They are anisotropic marginal Fermi liquids.
A commenter on my recent AI blog post mentioned the following preprint, with a very different point of view.
Superconductivity in overdoped cuprates can be understood from a BCS perspective!
B.J. Ramshaw, Steven A. Kivelson
The authors claim:
" a theoretical understanding of the "essential physics" is achievable in terms of a conventional Fermi-liquid treatment of the normal state...
...observed features of the overdoped materials that are inconsistent with this perspective can be attributed to the expected effects of the intrinsic disorder associated with most of the materials being solid state solutions"
On the latter point, they mention two papers that found the resistivity versus temperature can have a linear component. But there is much more.
The authors appear unaware of the experimental data and detailed theoretical analysis showing that the overdoped cuprates are anisotropic marginal Fermi liquids.
Angle-dependent magnetoresistance measurements by Nigel Hussey's group, reported in 2006, were consistent with a Fermi surface anisotropy in the scattering rate.
Papers in 2011 and 2012 pushed the analysis further.
Consistent Description of the Metallic Phase of Overdoped Cuprate Superconductors as an Anisotropic Marginal Fermi Liquid, J. Kokalj and Ross H. McKenzie
Transport properties of the metallic state of overdoped cuprate superconductors from an anisotropic marginal Fermi liquid model, J. Kokalj, N. E. Hussey, and Ross H. McKenzie
The self-energy is the sum of two terms with characteristic dependencies on temperature, frequency, location on the Fermi surface, and doping. The first term is isotropic over the Fermi surface, independent of doping, and has the frequency and temperature dependence characteristic of a Fermi liquid.
The second term is anisotropic over the Fermi surface (vanishing at the same points as the superconducting energy gap), strongly varies with doping (scaling roughly with 𝑇𝑐, the superconducting transition temperature), and has the frequency and temperature dependence characteristic of a marginal Fermi liquid.
The first paper showed that this self-energy can describe a range of experimental data including angle-dependent magnetoresistance and quasiparticle renormalizations determined from specific heat, quantum oscillations, and angle-resolved photoemission spectroscopy.
The second paper, showed, without introducing new parameters and neglecting vertex corrections, that this model self-energy can give a quantitative description of the temperature and doping dependence of a range of reported transport properties of Tl2Ba2CuO6+𝛿 samples. These include the intralayer resistivity, the frequency-dependent optical conductivity, the intralayer magnetoresistance, and the Hall coefficient. The temperature dependence of the latter two are particularly sensitive to the anisotropy of the scattering rate and to the shape of the Fermi surface.
For a summary of all of this, see slides from a talk I gave at Stanford back in 2013.
I am curious whether the authors can explain the anisotropic part of the self-energy in terms of disorder in samples.
The commenter asked a question. I have moved it here from the AI post.
ReplyDelete"I have a question for you now: If I add a small dose of non-magnetic point disorder such as through low temperature MeV scale irradiation to a sample of clean overdoped cuprate, what measurement (ARPES or ADMR) and simple scaling such as in T or omega would decisively separate anisotropic Marginal Fermi Liquid theory from Fermi Liquid theory plus disorder? If the scaling fails in the marginal case would you change the proposed self-energy?"
Thanks for the question.
DeleteThe claim of the papers that I reference is that ARPES and ADMR can (reasonably) reliably extract the angular and temperature dependence of the self energy. ARPES can give the frequency dependence as well.
I expect that systematically adding non-magnetic point disorder will simply added a term in self energy that scales with the amount of disorder and will be temperature and angle dependent. This is basically Mattheisen's rule. [Whether it holds in optimally doped cuprates is debatable].
Non-magnetic disorder will reduce Tc (and the energy gap) in a d-wave superconductor. It may also reduce the amplitude of the pseudogap. Hence, there is a change it may also reduce the magnitude of anisotropic part of the self energy. In case you are thinking of doing the experiment, you should estimate how much disorder you will need to see these effects. Roughly the scattering rate needs to comparable to Tc.
There is another issue that is alluded to in the Ramshaw paper: that the overdoped samples, like all cuprates, may be solid state solutions, i.e., they may not spatially homogeneous with the same doping throughout. They could include some mixture of underdoped, optimally doped, and overdoped. If so, they could the experiments that I cite as evidence for anisotropic marginal FL behaviour could be an artefact. I don't know enough about the materials to say whether this is a reasonable possibility or how one might produce better samples.
Have I answered your question?