Dynamics of the effective mass and the anomalous velocity (Dr. J. Sipe)

The band curvature isassociated with the inverse effective mass, and the cross product of the Berry curvature with an applied force leads to the anomalous velocity. Yet the link of these "kinematical" quantities of curvature and Berrycurvature to dynamics holds only approximately; the effective mass theorem, for example, only holds if an applied force is applied adiabatically. If instead a force is applied rapidly a wave packet constructed from Bloch functions in one band responds initially not with that band's effective mass, but with the bare mass of the particle [1]; further, under a rapid application of a force there is initially no anomalous velocity [2]. We discuss the theory for this, and show how the complicated motion of a wave packet can be described with the aid of a "dynamical effective mass" and a "dynamical anomalous velocity" that change with time and are characterized by dynamics of their own. We present the results of experiments on atoms in optical lattices that have revealed the dynamical effective mass [3], and consider the possibility of experiments of this type that would reveal the dynamical anomalous velocity [2]. We conclude by considering the possibility of observing these dynamics in solid-state systems, in the light of new developments in attosecond spectroscopy.

References:
[1.] For a recent discussion and theory see: Federico Duque-Gomez and J.E. Sipe, Phys. Rev. A85, 053412 (2012)
[2.] Yuan Sheng Fang, Federico Duque-Gomez, and J.E. Sipe, Phys. Rev. A (in press)
[3.] Rockson Chang, Shreyas Potnis, Ramon Ramos, Chao Zhuang, Matin Hallaji, Alex Hayat, Federico Duque-Gomez, J.E. Sipe, and Aephraim Steinberg, Phys. Rev. Lett. 112, 170404 (2014)