Phasorlike interpretation of tightbinding electronic motion in the singleband approximation
Abstract
We present a specific interpretation of a previously derived general method [1] for studying electronic wavepacket evolution within the singleband approximation. As a result of analytical properties of Bessel functions, it is shown that in a homogeneous timedependent electric field an electronÂ´s motion in a onedimensional nearestneighbor tightbinding band can be described in terms of a phasor (polygonal) construction in the complex plane. Based upon our polygonal construction, an analogy is established between motion in a constant or in a linearly timedependent electric field and the optical phenomena of Fraunhofer or Fresnel diffraction, respectively. The first type of diffraction, associated to the figure of a "circumference", 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. Furthermore, for periodically driven fields dynamical localization can also be elucidated within our complexplane representation. Finally, a phasorlike generalized formula for inhomogeneous applied electric fields, general band structure and dimensionality of electronic motion is given in terms of a multidimensional integral of appropriate discrete Fourier transforms of the corresponding applied potential. [1] D. Sanjinés and J.P. Gallinar, J. Phys. Condens. Matter 11, 3729 (1999).
 Publication:

APS March Meeting Abstracts
 Pub Date:
 March 2004
 Bibcode:
 2004APS..MAR.K1074S