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I am working on the transport properties of two dimensional electron gas in semiconductor heterostructures and am interested in the characteristic length and time scales of the system like elastic scattering time and length, phase coherence length, thermal length, etc. Kindly suggest a good review paper on explaining the significance of each of these scales in relation to fermi wavelength and their effect in gauging the electronic transport properties as a function of the dimensions of our system (like [ballistic (XOR)diffusive] (AND) [classical (XOR) quantum regimes]).

As any analysis of a particular property of a condensed matter system involves characteristic length and time scales, I would be grateful if you could suggest a reference which deals with the problem of finding the scales in a unified framework. else even a reference which deals satisfactorily the electron transport problem also would do good.

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Hi baalkikhaal - it's generally better if you ask about what you want to know directly, rather than asking for a reference. People will still point you to references as needed. In this case your question title could be something like "How does one find characteristic length and time scales in a unified framework?" and the body would be an elaboration on that. – David Z Oct 21 '12 at 14:56
@DavidZaslavsky thank you for the suggestion. I will keep that in mind. – baalkikhaal Oct 21 '12 at 18:34
up vote 2 down vote accepted

This is an extremely comprehensive review of electronic properties in two-dimensional electron systems (2DESs):

but, as you can imagine, it covers almost everything there is to cover in 2DESs. For areas (in transport) you're focusing on you will find only sections IV C and D useful; it involves computation of relaxation times in certain regimes. The research/review articles that I have come across so far do not talk comprehensively about transport; most of them are limited to certain cases. General transport theory is covered in many excellent textbooks. One such example is this book by Lundstrom:

Chapter 2 of the about book discusses computing relaxation times due to various scattering mechanisms: electron-impurity, electron-phonon (optical and acoustic), electron-electron, as well as various types of scattering: inter- and intra-valley scattering etc. The rest of the characteristic scales can easily be determined from the relaxation time (except the phase coherence length). The core of the book, however, makes use of the Boltzmann Transport Equation (BTE), discussed in Chapter 4, which is inherently classical. However, since we often use band theory (quantum) alongside the BTE, this is called semiclassical transport. This is why I said that you can compute all characteristic scales except for the phase coherence length. You need a fully quantum treatment to determine the phase coherence length. Such a treatment is possible using Non-Equilibrium Green's Function (NEGF) formalism. This book by Datta:

gives you a very good intuition for NEGF since it approaches NEGF from the Landauer formalism. If you are already familiar with the Landauer formalism then all you need to do is take a look at the comparison between NEGF and Landauer on page 27, and then skip to chapters 8-10. Even towards the end of Lundstrom's book, i.e. chapter 8 and 9, you will start seeing crossovers from semiclassical to quantum, diffusive to ballistic etc. the two books by Datta and Lundstrom are mutually complementary, and serve as an extremely valuable resource on carrier transport. If you are overwhelmed by the content in these books (not surprising if true) and then you can always visit the website to watch video lectures given by both these authors. This is an excellent class taught by Datta:

and follows the same textbook I listed above.

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thank you for such informative reply:) – baalkikhaal Oct 21 '12 at 18:39

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