free electrons – or simple metals isolated atom – or good insulator from isolation to...
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![Page 1: Free electrons – or simple metals Isolated atom – or good insulator From Isolation to Interaction Rock Salt Sodium Electron (“Bloch”) waves Localised electrons](https://reader035.vdocuments.net/reader035/viewer/2022062516/56649d575503460f94a3550d/html5/thumbnails/1.jpg)
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
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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
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Narrow Bands – but where?Narrow Bands – but where?
Organic Organic molecular molecular
crystalscrystalsTransition metal Transition metal oxides & compoundsoxides & compounds
Heavy Heavy fermion fermion
compoundscompounds
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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
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Electron CountingElectron Counting
Transition Transition metal oxidesmetal oxides
Leftover d-Leftover d-electronselectronsCorrelated Correlated
metalmetal
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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
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• 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.
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• 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.
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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.
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Creating Low TemperaturesCreating Low Temperatures
Adiabatic demagnetisation:
50 mK
Outer space:
3000 mKDilution fridge:
5 mK
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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
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Creating High PressuresCreating High Pressures
Clamp cell:
30 kbarOcean floor:
1 kbarAnvil cell:
150 kbar
Volume compression of order 10%
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Suppress Magnetism…Suppress Magnetism…
Antiferromagnetism in CePd2Si2
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……and Create Superconductivity!and Create Superconductivity!
Superconductivity in CePd2Si2 at 28 kbars and 400 mK(Mathur, Julian, Lonzarich et al. 1998)
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Ferromagnets Too…Ferromagnets Too…
Superconductivity in UGe2 at 13 kbars and 600 mK(Saxena,Lonzarich et al. 2000)
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New MechanismNew MechanismSuperconductivity needs “glue” – attractive inter-action between electrons (see Part III Minor Option in Lent)
Conventional theory:
phonon
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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
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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
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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?
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Doped Magnetic InsulatorsDoped Magnetic Insulators
Cu2+: One Electron per Site Antiferromagnetic Insulator
Cu
O
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Doped Magnetic InsulatorsDoped Magnetic Insulators
Cu(2+)+: Mobile Holes High-Tc Superconductor
Cu
O
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High-THigh-Tcc Phase DiagramPhase DiagramTem
pera
ture
Holes per CuO2
Square
anti
ferr
om
agn
et
super-conductivit
y
Non-metallic
metallic