A sign of something important

The Hall coefficient is a fundamental property of metals. In simple Fermi liquid metals it is temperature independent and inverse proportional to the charge carrier density. It has the same sign as the charge carriers (electrons or holes). A major triumph of the Bloch model of metals is that it could explain the sign of the Hall coefficient for simple metals in terms of their Fermi surface.

In contrast, the Hall coefficient of cuprate superconductors has a complex temperature and doping dependence which defies a simple description. Basic questions about the Hall coefficient are:

• What determines its sign?
• What is the origin of its temperature dependence?
• What is the relationship between it and the structure (or absence) of the Fermi surface?  

A 2006 PRB by Tsukada and Ono describes measurements of the Hall coefficient in the cuprate LSCO. The graph below shows the temperature dependence of the Hall coefficient for a range of dopings x of La2-xSrxCuO4 in the overdoped region. For reference, optimal doping is around x ~ 0.2, and for x larger than 0.3 there is no superconductivity. Note the sign change with increasing x.

The authors emphasize how this is a tricky measurement because one has to be careful that the current paths that are measured [to get both sigma_xx and sigma_xy needed for the Hall coefficient] really do lie in the plane of the layers and do not contain spurious contributions (see this earlier post about the challenge of electronic transport measurements in highly anisotropic materials).

The sign change may be an important signature of strong electronic correlations. I find it interesting (and surprising) that the observed sign change at x=0.3 is obtained in a high temperature series expansion of the high frequency Hall coefficient for the t-J model [in this 1994 PRL by Shastry, Shraiman, and Singh (SSS!)]. [An earlier post discusses Shastry's approach]. [Note: this calculation does not have a t' hopping term, which may be relevant. For example, it has a significant effect on the shape and  curvature of the Fermi surface and the proximity to van-Hove singularities. See below].

An alternative explanation of the sign change in terms of Mott physics was given by Stanescu and Phillips.

There may be a more mundane explanation in terms of changes in the Fermi surface associated with the proximity of the van Hove singularity in LSCO. Indeed ARPES experiments do find an electron-like Fermi surface for x~0.3. Furthermore, experiments on Tl2201 [which does not have a close van Hove singularity] do not see any hint of a decreasing Hall coefficient [or sign change] as one increases the doping on the overdoped side towards samples with Tc=0. [Higher dopings seem problematic for Tl2201].
Furthermore, one can quantitatively describe the temperature dependence of data for x=0.3  [including the sign change with temperature] if one uses a realistic Fermi surface and assumes that the impurity scattering rate is anisotropic over the Fermi surface. See this PRB; I thank Nigel Hussey for bringing it to my attention.

I thank Jure Kokalj for some helpful discussions.