Download Electronic Structure of Sr2RuO4

Literature Reviews 2005/06
1. Electronic Structure of Quasicrystals
2. 20 Years of High-Tc Superconductivity –
Why Isn’t My Power Cord Made of It?
3. The Quest for Metallic
(and Superconducting!) Hydrogen
4. Focusing X Rays to
Nanometer Dimensions
Christoph Bergemann
Quantum Matter Group, Cavendish Laboratory
[email protected] Phone: 37389
Quasicrystals
• Ordinary crystals have periodic lattices
Major result in
QCMP course (Lent)
• 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!
Laue XRD
pattern
• Quantum mechanics in quasiperiodic potential solutions are tricky – Bloch’s theorem is violated
Quasicrystals
Some more food for thought:
• Quasicrystals are 3D slices through periodic
structures in higher-D “hyperspace”
• 1D Quasicrystal: Fibonacci stack
Substitution rule: A ! AB, B ! A
ABAABABA Ã ABAAB Ã ABA Ã AB Ã A
• 2D Quasicrystal:
Penrose tilings
Quasicrystals
Some 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 Superconductivity
Many 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?
Not the subject
of this review
Crystal Structure
of YBa2Cu3O7-
High-Tc Superconductivity
Engineering issues:
• How to form cables from brittle ceramics?
This literature
review
• 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?
High-Tc Superconductivity
Some examples:
Power cables
Maglev trains
High-Tc SQUIDs
Fault current limiters
Metallic Hydrogen
• We all know hydrogen as a gas
• Under high pressures, it
becomes a liquid
• Speculation since 1935 that
hydrogen might become
metallic!
Wigner
Is 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
Ocean floor:
1 kbar
Clamp cell:
30 kbar
Anvil 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 Hydrogen
Latest 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
Vortex tornados inside a
metallic superfluid – or merely
inside the mind of a theorist?
• This review: physics background,
history, experiment & latest ideas
X-Ray Nanofocusing
• Flux gain
• X-ray microscopy –
with nm resolution?
• Nanoparticle (and
single molecule?)
imaging (diffraction/
fluorescence)
• Nanolithography
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 ultrahigh 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?