Are conduction electrons localized in space?by JoAuSc Tags: conduction, electrons, localized, space 

#73
May3009, 09:39 PM

P: 480





#74
May3009, 09:49 PM

P: 34

You know what i enjoy (among lots of things in life) is to chat with a smart person, say by the blackboard and reason about things from basic principles, perhaps not knowing exactly the answers but coming up with such during the interaction and exchange of ideas. you know how i feel when i 'talk' to you? like i'm going through molasses that drags me more and more the more i try to reach the goal (which is answering the question raised by original post). perhaps that's not your intention and we just clash on the style differences, i don't know... what i do know that i came to this thread in attempt to learn something i didn't know about localization versus delocalization (on the basic level, which i think i understand and wanter reconfirmation) to perhaps more advanced level where i could gain some knowledge. i'm getting nothing except my every phrase turned back at me as a question. I asked you to share something interesting about physics of nanostructures (when we were on the topic of boundary conditions)  denied! I tried to reason that ISW can be still 'savlaged' despite its simplicity to recover some real aspects of physics  denied! i asked to share about what books would you suggest reading on condensed matter physics  denied. shall we just quit or are you going to come back with another question on something within this post? 



#75
May3009, 11:05 PM

P: 34

as for addressing saaskis point, i must have overlooked it.. i've been busy answering your mirriad of questions :) By the way, what is UCF? I know that meanfree path is classical concept (back to Drude in our context) while dephasing length is ? the length scale on which coherence is lost? in other words wavelike behavior is not there  in other words  particlelike picture  i.e. back to Drude? Seems like dephasing length is length scale beyond which Drude model would apply. So, they are of the same nature and i would then think of the order of the same length (scale) in the problem. since saaskis is talking about mesoscopic structures, maybe he can share something with us that contributes to this 'everythinggoessolidstatethread'? 



#76
May3109, 12:32 AM

P: 66





#77
May3109, 01:47 AM

P: 34

I think there might be a language issue here, so i would ask you: what does it mean to you  localized versus delocalized? There are effects like weak localization, Anderson localization, dynamic localization. Are you implying localization in the context of a trapped excitation? If so, than that's not what i have been talking about (and i think that's not what original post was asking). I'm thinking about consistent model that recovers both Bloch states and Drude picture in the two extremes. As Landau would say: theory that has a knob(s) on a scale from 0 to 1 that recovers known behaviors in the limits. what is that knob? what is that description? i don't see how we can find these answers by envoking mesoscopic structures, nanotubes, etc... maybe the answer is in the solid state book, staring right at me and i'm just too stupid to see it? In such case, please point it out. if you're talking about Si in an ISW  then both lattice periodicity and ISW boundary conditions have to be taken into account. i think i already discussed that, but i'll just say that once potential length b becomes comparable to interatomic lattice spacing a, you'll start seeing the effect of boundary conditions in the appearance of energy gaps within the silicon 'bulk' like bands. 



#78
May3109, 02:27 AM

P: 66

Remember that it is all about length scales. Your theory should be able to tackle the whole complex dependence on the relative sizes of Fermi wavelength, elastic mean free path, dephasing length, energy relaxation length and the size of your structure. 



#79
May3109, 02:54 AM

P: 34

Let me define a problem: we have a perfectlyperiodic (no impurity) 1D lattice of scale 'a' and bounding potential of scale 'b'. we have noninteracting electrons (so ignoring elastic scattering here) and electronphonon scattering (inelastic scattering). we also have a temperature T that describes both electron and phonon distributions (assuming equilibrium). This is a toy model of a solid  true. But adopting such model can we now answer the question: are electrons in localized or delocalized states? And even more interestingly, what aspects of condensedmatter physics such model recovers (we agree that it omits plenty, like nanotubes for instance). So, as a starting point, can we, within the constraints stated above, come to some agreements, for example: 1) electrons are definitely delocalized because they are described by Bloch states (i'm saying thats wrong, but i'm open for discussion) 2) electrons are definitely localized (in a sense of classical particles, there are no other localizations  we have perfect lattice without external fields). 3) neither of the above: the relevant energy/length scale is ..... 4) the constraints are not sufficient to talk answer the posed question. Can we 'solve' this problem (which is in essence how i took the original post and therefore found it interesting to participate in this thread) first? 



#80
May3109, 03:22 AM

P: 66

And if your bounding potential is periodic, then why introduce a different length scale for lattice? The lattice usually represents the periodicity of the potential landscape, right? 


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