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