Session J1 - Poster Session II.
POSTER session, Tuesday afternoon, March 04
Room Exhibit Hall 2/3, Austin Convention Center
We present a specific interpretation of a previously derived general method [1] for studying electronic wave-packet evolution within the single-band approximation. As a result of analytical properties of Bessel functions, it is shown that in a homogeneous time-dependent electric field an electron’s motion in a tight-binding band can be interpreted in terms of a phasor (polygonal) construction in the complex plane. The length of the phasors is proportional to the electronic hopping matrix element and to the time increment of the dynamical evolution. When this time increment is infinitesimal, the directions of the phasors are expressed in terms of a time integral of the external field. Wave-packet mean position and velocity are also geometrically interpreted. Based upon our polygonal curve construction, an analogy is established between wave-packet evolution in a constant or in a linearly time-dependent electric field, and the optical phenomena of Fraunhofer or Fresnel diffraction, respectively. The first type of diffraction leads to the usual Bloch oscillation effect, while -associated to the mathematical properties of the Cornu spiral- the second one leads to “asymptotic localization” of the electron. For periodically repeated asymptotic localizations, an overall distinctive Bloch oscillation is also present under suitable conditions for the existence of an associated (static) average electric field. Finally, we also give a phasor-like generalization, in terms of a multidimensional integral of appropriate Fourier transforms of the applied potential, for the case of non-homogeneous electric fields. [1] D. Sanjinés and J.-P. Gallinar, J. Phys. Condens. Matter 11, 3729 (1999).