Difference: Fermi wave length vs. phase-breaking length?

I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that:

Phase breaking length= length over which electron remains its phase.

Fermi wavelength= Wavelength associated with the maximum energy of electron (Fermi energy). This is often equal to the distance between 2 electrons.

What I couldn't find, however (and in which I am interested) is:

1) What is the difference between the Fermi wave length and the phase-breaking length?

2) In which transport regimes do they play a role?

• I think "regions", instead of "regimes", is apposite. Aug 31, 2016 at 11:18

1 Answer

You have the correct definition for the two lengths. From them you realise that they are not connected to each other, so both your questions make no real sense.

The Fermi wave-length is a property of a Fermi gas, the phase-breaking length (also called coherence length) is a property of coherent gas. Bosons have a coherence length as well, not only fermions, whereas only fermions have a Fermi length...

Quantum effects are associated with the coherence length, i.e. quantum effects emerge at length scale below the coherence length. Typically, if you have a mesoscopic structure of length smaller than the coherence length, then you can see coherent effect (Aharonov-Bohm, quantum Hall among others). The coherence length depends strongly on the interaction in the system, the temperature, ...

There are not a lot of physics associated with the Fermi wave-length, since this is usually the smallest one. It is usually of the order of magnitude of the distance between atoms/electrons in a solid. It tells you that there are not much higher energy than the Fermi one in a degenerate fermionic gas. The Fermi length does not depend strongly on temperature, interaction, ...