Phasor-like interpretation of tight-binding electronic motion in the single-band approximation
Abstract
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 one-dimensional nearest-neighbor tight-binding 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 time-dependent 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 complex-plane representation. Finally, a phasor-like 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