no animals
There would be no Universe as we know it.
It would be one giant black hole
1945 Nobel Prize “for his decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle”
The solid state: a giant molecule
Energy levels become energy bands
Band gaps determine electrical and optical properties of materials
Metal Semiconductor Insulator
Forbidden zone
Elec
tron
Ene
rgy
Incomplete classification
Now we are ready to discuss…..sand
SiO2 or quartz is an electrical insulatorSilicon is a semiconductor
Silicon also crystallizes in diamond lattice but its band gapis much smaller than that of diamond
Enhancing the electrical performance of silicon through chemical doping
Introducing P or As produces electron conduction (n-type)Introducing B results in ‘hole conduction’ (p-type)
The first transistor
1956 Nobel Prize to Bardeen, Brattain and Schockly“for their researches on semiconductorsand their discovery of the transistor effect”
Transistor amplifies weak electronic signalsand acts like a tiny on/off switch
Modern day transistors and transistor packaging
on off
1 0
Moore’s law
Where is the limit??
What I want to talk about is the problem of manipulating and controlling things on a small scale. As soon as I mention this, people tell me about miniaturization, and how far it has progressed today. They tell me aboutelectric motors that are the size of the nail on your small finger. And there is a device on the market, they tell me,by which you can write the Lord's Prayer on the head of a pin. But that's nothing; that's the most primitive, halting step in the direction I intend to discuss. It is a staggeringly small world that is below. In the year 2000,when they look back at this age, they will wonder why it was not until the year 1960 that anybody beganseriously to move in this direction.
Caltech 1959
Al Gore versus Eric Drexler
at 1992 Senate science subcommittee hearing on Nanotechnology
Gore:"What you're talking about when you use the phrase molecular nanotechnology, is really a brand new approachto fabrication, to manufacturing,"
The way we make things now, we take some substance in bulk and then whittle down the bulk to the size ofthe component we need, and then put different components together, and make something. What you'redescribing with the phrase molecular nanotechnology is a completely different approach which restson the principle that your first building block is the molecule itself. And you're saying that we have all of the basicresearch breakthroughs that we need to build things one molecule at a time all we need is the applicationsof the research necessary to really do it. And you're saying that the advantages of taking a molecular approachare really quite startling and that as a result, you believe it is advisable to really explore what it would take to developthese new technologies. "
Dr. Drexler:As I said, I think that we will need a lot of applied science research in pursuing these goals, but you are correct instating that the basic science is in place.
Atom Manipulation
Molecular Motorsor
‘nano car’
M. Crommie et al.
B. Feringa group, Groningen
The 2016 Nobel Prize in Chemistry 2016 was awarded jointly to Jean-Pierre Sauvage, Sir J. Fraser Stoddart and Bernard L. Feringa "for the design and synthesis of molecular machines".
New forms of carbon
……. new Lego® blocks
‘100 times stronger than steel, more conductive than anything’
GrapheneA monatomic sheet of carbonwith ‘massless’ electrons
2010
Macroscopic Quantum Phenomena
superfluidity
magnetism superconductivity
quantum Hall effects
FERROMAGNETISM: A MACROSCOPIC QUANTUM PHENOMENON
Origin of magnetism: Pauli’s Principle
antiferromagnet
"for his investigations on the properties of matter at low temperatureswhich led, inter alia, to the production of liquid helium"
Nobel Prize in Physics 1913
SUPERCONDUCTIVITY: One of the greatest discoveries of the 20th century
Name these famous physicists
33
Superconductivity = Perfect conductivity + Perfect diamagnetism
34
R
Temperature
R0
Tc
Elec
tric
al re
sista
nce
BCS theory of Superconductivity
35
The general idea behind the BCS theory is that twoelectrons can bind together by polarizing the crystal lattice.The ‘composite particles’ have zero spin. As they no longercare about the Pauli principle, they condense into amacroscopic coherent quantum state
1972
Time Line
36
High temperature superconductorsdoped antiferromagnetic insulators
Can this happen in much simpler materials?ask me in a year or two
Keimer et al. Nature ‘15
Classicallimit
Quantum Hall Effect
1985 Klaus von Klitzing1998 Laughlin, Störmer, and Tsuei2017 Thouless, Kosterlitz, Haldane
Transverse resistance
Magnetic field
Longitudinal resistance
Electron trajectory bent due to Lorentz force
Quantized orbits and quantized edge conduction
Chiral edge state
Topological edge state
1D conductance quantized in units of
e2/h
FAMILY OF QUANTUM HALL EFFECTS
A topological phase is electrically insulating but always has metallic edges or surfaceswhen put next to a vacuum or an ordinary phase
CourtesyDi Xiao
Majorana ‘quasi particles’ for quantum computingedge states of a topological superconductor
Superconducting equivalent of the ordinary quantum Hall effect
Majorana states define a topologically protected quantum memory
Yazdani group, Princeton
Classical computer stores and manipulates information in binary digits or ‘bits’, i.e. 000 100 010 001 110 101 011 111 (3-bit string)
Quantum computer stores and manipulates information in quantum bits which are a linearsuperposition of quantum states
|qubit> = α|0> + β|1> OR |qubit> = α|↑> + β|↓>
entanglement
( )alivedeadkitty ψψ ±=Ψ2
1
Schrödinger’s famous thought experiment (1935)
Measurement implies quantum decoherence
…..must be in perfect isolation from environment
Majorana states are immune from local decoherence
Topological quantum computing
IBM’s 50 qubit machine
History in the making
Thank you for your attention