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I hear about the quenching of kinetic energy of electrons in two different contexts (flat bands (Energy vs k) and Landau levels caused by applying a strong magnetic field perpendicular to the 2DEG).

In both cases, looking at the electronic band structure (E vs k), it seems that they both boil down to the energy of the electrons not having any momentum (k) dependence.

But, it appears to me that, if the system has multiple flat bands or if the electrons reside in not just the lowest LL, but across multiple LLs, they are allowed to have different kinetic energies.

So, my question is the following:

When they say the kinetic energy of electrons is quenched, it does not necessarily mean that the actual value is zero but all those electrons are forced to have the same kinetic energy. If this is a true statement, how should I understand that electrons residing on different flat bands or Landau Levels end up having the same kinetic energy? (or do they not?)

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  • $\begingroup$ Could you explain the statement "...it appears to me that, if the system has multiple flat bands or if the electrons reside in not just the lowest LL, but across multiple LLs, they are allowed to have different kinetic energies"? I don't understand why multiple flat-bands would lead to this condition. $\endgroup$
    – Niall
    Commented Jun 27, 2022 at 8:52
  • $\begingroup$ @Niall I made that statement because when B field is applied, Landau quantization leads to electrons taking on discrete kinetic energies in the form of $E_n = \hbar \omega_c (n+1/2)$ $\endgroup$
    – Blackwidow
    Commented Jun 27, 2022 at 11:12
  • $\begingroup$ A precise reference would be helpful. Who is "they"? Are you referring to fluorescence. quenching? $\endgroup$
    – Andrea Alciato
    Commented Jul 1, 2022 at 15:46
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    $\begingroup$ @Blackwidow Still not sure we're on the same page. Anyway, flat band means d2E/dk2=0. Now 1/m*=d2E/dk2=0, m* being the reduced mass, which becomes infinite. So electrons are stuck, "quenched". $\endgroup$
    – Andrea Alciato
    Commented Jul 5, 2022 at 7:13
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    $\begingroup$ @Blackwidow. Have a look at this: en.m.wikipedia.org/wiki/Shubnikov%E2%80%93de_Haas_effect . "In the presence of a magnetic flux density B, the energy eigenvalues of this system are described by Landau levels. As shown in Fig 1, these levels are equidistant along the vertical axis. Each energy level is substantially flat inside a sample (see Fig 1). " Is this what you mean? $\endgroup$
    – Andrea Alciato
    Commented Jul 5, 2022 at 18:54

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I have never heard the word "quenching" in this context, but it seems you are mixing up some concepts. The energy of the Landau levels $E_n = \hbar \omega_c (n+1/2)$ do not represent kinetic energy, but are instead the eigenvalues you get by applying the Hamiltonian $H$ which must include at least kinetic energy and the magnetic field.

I am not sure what you would get by only applying the kinetic energy operator, but you can see from the flat dispersion that the group velocities are zero, $v_g = dE/dk = 0$, which in a Newtonian sense could be understood as zero kinetic energy. I would guess this is what is meant by quenching, the flat band means zero group velocity which again means that the electrons are not moving anywhere (in the particle picture).

Hopefully that helps!

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