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I was pointed towards the use of the Deformation Potential (DP) theory to calculate the electron relaxation time in a previous question.

However, I still have a doubt regarding its applicability to 2D and 1D systems.

Are there any special considerations which I should take before applying the DP theory to such low-dimensional systems?

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Deformation potential theory is almost always used to study 2D materials. The first line of the abstract of the original Bardeen-Shockley paper mentions "deformations of the crystal lattice".

So the considerations you should take when applying the DP theory to 2D systems are not "special", they are the standard. If you need help getting started on applying the DP theory to your specific 2D system, then it would be wise to look at some examples of the DP theory being used on real systems. It is discussed in a plethora of a papers and even books, for example in Section 1.3.C of this version of Mahan's Many-Particle Physics book (this book also contains references to some of the older papers on deformation potentials, and you can look at papers that have cited those papers recently in order to find more recent examples of related literature).

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