Deconstructing the chemical potential of the cuprate superconductors

I have been reading through the nice review Finite temperature properties of doped antiferromagnets by Jaklic and Prelovsek from 2000. They summarise their studies of the t-J model by the Finite temperature Lanczos method.
At first sight the graph below of the temperature and doping dependence of the chemical potential does not look particularly interesting [at least to me]. However, they highlight its significance.
Here are a few points.
  • In a simple Fermi liquid the chemical potential has a positive, quadratic and weak temperature dependence. This is only seen for doping c_h=x=0.3
  • For a wide doping range [0.05 < c_h < 0.3] the temperature dependence is approximately linear. The slope changes sign for approximately optimal doping (c_h ~ 0.15).
  • The weak temperature dependence for c_h ~ 0.15 means that optimal doping corresponds to maximum entropy!  [This can be deduced via the Maxwell relation below. Don't you love thermodynamics!]
  • This relation is also related [approximately] to the thermopower via a relationship [equation 8.6], which is essentially a restatement of the Kelvin formula [discussed  by Peterson and Shastry].
  • The latter means the thermopower should change sign around optimal doping, as is indeed observed [more on that later].
  • The large entropy near optimal doping emerges from the interplay of the localised spins [from the remnants of the Mott insulator] and frustration of the antiferromagnetic spin interactions via doping.
I would be interested to see a similar calculation for the Hubbard model on the anisotropic triangular lattice at half filling to see how the chemical potential varies as a function of U/t as the Mott insulator is approached from within the metallic phase.

Comments

  1. Seth OlsenNovember 9, 2011 at 8:17 PM

    So s, T, ch and mu are entropy, temperature, hole concentration and hole chemical potential?

    ReplyDelete
  2. Ross H. McKenzieNovember 10, 2011 at 11:11 AM

    yes. sorry i should have defined them.

    ReplyDelete
  3. UnknownSeptember 11, 2012 at 3:41 AM

    This comment is regarding this post and this post
    http://condensedconcepts.blogspot.com.au/2011/12/optimal-doping-corresponds-to-maximum.html

    You mention the paper by Jaklic-Prelovsek and Eq. 8.6 in particular--I looked at the arxiv version so hopefully they are the same. Eq. 8.6 is not exactly S_Kelvin but is instead just the so-called Mott-Heikes formula. It originates from the Kubo formula where they argue that the transport terms, the current-current and current-heat-current correlation functions are closely related to one another and are nearly \omega independent. They find that this term just looks like \mu(T=0) and they get the Mott-Heikes formula.

    Jaklic-Prelovsek can connect entropy to chemical potential but cannot quite connect entropy to thermopower since their formula for thermopower is must \mu/T. S_Kelvin allows a precise connection from the entropy to the thermopower.

    Anyway, I agree that the Jaklic-Prelovsek paper is filled with interesting things and FTLM appears very powerful.

    ReplyDelete
  4. Ross H. McKenzieSeptember 11, 2012 at 3:29 PM

    Hi Michael,
    Thanks for the clarifying comment.
    You are correct. Indeed, Jaklic-Prelovsek do not use Kelvin [contrary to my suggestion] but rather the Mott-Heikes formula for thermopower.
    Cheers

    ReplyDelete
  5. VipinAugust 5, 2013 at 6:13 AM

    Dear Prof. McKenzie,

    This comment is regarding the post "Deconstructing the chemical potential of the cuprate superconductors".

    You point out that the T^2 dependence of the chemical potential has a positive coefficient in a Fermi liquid. I'm afraid I do not see how this is true in general: My understanding is that the value of the T^2 coefficient (and consequently the sign as well, I imagine) changes with the dependence of the effective quasiparticle mass on the system density; perhaps even dimensionality plays a role.

    Any clarifications will be greatly welcome.

    Thanks a lot.

    ReplyDelete

Post a Comment

Popular posts from this blog

What is Herzberg-Teller coupling?

Image
Is it something to do with breakdown of the Born-Oppenheimer approximation? In molecular spectroscopy you occasionally hear this term thrown around. Google scholar yields more than 3000 hits. But I have found its precise meaning and the relevant physics hard to pin down. Quantum mechanics in chemistry by Schatz and Ratner is an excellent book , but the discussion on page 204 did not help me. "Herzberg-Teller" never appears in Atkins' Molecular quantum mechanics. So here is my limited understanding. Herzberg and Teller wanted to understand why one observed certain vibronic (combined electronic and vibrational) transitions that were not expected, particularly some that were expected to be forbidden on symmetry grounds. " Intensity borrowing " occurred. Herzberg and Teller pointed out that his could be understood if the dipole transition moment for the electronic transition depended on the nuclear co-ordinate associated with the vibration. In the Franck-Condo
Read more

Is it an Unidentified Superconducting Object (USO)?

If you look on the arXiv and in Nature journals there is a continuing stream of people claiming to observe superconductivity in some new material. There is a long history of this and it is worth considering the wise observations of Robert Cava , back in 1997, contained in a tutorial lecture. It would have been useful indeed in the early days of the field [cuprate superconductors] to have set up a "commission" to set some minimum standard of data quality and reproducibility for reporting new superconductors. An almost countless number of "false alarms" have been reported in the past decade, some truly spectacular. Koichi Kitazawa from the University of Tokyo coined these reports "USOs", for Unidentified Superconducting Objects , in a clever cross-cultural double entendre likening them to UFOs (Unidentified Flying Objects, which certainly are their equivalent in many ways) and to "lies" in the Japanese translation of USO.   These have caused g
Read more

What should be the order of authors on a conference poster or talk?

I welcome discussion on this point. I don't think it is as sensitive or as important a topic as the author order on papers. With regard to paper authorship my general rule is that the person who does the bulk of the work, including actually writing the paper should be the first author. Doug Natelson has a good post on co-authorship , that I largely agree with. My only difference is that I am not really convinced that good practice prevails in the majority of circumstances. I fear there are increasing numbers of co-authors, particularly senior ones, with marginal contributions. But, what about conference talks and posters? Many of these are based on work that is already or about to be published. Should the author order be identical as the associated papers? I am not sure it should necessarily be. My tentative view is that the person who writes and submits the abstract and actually prepares and presents the post/talk should be the first author. Perhaps they should also highlig
Read more