literature reviews 2005/06 christoph bergemann quantum matter group, cavendish laboratory...
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Literature Reviews 2005/06
Christoph BergemannQuantum Matter Group, Cavendish Laboratory
[email protected] Phone: 37389
1. Electronic Structure of Quasicrystals2. 20 Years of High-Tc Superconductivity
– Why Isn’t My Power Cord Made of It?3. The Quest for Metallic
(and Superconducting!) Hydrogen4. Focusing X Rays to
Nanometer Dimensions
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Quasicrystals
Major result in QCMP course
(Lent)
•Ordinary crystals have periodic lattices
•Solid state physics = quantum mechanics in periodic potential (+ interactions…)
•Solutions are wave-like – Bloch’s theorem
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Quasicrystals•Quasicrystals have non-periodic lattices•But still perfectly ordered – sharp Bragg peaks in X-ray diffraction!
•5-fold and 10-fold symmetry axes forbidden for ordinary crystals –dodecahedral shapes!
•Quantum mechanics in quasiperiodic potential -solutions are tricky – Bloch’s theorem is violated
Laue XRDpattern
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QuasicrystalsSome more food for thought:•Quasicrystals are 3D slices through periodic structures in higher-D “hyperspace”
•1D Quasicrystal: Fibonacci stackSubstitution rule: A ! AB, B ! A
ABAABABA Ã ABAAB Ã ABA Ã AB Ã A
•2D Quasicrystal: Penrose tilings
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QuasicrystalsSome theoretical results:•Electrons are (probably) localised•Density of states is fractal or even wilder
Experimental situation is highly unsatisfactory:
•Metallic constituents (Al, Ni, Co, Pd, Mn, …) but bad conductivity
•Some experiments see “proper” bands, even though they shouldn’t
This literature review:•Survey both theory and experiment as to what’s going on
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High-Tc Superconductivity
Bednorz Müller
Nobel Prize 1987
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High-Tc SuperconductivityMany scientific issues:•Why copper oxides, and why such complicated materials?
•What is the superconducting mechanism?
•The “normal” state is actually quite abnormal – why?
•Can we reach room temperature superconductivity?
Crystal Structure of YBa2Cu3O7-
Not the subject of this
review
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High-Tc SuperconductivityEngineering issues:•How to form cables from brittle ceramics?
•How to beat the cooling challenge?•How to exploit superconducting phase coherence effects? ! SQUIDs etc.
•How are high-Tc materials used today? – And what are realistic future prospects?
This literature review
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High-Tc SuperconductivitySome examples:
Maglev trains
Power cables
Fault current limitersHigh-Tc SQUIDs
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Metallic Hydrogen•We all know hydrogen as a gas•Under high pressures, itbecomes a liquid
•Speculation since 1935 thathydrogen might becomemetallic!
WignerIs Jupiter a giant blob of superhot liquid metal?
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Metallic Hydrogen•“Arms race” between theorists and experimentalists re: the pressure needed for metallisation
•High pressure techniques: need 2 Mbars
Clamp cell:
30 kbarOcean floor:
1 kbarAnvil cell:
150 kbar
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Metallic Hydrogen•Experiment finally caught up in 1996…
•Not just experimental tour de force, but also deep theoretical statement – metal-insulator transition is highly non-trivial phenomenon relating to electron correlations
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Metallic HydrogenLatest results: theory, again…
•At very low temperatures, de Broglie wavelength becomes comparable to inter-atom separation
• ! Metallic superfluid - or even a superconducting superfluid - at 4 Mbars?
•Electron vs. proton flow
•This review: physics background, history, experiment & latest ideas
Vortex tornados inside a metallic superfluid – or
merely inside the mind of a theorist?
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X-Ray Nanofocusing• Flux gain • X-ray microscopy –
with nm resolution?
• Nanoparticle (and single molecule?) imaging (diffraction/ fluorescence)
• Nanolithography
J. K
irz,
Sto
ny B
rook
Latest Intel chip, launched this month:Pentium 4 “Prescott”90nm (!) features
Roadmap: 13nm EUV
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X-Ray Nanofocusing
• Small absorption• Index of refraction near
unity…• …and actually smaller than
1• Any lensing is a tremendous
challenge!• Things get tougher for hard
X rays ie. short wavelengths
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X-Ray Nanofocusing
• Some approaches:
“Swiss cheese” lens
Zone plates with ultra-high aspect ratios
Orthogonal curved mirrors
(Kirkpatrick-Baez)
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X-Ray Nanofocusing
Fundamental focusing limits?• Full wave optics approach is similar to
Schrodinger equation – does uncertainty relation apply?