This week we are discussion sections 7.5 and 7.6 of Advanced Solid State Physics by Philip Phillips. He gives a nice discussion of poor mans scaling of the Kondo model. One important feature emerges from this analysis is the existence of a strong-coupling fixed point to which is associated a non-trivial energy scale, the Kondo temperature, TK.
This means that all physical quantities should be universal functions of the ratio T/TK where T is the temperature.
Below is a plot of the measured conductance through a quantum dot. It can be seen that all values lie on a single universal curve, regardless of the value of epsilon (the impurity energy relevative to the Fermi energy) and Gamma (the hybridisation energy), parameters in the underlying Anderson model.
The data is taken from this landmark PRL, From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor
It's important to remember that there should only be universality in certain idealized limits (e.g., such that T_K is the only important energy scale in the problem). Once you no longer have the ideal Kondo model (for example, when multiple levels may be relevant, or there is moderate asymmetry between couplings to the left and right leads of the dot), universality is lost. For some interesting experiments, consider this paper on GaAs dots and this paper on Kondo effects in single-molecule transistors.
ReplyDeleteOn an unrelated note, I wonder why are url links allowed in comments, but formatting tags for super- and subscripts are not. Weird.
ReplyDeleteHi Doug,
ReplyDeletethanks for the clarifying comments and for pointing out the two papers. I did not know about your nice work on the Kondo effect in the single molecule transistors and warmly recommend it. Another nice systematic study which shows things are more complicated than theorists would like.