Free electrons –or simple metals

Isolated atom – or good insulator

From Isolation to InteractionFrom Isolation to Interaction

Rock Salt Sodium

Electron (“Bloch”) waves

Localised electrons

“particle wave duality” in the solid

state

Interestingstuff happens in between

Credits C. Bergmann

Energy

Orbital OverlapAtomic Distance

BandwidthBandwidthA

tom

ic

en

erg

y

levels

Con

tin

uou

s en

erg

y s

pect

rum

Bandwidth

Interestingstuff happenshere: U ~ W

Narrow Bands – but where?Narrow Bands – but where?

Organic Organic molecular molecular

crystalscrystalsTransition metal Transition metal oxides & compoundsoxides & compounds

Heavy Heavy fermion fermion

compoundscompounds

Electron CountingElectron Counting

Transition Transition metal oxidesmetal oxides

Ordinary oxide: AlOrdinary oxide: Al22OO33Ordinary oxide: AlOrdinary oxide: Al3+3+2 2 OO2-2-

33

Good insulatorGood insulator

Transition metal oxide: SrTransition metal oxide: Sr22RuORuO44

AlAl3+3+: [Ne] O: [Ne] O2-2-: [Ne]: [Ne]

Transition metal oxide: SrTransition metal oxide: Sr2+2+22RuRu4+4+OO2-2-

44

SrSr2+2+: [Kr] O: [Kr] O2-2-: [Ne] Ru: [Ne] Ru4+4+: [Kr]4d: [Kr]4d44

Leftover d-Leftover d-electronselectronsCorrelated Correlated

metalmetal

Electron CountingElectron Counting

Transition Transition metal oxidesmetal oxides

Leftover d-Leftover d-electronselectronsCorrelated Correlated

metalmetal

Magnetism and Narrow BandsMagnetism and Narrow Bands

Magnetism is a narrow band phenomenon that arises from electron correlations

MAGNETICMETAL

INSULATORNONMAGNETIC

METAL

narrower bands

Pressure at low-T

• Electron correlations

The way the particles are organised is determined by

strong interactions between the particles.

Many of these correlations are intimately related to

magnetic degrees of freedom of the particles, including

collective effects such as ordering, dynamics, and

unusual excitations.

• These new behaviours of the whole system may not have

any obvious relationship to the properties of the individual

particles, but rather may arise from collective or

cooperative behaviour of all the particles.

• Such phenomena are often referred to as "emergent

phenomena" because they emerge as the complexity of a

system grows with the addition of more particles.

Big questions about the origins of collective behaviour in matter

1 . What is the origin of high temperature superconductivity?

2. What is the nature of  strange metals?

3. Why don't glasses flow like liquids?

4. What principles govern the organisation of matter away from equilibrium?

5. How do singularities form in collective matter and in space-time?

6. What principles govern the flow of electronically granular materials?

• When you put a lot of atoms together you get strange, wonderful and

sometimes useful new kinds of behaviour: superconductivity, magnetism,

superfluidity.

Creating Low TemperaturesCreating Low Temperatures

Adiabatic demagnetisation:

50 mK

Outer space:

3000 mKDilution fridge:

5 mK

Using basic knowledge to Using basic knowledge to manipulate nature: High Magnetic manipulate nature: High Magnetic

FieldsFields

Superconducting solenoids:

up to 21 T

Earth’s magnetic field:

0.0001 T

NHMFL hybrid:

45 T

Creating High PressuresCreating High Pressures

Clamp cell:

30 kbarOcean floor:

1 kbarAnvil cell:

150 kbar

Volume compression of order 10%

Suppress Magnetism…Suppress Magnetism…

Antiferromagnetism in CePd2Si2

……and Create Superconductivity!and Create Superconductivity!

Superconductivity in CePd2Si2 at 28 kbars and 400 mK(Mathur, Julian, Lonzarich et al. 1998)

Ferromagnets Too…Ferromagnets Too…

Superconductivity in UGe2 at 13 kbars and 600 mK(Saxena,Lonzarich et al. 2000)

New MechanismNew MechanismSuperconductivity needs “glue” – attractive inter-action between electrons (see Part III Minor Option in Lent)

Conventional theory:

phonon

New MechanismNew MechanismSuperconductivity needs “glue” – attractive inter-action between electrons (see Part III Minor Option in Lent)

Near magnetic phase transition:

spin fluctuation

usually S = 0

New MechanismNew MechanismSuperconductivity needs “glue” – attractive inter-action between electrons (see Part III Minor Option in Lent)

Near ferromagnetic phase transition:

spin fluctuation

possibly S = 1

Paradigm ShiftParadigm ShiftPreviously, superconductivity and magnetism were thought to be mutually exclusive.

Now, we realise that magnetism can promote superconductivity.

Magnetism and unconventional superconductivity are natural neighbours in phase diagrams of correlated materials.

Does this statement hold forthe high-Tc superconductors?

Doped Magnetic InsulatorsDoped Magnetic Insulators

Cu2+: One Electron per Site Antiferromagnetic Insulator

Cu

O

Doped Magnetic InsulatorsDoped Magnetic Insulators

Cu(2+)+: Mobile Holes High-Tc Superconductor

Cu

O

High-THigh-Tcc Phase DiagramPhase DiagramTem

pera

ture

Holes per CuO2

Square

anti

ferr

om

agn

et

super-conductivit

y

Non-metallic

metallic