Berry's curvature eludes experimental signatures

An important discovery of the past decade is that the Berry phase and associated geometric curvature may play a role in the electronic properties of many solids. [A nice review is here].
The curvature enters the semi-classical equations for the electron dynamics in a magnetic field. This gives rise to some forms of the anomalous Hall effect.
One might also expect the curvature to be readily manifested in orbital magnetoresistive properties.
However, for subtle reasons this turns out not to be the case.

Tony Wright and I just published a paper
Signatures of the Berry curvature in the frequency dependent interlayer magnetoresistance in tilted magnetic fields

The abstract is below with the result that I found the most surprising [and discouraging] in bold.

We show that in a layered metal, the angle dependent, finite frequency, interlayer magnetoresistance is altered due to the presence of a non-zero Berry curvature at the Fermi surface. At zero frequency, we find a conservation law which demands that the 'magic angle' condition for interlayer magnetoresistance extrema as a function of magnetic field tilt angle is essentially both field and Berry curvature independent. In the finite frequency case, however, we find that surprisingly large signatures of a finite Berry curvature occur in the periodic orbit resonances. We outline a method whereby the presence and magnitude of the Berry curvature at the Fermi surface can be extracted.

The frequency experiments we propose are doable but challenging and involve subtle effects. 

One simple effect we did not explicitly highlight in the paper but should have.
The curvature is chiral, i.e. it has a unique direction perpendicular to a two-dimensional system. Thus, reversing the direction of a tilted magnetic field will change the magnitude of the cyclotron frequency.