Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

Why are so many condensed matter phenomena so dependent upon impurities?

+ 7 like - 0 dislike
18 views

Why are so many condensed matter phenomena so sensitive to impurities? In fact, quite a number of them depend upon impurities for their very existence!

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user jsp
asked Feb 23, 2011 in Theoretical Physics by jsp (35 points) [ no revision ]

3 Answers

+ 6 like - 0 dislike

A. You cannot find a condensed matter system without impurities. Even with the most stringent manufacturing processes you are always left with some (however small) fraction of defects and impurities in any material.

B. The most interesting physics (Kondo Effect, Anderson Localization, Quantum Hall Effect) occurs only in the presence of defects. If you read Jain's excellent book "Composite Fermions" (or any other review on the QHE) you will discover that in a perfect sample one cannot have the QHE because of Lorentz invariance of the sample. Defects break this symmetry and one can no longer boost to a frame where the induced magnetic field cancels the external one.

Defects and impurities allow us extremely fine control over the electronic properties of materials and we would not have things as beautiful as transistors or SQUID devices without them.

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user user346
answered Feb 24, 2011 by Deepak Vaid (1,975 points) [ no revision ]
Just a quick comment: the integer QHE depends on impurities as you point out, but the fractional one needs a clean sample, which is why it was discovered later. The physics there depends on unscreened Coulomb interaction between the electrons.

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user user566
@Moshe This is not true, FQHE still needs disorder even though interactions are crucial to its existence. The reason why it was discovered later than the IQHE was that the temperatures which are necessary to see it are much lower $T < 1.0$K

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user DaniH
+ 3 like - 0 dislike

Let me try to identify a generic reason for why are impurity-free condensed matter systems likely to be boring. A condensed matter system without defects:

  1. has a perfect spatial symmetry, so its low energy excitations can be described by an effective field theory, regularized at atomic energies by the actual lattice.

  2. the correspondng vaccuum is "empty", so there is not too much space for macroscopically observable qualitatively different phenomena unless they involve excitation on the cut-off (lattice) level. But such excitaions are nothing but defects/microscopic disorder/inhomogeneity that we want to avoid.

It is similar to QFT in the usual (God-given) vacuum: continuous symmetries put a strong restriction on the type of possible particles & interactions.

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user Slaviks
answered Aug 17, 2011 by Slaviks (610 points) [ no revision ]
+ 2 like - 0 dislike

Primary reference: http://www.tcm.phy.cam.ac.uk/~bds10/publications/lesh.ps.gz

Disorder is very important in the so-called mesoscopic regime, where the sample size is larger than the coherence length of electrons, and the coherence length is much larger than the Compton wavelength. Roughly speaking, due to the multiple scattering which occurs across the entire sample, transport is a diffusive process, but the scattering centres (i.e. impurities) are dilute and/or weak so that electrons propagate coherently between close ones.

One can imagine trying to compute the probability of transmission as the square of a propagator/two-point correlation function. Using field integral methods, one finds that the probability corresponds to a Feynmann diagram which contains a path going forwards then backwards. In particular, for the phases to not strongly cancel, the paths need to remain within a Compton wavelength of each other. The introduction of scattering centres gives rise to a quantum phenomenon where one can get a constructive interference by making a loop somewhere in the middle and making the forward and return paths go in the same direction instead.

The introduction of an intermediate length scale also introduces new effective modes, the most important of which are the diffuson (the classical diffusive mode) and the cooperon which is purely quantum mechanical (and corresponds roughly to the description above of forward and backward paths going in the same direction). The field theory then allow you to join these together arbitrarily and resumming the entire series then predicts various interesting phenomenon.

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user genneth
answered Aug 17, 2011 by genneth (565 points) [ no revision ]
+1; a very nice explanation of what is mesoscopic physics within the broad realm of condensed matter theory

This post imported from StackExchange Physics at 2014-04-01 17:32 (UCT), posted by SE-user Slaviks

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\varnothing$ysicsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...