Friday, October 5, 2012

Deconstructing the Hall effect in quasi-one-dimensional metals

Understanding the Hall effect in strongly correlated electron materials is a challenge. In simple metals, the Hall coefficient R_H is, to a good approximation, equal to the inverse of the charge carrier density, and so is weakly dependent on temperature.
Furthermore, it has the same sign as the charge carriers.

In contrast, in strongly correlated metals, R_H can vary significantly with temperature, including changing sign, and its magnitude and signh can be significantly different from the charge carrier density estimated from band structure calculations or alternative experimental measurements such as the Drude weight in the optical conductivity.
I have written several previous posts about this issue. A post on the cuprates illustrates the problem.

There is a really nice paper Hall effect in quasi-one-dimensional metals in the presence of anisotropic scattering by Nicholas Wakeham and Nigel Hussey.
They show that due to the highly anisotropic band structure in a quasi-one-dimensional Fermi liquid metal, a variation of the scattering rate of just a few per cent over the Fermi surface, can significantly modify the Hall coefficient.
The figure below compares experimental data for the cuprate PrBa2Cu4O8 to a simple model with a temperature dependent anisotropy of less than 4 per cent.
The measured Hall coefficient is an order of magnitude smaller than the band structure value and changes sign twice as a function temperature.
This relatively simple explanation of complex behaviour should caution against exotic and non-Fermi liquid interpretations of Hall effect data (e.g., this PRL).


  1. I love these papers that propose simple answers to unexplained phenomena. They are very valuable.

    Why would the Drude weight of the OC be related to R_H?

  2. The Drude weight of the optical conductivity (in a Drude/Sommerfeld/Bloch) model is approximately
    n e^2/m* where n is the charge carrier density, e is the electronic charge, and m* is the effective mass.