Condensed Matter Physics: From Stone Age Pottery to Topological Quantum Computing

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1 Condensed Matter Physics: From Stone Age Pottery to Topological Quantum Computing Hanno Weitering Department of Physics and Astronomy The Joint Institute for Advanced Materials

BC) alloy of copper and tin Iron age (1200 BC middle ages)

2 A physicist s view of the time line of human history Stone age (until ~ 5000 BC) Venus of Dolni Vestonice Bronze age ( BC) alloy of copper and tin Iron age (1200 BC middle ages) Archimedes Silicon/digital age ( ) Quantum age ( history in the making )

3 Roman Lycurgus cup around 400 AD Roman Nanotechnology

4 Early Periodic Table of the Elements but what about chromium? we mustn t forget chromium

6 Building block of solid matter: the ATOM

Bohr s (somewhat incorrect) model of the atom (1913) Electrons orbit the

7 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 2n 2 electrons Electrons can jump between orbits through absorption or emission of light Complete description requires solving the Schrödinger equation (1926).

8 Atomic and molecular fingerprinting Carbon Oxygen Nitrogen wavelength

9 Pauli s Exclusion Principle Electrons are constantly spinning, either clockwise or counter-clockwise. As such they behave as tiny magnets. A Bohr (sub)orbit can accommodate two electrons only if they have opposite spins

11 Quantum mechanics of molecules H 2 or H H C 6 H 6 (benzene)

12 Without Pauli s Principle: A moment of reflection 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

13 The solid state: a giant molecule

14 Energy levels become energy bands Band gaps determine electrical and optical properties of materials

15 Metal Semiconductor Insulator Electron Energy Forbidden zone Incomplete classification

16 Now we are ready to discuss..sand SiO 2 or quartz is an electrical insulator Silicon is a semiconductor

17 Silicon also crystallizes in diamond lattice but its band gap is much smaller than that of diamond

18 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)

19 The first transistor 1956 Nobel Prize to Bardeen, Brattain and Schockly for their researches on semiconductors and their discovery of the transistor effect

20 Modern day transistors and transistor packaging Transistor amplifies weak electronic signals and acts like a tiny on/off switch on off 1 0

21 Moore s law Where is the limit??

22 Caltech 1959 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 about electric 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 began seriously to move in this direction.

components together, and make something.

23 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 approach to fabrication, to manufacturing," The way we make things now, we take some substance in bulk and then whittle down the bulk to the size of the component we need, and then put different components together, and make something. What you're describing with the phrase molecular nanotechnology is a completely different approach which rests on the principle that your first building block is the molecule itself. And you're saying that we have all of the basic research breakthroughs that we need to build things one molecule at a time all we need is the applications of the research necessary to really do it. And you're saying that the advantages of taking a molecular approach are really quite startling and that as a result, you believe it is advisable to really explore what it would take to develop these 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 in stating that the basic science is in place.

24 Atom Manipulation Molecular Motors or nano car M. Crommie et al. B. Feringa group, Groningen

25 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".

26 New forms of carbon. new Lego blocks 100 times stronger than steel, more conductive than anything

27 Graphene A monatomic sheet of carbon with massless electrons 2010

29 Macroscopic Quantum Phenomena superfluidity magnetism superconductivity quantum Hall effects

30 FERROMAGNETISM: A MACROSCOPIC QUANTUM PHENOMENON

31 Origin of magnetism: Pauli s Principle antiferromagnet

investigations on the properties of matter at low

32 SUPERCONDUCTIVITY: One of the greatest discoveries of the 20 th century Nobel Prize in Physics 1913 "for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium"

33 Name these famous physicists 33

34 Superconductivity = Perfect conductivity + Perfect diamagnetism Electrical resistance R R 0 T c Temperature 34

lattice. The composite particles have zero spin.

35 BCS theory of Superconductivity 1972 The general idea behind the BCS theory is that two electrons can bind together by polarizing the crystal lattice. The composite particles have zero spin. As they no longer care about the Pauli principle, they condense into a macroscopic coherent quantum state 35

36 Time Line 36

37 High temperature superconductors doped antiferromagnetic insulators Can this happen in much simpler materials? ask me in a year or two Keimer et al. Nature 15

38 Quantum Hall Effect Transverse resistance Classical limit Longitudinal resistance Electron trajectory bent due to Lorentz force 1985 Klaus von Klitzing 1998 Laughlin, Störmer, and Tsuei 2017 Thouless, Kosterlitz, Haldane Magnetic field

39 Quantized orbits and quantized edge conduction 1D conductance quantized in units of e 2 /h Chiral edge state Topological edge state

40 FAMILY OF QUANTUM HALL EFFECTS A topological phase is electrically insulating but always has metallic edges or surfaces when put next to a vacuum or an ordinary phase

41 Courtesy Di Xiao

42 Majorana quasi particles for quantum computing edge states of a topological superconductor Yazdani group, Princeton Superconducting equivalent of the ordinary quantum Hall effect Majorana states define a topologically protected quantum memory

43 Classical computer stores and manipulates information in binary digits or bits, i.e (3-bit string) Quantum computer stores and manipulates information in quantum bits which are a linear superposition of quantum states qubit> = α 0> + β 1> OR qubit> = α > + β > entanglement

44 Schrödinger s famous thought experiment (1935) Ψ kitty = 1 2 ( ψ ± ψ ) dead alive Measurement implies quantum decoherence

45 ..must be in perfect isolation from environment Majorana states are immune from local decoherence Topological quantum computing

46 History in the making IBM s 50 qubit machine

47 Thank you for your attention

Modern Physics for Scientists and Engineers International Edition, 4th Edition

Modern Physics for Scientists and Engineers International Edition, 4th Edition http://optics.hanyang.ac.kr/~shsong 1. THE BIRTH OF MODERN PHYSICS 2. SPECIAL THEORY OF RELATIVITY 3. THE EXPERIMENTAL BASIS