What is the origin of magnetoresistance in silver chalcogenides?

Silver chalcogenides (e.g., Ag2Te) with slightly altered stoichiometry exhibit an unusual magnetoresistance. It is large and linear in field for magnetic fields up to about 6 tesla and temperatures between 5 and 300 K. [See this 1997 Nature paper].
Several possible physical origins of the magnetoresistance have been proposed.

1. A PRL earlier this year proposes is the material is a topological insulator with gapless surface states described by a highly anisotropic Dirac cone.

2. In 1998 Abrikosov proposed the materials are gapless semiconductors with a linear spectrum, doped to a small carrier concentration, and that only one Landau level contributes to the conductivity.

3. Parish and Littlewood's proposal that the key physics is that of a strongly spatially inhomogeneous semiconductor which can be described by a random resistor network.

4. I also note that a band structure which produces a non-zero Berry curvature can produce a linear magnetoresistance, according to p. 1984 of this Rev. Mod. Phys. [However, I suspect this is a very small effect].

The challenge is to come up with experimental signatures which can distinguish between the four different theoretical proposals.

From every angle

I am enjoying re-reading the book 5 Minds for the Future by Howard Gardner. The 5 minds are Disciplined, Synthetic, Creative, Respectful, and Ethical.

With regard to all of the first three he puts emphasis on the importance of considering the same topic from several angles and perspectives. In particular, creative needs to occur within a context of mastering earlier work.

I wonder how might this does and might happen in condensed matter theory?

Phenomenological vs. microscopic.
Strong coupling vs. weak coupling treatments.
Numerical vs. variational wave functions vs. field theories vs. renormalisation group.
A "chemical" approach concerned with specific details vs. a "physics" approach which neglects many details.

Other ideas?

I actually wonder whether we actually do this more often and better than some disciplines.   But that perception may be based on ignorance and hubris!

Seeking a unified theory for unconventional superconductors II

Phil Anderson has written an interesting comment on my earlier post on this subject. His comment might be read in conjunction with two earlier posts that are revelant.

Glueing together a theory is relevant to his comment about whether the pairing interaction is instantaneous.

Overdoped cuprates are an anisotropic marginal Fermi liquid is relevant to his comment about the Anderson-Casey theory of non-Fermi liquid effects.

I welcome further comments.

Deconstructing sodium cobaltate

Sodium cobaltate (NaxCoO2) is a strongly correlated electron material which achieved a lot of attention before the mass migration to the new iron pnictide superconductors following their discovery around 2008.
Some of the interest was motivated by the large thermopower, spin frustration associated with the underlying triangular lattice, and superconductivity from water!

Jaime Merino, Ben Powell, and I wrote several papers on the subject. At the cake meeting today we reviewed two papers which focused on the doping x=0.5.

Electronic and magnetic properties of the ionic Hubbard model on the striped triangular lattice at 3/4 filling

Ionic Hubbard model on a triangular lattice for Na0.5CoO2, Rb0.5CoO2, and K0.5CoO2: Mean-field slave boson theory
The latter features some really cool movies.

Here are some of the outstanding questions raised by the strange ground state of the x=0.5 material. It appears to be an insulator, with a small amount of charge order, a large magnetic moment which antiferromagnetically orders, and very small Fermi surface which produces quantum oscillations.
All these properties cannot be described by the strong coupling ground state [an antiferromagnetic insulator with charge order] shown below.

What is the ground state of the ionic Hubbard model on the triangular lattice at 3/4 filling for small Delta/t where Delta=measure of ionicity between the two sublattices?
Is it a covalent insulator? Does such a state have experimental signatures which are distinct from a charge ordered insulator?

How can an "insulating" state co-exist with a very small Fermi surface?

A simple concrete proposal to improve the quality of Australian undergraduate education

There is an opinion piece Up-end attendance rules for tutorial and lectures by Peter Van Onselen in the Higher Education Section of today's Australian newspaper. He is a Professor of Political Science at U. of Western Australia and a contributing editor to The Australian. He says that Arts/Humanities courses follow the "tried and true" format of two lectures and one tutorial per week. The former are optional and typically attract less than 50 per cent attendance. Tutorials are compulsory, are over-crowded, and diluted by students who have not done the assigned reading. He argues that the quality of education could be improved, without any additional costs, by making the lectures compulsory and the tutorials optional.

I prefer my own proposals: Fail more students and set the pass rate at the lecture attendance rate.

Ph.D completion time as a statistical variable

Seth Olsen brought to my attention an article Examining the Relationships among Doctoral Completion Time, Gender, and Future Salary Prospects for Physical Scientists in the Journal of Chemical Education.

It is based on a survey of more than 3000 Ph.D graduates of physics and chemistry in the USA. It claims there is a correlation (for men but not women) between Ph.D completion time and future salary. It also debates whether completion time is a good measure of the scientific merit of the graduate (the shorter the better) and the quality of the program (the longer the better!).

I found I was rather skeptical of many of the claims, values, and assertions in the article. [I also wonder about the reliability of the statistical methodology but am not claiming I could do any better...]. Nevertheless, the article is worth reading because all of the issues it raises and the literature that it surveys.

I welcome any comments on the article.

Optimal doping corresponds to maximum entropy

What is so unique about the optimal doping at which the superconducting transition temperature is a maximum in the cuprates?

There is an interesting paper Unified electronic phase diagram for hold-doped high-Tc cuprates by Honma and Hor. It builds on their earlier work which argued the existence of a universal planar hole scale (P_pl), which can be characterised by the thermopower at T=290 K, denoted S^290. P_pl is independent of the nature of the dopant, the number of CuO2 plane layers per unit cell, the structure, and the sample quality. The figure below shows S^290 versus P_pl for a wide range of cuprates.

Note that the thermopower changes sign at a doping of P_pl ~ 0.25 which is comparable to that at which  Tc is a maximum [except for Sr doped La214]. 

What is the significance of this sign change of the thermopower?

For a simple Fermi liquid it would correspond to a change in the sign of the charge carriers, i.e., from electrons to holes.

Recently Peterson and Shastry interpreted this sign change in terms of the Kelvin formula for the thermopower, which gives the thermopower as -1/e times the derivative of the entropy with respect to the particle number. This can be related to the temperature dependence of the chemical potential via the Maxwell relation,

Here s=specific entropy, c_h=hole density, mu_h = chemical potential.

It is rather surprising that a transport property can be expressed in terms of a thermodynamic property.

Thus the change in sign of the thermopower means that the entropy is a maximum as a function of hole doping.

Indeed, a maximum in the entropy near optimal doping is was found for the t-J model via 

Finite temperature Lanczos calculations on small lattices of up to 20 sites and summarised in a 2000 review by Jaklic and Prelovsek.

The paper also considers a Kelvin type relation for the thermopower, but does not mention Kelvin, and shows how the maximum in the entropy vs. doping is associated with a change in sign of the thermopower.

[Peterson and Shastry do not mention this earlier work.]

A recent preprint by Garg, Shastry, Dave, and Philips, argue that the sign change reflects an underlying quantum critical point at optimal doping. However, I wonder about the extent that one can see a quantum critical effect on lattices as small as 20 sites. 

This is related to a 2009 PRB by Mark Jarrell and collaborators who calculated the temperature and doping dependence of the entropy using the cluster dynamical approximation. They found entropy was a maximum at optimal doping [~0.15-0.2]. They also don't mention the earlier work by Jaklic and Prelovsek.