×

Relativistic energy-dispersion relations of 2D rectangular lattices. (English) Zbl 1362.82003

Summary: An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters \(V_0\), core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
81V70 Many-body theory; quantum Hall effect
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bloch, F., Z. Phys.52, 555 (1928). · JFM 54.0990.01
[2] Peierls, R. E., Ann. Phys.5(2), 244 (1930).
[3] Dresselhaus, G. and Dresselhaus, M. S., Phys. Rev.160(3), 649 (1967).
[4] Slater, J. C., Phys. Rev.51(10), 846 (1937). · Zbl 0017.04605
[5] Bardeen, J., Phys. Rev.52(7), 688 (1937). · JFM 63.1419.03
[6] Shockley, W., Phys. Rev.78(2), 173 (1950). · Zbl 0037.13901
[7] Luttinger, J. M. and Kohn, W., Phys. Rev.97(4), 869 (1955). · Zbl 0064.23801
[8] Dresselhaus, G., Kip, A. F. and Kittel, C., Phys. Rev.98(2), 368 (1955).
[9] Cardona, M. and Pollak, F. H., Phys. Rev.142(2), 530 (1966).
[10] Anderson, J. B., Quantum Monte Carlo: Origins, Development, Applications (Oxford University Press, 2007). · Zbl 1144.81003
[11] Bartolotti, L. J., Phys. Rev. A26(4), 2243 (1982).
[12] Gross, E. K. U. and Kohn, W., Adv. Quantum Chem.21, 255 (1990).
[13] Barbier, M.et al., Phys. Rev. B77(11), 115446 (2008).
[14] Barbier, M., Vasilopoulos, P. and Peeters, F. M., Phys. Rev. B80(20), 205415 (2009).
[15] Barbier, M., Vasilopoulos, P. and Peeters, F. M., Phys. Rev. B81(7), 075438 (2010).
[16] Barbier, M.et al., Phys. Rev. B79(15), 155402 (2009).
[17] Barbier, M., Vasilopoulos, P. and Peeters, F. M., Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci.368(1932), 5499 (2010). · Zbl 1211.82073
[18] Barbier, M., Vasilopoulos, P. and Peeters, F. M., Phys. Rev. B82(23), 235408 (2010).
[19] Ata, E., Demirhan, D. and Büyükkılıç, F., Phys. E, Low-Dimens. Syst. Nanostruct.62, 71 (2014).
[20] Ata, E., Demirhan, D. and Büyükkılıç, F., Phys. E, Low-Dimens. Syst. Nanostruct.67, 128 (2015).
[21] Ashcroft, N. W. and Mermin, N. D., Solid State Physics (Harcourt College Publishers, 1976). · Zbl 1118.82001
[22] Kittel, C. and Fong, C.-Y., Quantum Theory of Solids (Wiley Publishing, 1987). · Zbl 0121.44701
[23] Strange, P., Relativistic Quantum Mechanics: With Applications in Condensed Matter and Atomic Physics (Cambridge University Press, 1998).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.