Why is condensed matter in flatland so interesting?

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].

Comments

  1. AnonymousJanuary 31, 2020 at 3:35 AM

    Thanks for your thought provoking article. How about the following sport-oriented analogy for the question 2:

    Fencing 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.

    ReplyDelete
  2. SimOJanuary 31, 2020 at 9:59 PM

    Analogy about railways (1D), motorways (2D) and air traffic (3D) could be used for illustrative purposes.

    ReplyDelete
  3. AnonymousJanuary 31, 2020 at 11:25 PM

    Quantum wells are extensively used as common commercial laser diodes. As are Quantum cascade lasers which are superlattices of specially designed quantum wells.

    ReplyDelete
  4. AnonymousFebruary 12, 2020 at 3:48 AM

    Regarding #4, one very important application is the use of the quantum Hall effect as a resistance standard in electrical metrology.

    ReplyDelete

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