Beyond the semiclassical description of Bloch oscillations

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
IOP Publishing Ltd.
Google Scholar
Research Projects
Organizational Units
Journal Issue
Electrons moving in a tilted periodic potential perform a periodic motion, known as Bloch oscillation. Within a semiclassical description, the crystal momentum increases linearly with time until it reaches the boundary of the first Brillouin zone in reciprocal space. Then, it reenters the first Brillouin zone by the opposite edge. This periodic motion in reciprocal space is accompanied by an oscillation in real space. The angular frequency of the oscillations and their amplitude can be calculated within the semiclassical framework. Nevertheless, the semiclassical approach cannot explain the rich phenomenology of the Bloch oscillations, such as the breathing of the electronic wave packet. We present a simple description of the Bloch oscillations of tightly bound electrons in biased lattices at a basic level and calculate exactly the wavefunction as a function of time.
©IOP Publishing Ltd. The authors thank E D´ıaz and C Gonzalez-Santander for helpful discussions. This work has been supported by MEC (project MOSAICO).
[1] J. Adrian Reyes, H. A. Coyotécatlb, M. Castillo-Mussotc and G. H. Cocoletzic, Physica E 15, 124 (2002). [2] M. Combescot and T. Guillet, Eur. Phys. J. B 34, 9 (2003). [3] E. W. S. Caetano, V. N. Freire, G. A. Farias and E. F. da Silva, Brazilian J. Phys. 34, 702 (2004). [4] H. Hassanabadi, A. A. Rajabi, S. Zarrinkamar and M. M. Sarbazi, FewBody Syst. 45, 71 (2009). [5] M. Santhi and A. J. Peter, Eur. Phys. J. B 71, 225 (2009). [6] B. W. Knight and G. A. Peterson, Phys. Rev. 132, 1085 (1963). [7] P. R. Sievert and M. L. Glasser, Phys. Rev. B 7, 1265 (1973). [8] S. López and F. Domínguez-Adame, Semicond. Sci. Technol. 17, 227 (2002). [9] C. González-Santander and F. Domínguez-Adame, Physica E 41, 1645 (2009). [10] H. Sari, E. Kasapoglu, I. Sökmen and M. Güne¸s, Phys. Lett. A 319, 211 (2003). [11] H. Kramers, Collected Scientific Papers (North-Holland, Amsterdam, 1956), 866. [12] M. Marinescu and M. Gavrila, Phys. Rev. A 53, 2513 (1995). [13] M. Abramowitz and I. Stegun. Handbook of Mathematical Functions (Dover, New York, 1972). [14] D. Chruściński, Ann. Phys. 321, 840 (2006). [15] E. Kasapoglu, H. Sari, M. Bursal and I. Sökmen, Physica E 16, 237 (2003). [1] N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders Colledge Publishers, New ork, 1976), p. 213. [2] F. Bloch, Z. Phys. 52, 555 (1928). [3] C. Zener, Proc. R. Soc. London, Ser. A 145, 523 (1934). [4] T. Hartmann, F. Keck, H. J. Korsch and S. Mossmann, New J. Phys. 6, 2 (2004). [5] J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas and S. Schmitt-Rink, Phys. Rev. B 46, R7252 (1992). [6] K. Leo, P. Haring Bolivar, F. Brüggemann, R. Schwedler and K. Köhler, Solid State Commun. 84, 943 (1992). [7] M. BenDahan, E. Peik, J. Reichel, Y. Castin and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996). [8] S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu and M. G. Raizen, Phys. Rev. Lett. 76, 4512 (1996). [9] B. P. Anderson and M. A. Kasevich, Science 282, 1686 (1998). [10] Ch. Gaul, R. P. A. Lima, E. Díaz, C. A. Müller and F. Domínguez-Adame, Phys. Rev. Lett. 102, 255303 (2009). [11] R. Sapienza, P. Costantino, D. S. Wiersma, M. Ghulinyan, C. J. Oton and L. Pavesi, Phys. Rev. Lett. 91, 263902 (2003). [12] H. Sanchis-Alepuz, Y. A. Kosevich and J. Sánchez-Dehesa, Phys. Rev. Lett. 98, 134301 (2007). [13] D. H. Dunlap and V. M. Kenkre, Phys. Lett. A 127, 438 (1988).