Electron Dynamics in Solids

Shigeji Fujita¹, James McNabb III¹, Akira Suzuki^2*

¹Department of Physics, University at Buffalo, State University of New York, Buffalo, USA.
²Department of Physics, Faculty of Science, Tokyo University of Science, Tokyo, Japan.

DOI: 10.4236/jmp.2015.66079                

Abstract

Following Ashcroft and Mermin, the conduction electrons (“electrons” or “holes”) are assumed to move as wave packets. Dirac’s theorem states that the quantum wave packets representing massive particles always move, following the classical mechanical laws of motion. It is shown here that the conduction electron in an orthorhombic crystal moves classical mechanically if the primitive rectangular-box unit cell is chosen as the wave packet, the condition requiring that the particle density is constant within the cell. All crystal systems except the triclinic system have k-vectors and energy bands. Materials are conducting if the Fermi energy falls on the energy bands. Energy bands and gaps are calculated by using the Kronig-Penny model and its 3D extension. The metal-insulator transition in VO2 is a transition between conductors having three-dimensional and one-dimensional k-vectors.

Keywords

Electron Dynamics, Dirac’s Theorem, Primitive Rectangular-Box Unit Cell, Wave Packet, k-Vector

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ashcroft, N.W. and Mermin, N.D. (1976) Solid State Physics. Saunders College, Philadelphia, 116, 217.
[2]	Dirac, P.A.M. (1958) Principles of Quantum Mechanics. 4th Edition, Oxford University Press, London, 121-125. http://dx.doi.org/10.1063/1.3062610
[3]	Ehrenfest, P. (1927) Zeitschrift fur Physik, 45, 455-457. http://dx.doi.org/10.1007/BF01329203
[4]	Bloch, F. (1928) Zeitschrift fur Physik, 52, 555-600. http://dx.doi.org/10.1007/BF01339455
[5]	Kronig, R.L. and Penney, W.G. (1931) Proceedings of the Royal Society of London, 130, 499. http://dx.doi.org/10.1098/rspa.1931.0019
[6]	Wigner, E. and Seitz, F. (1933) Physical Review, 43, 204.
[7]	Drude, P. (1900) Annalen der Physik, 1, 566; 3, 369.
[8]	Haug, A. (1972) Theoretical Solid-State Physics, Vol. 1. Pergamon, Oxford, 64-69.
[9]	Shukla, K. (1990) Kronig-Penney Models and Their Applications to Solids. Ph.D. Thesis, State University of New York at Buffalo.
[10]	Fujita, S., McNabb III, J. and Suzuki, A. (2014) Journal of Modern Physics, 5, 171. http://dx.doi.org/10.4236/jmp.2014.55027
[11]	Debye, P. (1912) Annalen der Physik, 39, 789-839. http://dx.doi.org/10.1002/andp.19123441404
[12]	Kittel, C. (1986) Introduction to Solid State Physics. 6th Edition, John Wiley & Sons, Inc., New York, 10-12.
[13]	Morin, F.J. (1959) Physical Review Letters, 3, 34-36. http://dx.doi.org/10.1103/PhysRevLett.3.34
[14]	Goodenough, J.B. (1971) Journal of Solid State Chemistry, 3, 490-500. http://dx.doi.org/10.1016/0022-4596(71)90091-0
[15]	Mott, N.F. (1968) Reviews of Modern Physics, 40, 677-683. http://dx.doi.org/10.1103/RevModPhys.40.677
[16]	Wentzcovitch, R.M., Schulz, W.W. and Allen, P.B. (1994) Physical Review Letters, 72, 3389-3392. http://dx.doi.org/10.1103/PhysRevLett.72.3389
[17]	Rice, T.M., Launois, H. and Pouget, J.P. (1994) Physical Review Letters, 73, 3042. http://dx.doi.org/10.1103/PhysRevLett.73.3042
[18]	Fujita, S., Jovaini, A., Godoy, S. and Suzuki, A. (2012) Physics Letters A, 376, 2808-2811. http://dx.doi.org/10.1016/j.physleta.2012.08.027
[19]	Whittaker, L., Patridge, C.J. and Banerjee, S. (2011) The Journal of Physical Chemistry Letters, 2, 745-758. http://dx.doi.org/10.1021/jz101640n
[20]	Zhang, Y., Tan, Y.W., Stormer, H.L. and Kim, P. (2005) Nature, 438, 201-204. http://dx.doi.org/10.1038/nature04235
[21]	Kang, N., Lu, L., Kong, W.J., Hu, J.S., Yi, W., Wang, Y.P., Zhang, D.J., Pan, Z.W. and Xie, S.S. (2003) Physical Review B, 67, Article ID: 033404. http://dx.doi.org/10.1103/PhysRevB.67.033404
[22]	Saito, R., Dresselhaus, G. and Dresselhaus, M.S. (1998) Physical Properties of Carbon Nanotubes. Imperial College Press, London, 25. http://dx.doi.org/10.1142/9781860943799
[23]	Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V. and Firsov, A.A. (2005) Nature, 438, 197-200. http://dx.doi.org/10.1038/nature04233
[24]	Novoselov, K.S., Jiang, Z., Zhang, Y., Morozov, S.V., Stormer, H.I., Zeitler, U., Maan, J.C., Boebinger, G.S., Kim, P. and Gaim, A.K. (2007) Science, 315, 1379. http://dx.doi.org/10.1126/science.1137201