Abstract
We find a non-trivial Berry phase for a finite potential, even in the delocalized-electron limit. We obtain this result for a one-dimensional, periodic sawtooth potential, though our analysis is applicable to other systems. We show that this result is due to both the periodicity of the time-independent wave function and the effects of interband degeneracies. We also find, for the sawtooth potential, that each band is uniquely characterized by its Berry phase’s functional dependence on the potential’s parameters. Thus, each band may be identified by the behavior of its Berry phase.
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References
W.V. Berry, Proc. Roy. Soc. Lond. A 392, 45 (1984)
A. Shapere, F. Wilczek, Geometric Phases in Physics (World Scientific, 1989)
A. Mostafazadeh, Dynamical Invariants, Adiabatic Approximation and the Geometric Phase (Nova Science, 2002)
C.A. Mead, Rev. Mod. Phys. 64, 51 (1992)
R. Tycko, Phys. Rev. Lett. 58, 2281 (1987)
S. Pancharatnam, Proc. Indian Acad. Sci. Ser. A 44, 247 (1956)
Q. Niu, L. Kleinman, Phys. Rev. Lett. 80, 2205 (1998)
J. Ihm, Phys. Rev. Lett. 67, 251 (1991)
Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)
J. Ihm, J. Korean Phys. Soc. 26, 552 (1993)
J. Zak, Phys. Rev. Lett. 62, 2747 (1989)
J.E. Avron, D. Osadchy, R. Seiler, Phys. Today 56, 38 (2003)
R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 47, 1651 (1993)
D. Vanderbilt, R.D. King-Smith, Phys. Rev. B 48, 4442 (1993)
R. Resta, Rev. Mod. Phys. 66, 899 (1994)
M.C. Chang, Q. Niu, Phys. Rev. B 53, 7010 (1996)
G. Sundaram, Q. Niu, Phys. Rev. B 59, 14915 (1999)
M.J. Rave, W.C. Kerr, Eur. J. Phys. 31, 15 (2010)
M.J. Rave, W.C. Kerr, Eur. Phys. J. B 45, 473 (2005)
L. Michel, J. Zak, Europhys. Lett. 18, 239 (1992)
S. Yukawa, G. Tatara, M. Kikuchi, H. Matsukawa, Physica B 284–288, 1896 (2000)
P. Reimann, Phys. Rep. 361, 57 (2002)
A. Lorke, S. Wimmer, J.P. Jager, B.A. Kotthaus, W. Wegscheider, M. Bichler, Physica B 249–251, 312 (1998)
R. Bartussek, P. Hänggi, F. Sols, I. Zapata, Int. J. Bifurc. Chaos 8, 849 (1998)
P. Zeiner, R. Dirl, B.L. Davies, Phys. Rev. B 54, 16646 (1996)
J. Zak, Phys. Rev. Lett. 48, 359 (1982)
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Hodge, W.B., Welchman, E.D. & Rave, M.J. Non-trivial Berry phase for an asymmetric one-dimensional potential in the free electron limit. Eur. Phys. J. B 84, 351–355 (2011). https://doi.org/10.1140/epjb/e2011-20576-0
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DOI: https://doi.org/10.1140/epjb/e2011-20576-0