I am working on a chapter on condensed matter physics in dimensions different from three for Condensed Matter Physics: A Very Short Introduction.
This is a rich subject since it is associated with high-Tc superconductors, quantum Hall effects, Haldane spin chains, Kosterlitz-Thouless transition, critical phenomena in 4 - epsilon dimensions, .....
Obviously, I cannot only give the flavour of things.
I would like to get your perspective on a few questions. For some, I have my own answers but want to hear others. Bear in mind the answers have to be accessible to a non-expert audience.
1. What is the central idea or concept?
2. What is an analogy to explain how dimensionality changes things?
3. What is an example of cross-fertilisation with another field of physics or science?
4. What is a significant technological application where low-dimensionality is central?
[High mobility MOSFETs are not an example because the devices are not really using a property that only occurs in two dimensions].
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Thanks for your thought provoking article. How about the following sport-oriented analogy for the question 2:
ReplyDeleteFencing as 1D particle dynamics: The short-range interaction involves only two bodies and the relative positions of the two bodies cannot be changed if they are impenetrable.
Soccer as 2D particle dynamics: The short-range interaction can involve more than two bodies. For finite-size samples (or soccer fields), there can be interesting effects from boundaries (like a Throw-in).
Quidditch as 3D particle dynamics: Collisions can occur in every possible angle, which makes the game (or the dynamics) very complex.
Analogy about railways (1D), motorways (2D) and air traffic (3D) could be used for illustrative purposes.
ReplyDeleteQuantum wells are extensively used as common commercial laser diodes. As are Quantum cascade lasers which are superlattices of specially designed quantum wells.
ReplyDeleteRegarding #4, one very important application is the use of the quantum Hall effect as a resistance standard in electrical metrology.
ReplyDelete