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Interpretation to ARPES measured Fermi surface

  1. May 18, 2014 #1
    For any system, different experimental tools are able to measure the Fermi surface or electron dispersion. Then, are these Fermi surface or dispersion the ultimate outcome of the combined effects from the existing interactions? In other words, should the detected motion of electrons have been under the influence of all interactions in the system? These quasiparticles (if the Fermi surface is still sharp) should, then, have negligible residue interaction among them, is this?

    My guess is yes, but then I cannot understand the subsequent concerns. Take cuprate as an example. It is known to have hot spots and (pi,pi) magnetic instability, thus the quasi-particles have been influenced to have these properties, and the residue interactions among them should be few. But why measurement on conductivity etc shows serious deviation from the weakly interacting quasi-particle behaviors?

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  3. May 18, 2014 #2


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    First of all, your post is VERY confusing.

    A "Fermi Surface" is NOT the same as electron dispersion. An electron dispersion is the E vs. k line of occupied states. A Fermi surface is the highest occupied state at T = 0K. So they are not the same thing.

    Secondly, I am unsure what you mean by "residue interactions". I don't know if you are using the term "residue" in the pedestrian sense, or in the mathematical sense.

    Finally, if you are talking about all the interactions that affects the self-energy term that results in the broadening of the single-particle spectral function, i.e. A(k,w) = Im G(k,w), the imaginary part of the single-particle Green's function, then yes, we already have plenty of examples of ARPES measurement of that. See the reference I gave in this thread for a "standard", Fermi-liquid metal:


    Your statement on the cuprates is another puzzlement. Since you already acknowledge that the system has "hot spots" and magnetic instabilities, then one would expect that these will be additional interactions that the quasiparticles will experience. So why shouldn't these affect the lifetime and scattering rate of the quasiparticles, and thus, broaden the spectral function even more?

    BTW, width of the spectral function of the cuprates is highly doping-dependent. If you go into the overdoped side of the phase diagram, the ARPES spectra (see my avatar for the overdoped Bi2212) tends to have a stronger resemblance to what one would expect from a typical Fermi liquid metal.

  4. May 18, 2014 #3
    Thank you very much for your answer. I might have to say the title might be misleading. Actually the question is not restricted to ARPES measurement only. But instead, it is quite a general one, viz, what one measures should be the final status of a quasi-particle (if quasi-particle concept still holds), thus for a theoretical study based on these quasi-particles, only weak interaction should be introduced to account for their behavior (is this right?). But why would other measurements find behaviors deviating from a weak interaction picture? Does it mean the quasi-particles involved in ARPES measurement and conduction measurement are different for strongly correlated systems, say cuprates?

    To clarify some details, below are more explanations to my question.

    I actually referred to different measurements in my starting post, say Fermi surface from ARPES, and dispersion from neutron scattering.

    What I mean by "residual interaction" is the renormalized interaction between quasi-particles which should be small (not sure whether this is right)

    All the interaction by my definition is in the bare Coulomb interaction and its 2nd quantization expansion sense. Thus, additional scattering from hot-spots are allowed there. Although it can cause instabiility, the interaction can still be small to cause it. These SDW instabilities is conventionally explained in terms of weak coupling theory.
  5. May 18, 2014 #4


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    Are you asking for when the weak-coupling limit of Fermi Liquid theory breaks down that we can no longer consider the validity of the Landau quasiparticles? There is no such clear transition. Again, if you look at the spectral function, going from overdoped to underdoped, the sharpness of the quasiparticle peak diminishes. So at what point can you no longer assume weak-coupling?

    Why two different methodologies? If you look at my avatar, you'll see that I can show you directly the band dispersion crossing the Fermi level, all from ARPES measurement. Besides, can you get a clearer electronic band dispersion from neutron scattering than from ARPES? I'd figure that ARPES gives a more DIRECT measure of such a disperson.

    Then you are talking about the real and imaginary self-energy in the spectral function, because these are were the renormalization of the many-body interaction comes in in the Fermi Liquid theory. The reference I've given earlier has a clear description of all the factors involved that affects these self-energies. I'm not exactly sure what your question is exactly on these.

    Again, looked at the highly-overdoped regime. Refer to, for example, http://arxiv.org/abs/cond-mat/0104367. Look at Fig. 4. Here, the resistivity measurement as a function of temperature is compared to "Delta(k)", obtained from the ARPES measurement (specifically, from the MDC spectra), and which corresponds to the imaginary part of the self-energy of the quasiparticle. One can clearly see that the electrical transport property here matches that from APRES measurement. So for THIS particular cuprate, you cannot argue that the quasiparticles involved in these two measurements are different.

    I'm not saying that they are all like this. I've stated earlier that the spectral function starts to look very "strange" as one moves closer to the underdoped regime. This isn't surprising because one is getting closer to the antiferromagnetic insulating phase. However, you need to be extremely specific when you talk about cuprates, and the exact compound and phase. The hole-doped and the electron-doped cuprates are distinctively different from each other.

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