Literature Reviews 2005/06 Christoph Bergemann Quantum Matter Group, Cavendish Laboratory cb203@cam.ac.uk Phone: 37389 1.Electronic Structure of Quasicrystals.

Literature Reviews 2005/06

Christoph BergemannQuantum Matter Group, Cavendish Laboratory

cb203@cam.ac.uk 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

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

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

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

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

High-Tc Superconductivity

Bednorz Müller

Nobel Prize 1987

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

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

High-Tc SuperconductivitySome examples:

Maglev trains

Power cables

Fault current limitersHigh-Tc SQUIDs

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?

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

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

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?

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

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

X-Ray Nanofocusing

• Some approaches:

“Swiss cheese” lens

Zone plates with ultra-high aspect ratios

Orthogonal curved mirrors

(Kirkpatrick-Baez)

X-Ray Nanofocusing

Fundamental focusing limits?• Full wave optics approach is similar to

Schrodinger equation – does uncertainty relation apply?