Abstract
Due to the particular confinement and reduced dimensionality of quantum rings, Coulomb interaction plays an important role for their electronic structure. In this chapter, we discuss the dependency of the ground state of an idealized quantum ring contained a small number of interacting electrons on geometric parameters like ring radius, radial confinement and eccentricity. The ring geometry affects both the charge distribution and the spin configuration in a quantum ring. Numerically exact results obtained from path-integral quantum Monte Carlo demonstrate the strong connection between the structure and the total spin of the ground state emerging from the interplay between confinement and Coulomb interaction.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P. Singha Deo, P. Koskinen, M. Koskinen, M. Manninen, Europhys. Lett. 63(6), 846–852 (2003)
M. Szelag, M. Szopa, J. Phys. Conf. Ser. 104, 012006–012014 (2008)
Y.V. Pershin, C. Piermarocchi, Phys. Rev. B 72(12), 125348 (2005)
N. Yang, J.-L. Zhu, Z. Dai, J. Phys. Condens. Matter 20(29), 295202–295213 (2008)
T. Chakraborty, P. Pietiläinen, Phys. Rev. B 52, 1932–1935 (1995)
K. Niemelä, P. Pietiläinen, P. Hyvönen, T. Chakraborty, Europhys. Lett. 36(7), 533–538 (1996)
F. Pederiva, A. Emperador, E. Lipparini, Phys. Rev. B 66(16), 165314 (2002)
P. Borrmann, J. Harting, Phys. Rev. Lett. 86(14), 3120–3123 (2001)
V.M. Fomin (ed.), J. Nanoelectron. Optoelectron. 6(1) (2011)
Y. Saiga, D.S. Hirashima, J. Usukura, Phys. Rev. B 75(4), 045343–045354 (2007)
P. Koskinen, M. Koskinen, M. Manninen, Eur. Phys. J. B 28(4), 483–489 (2002)
L.A. Lavenere-Wanderley, A. Bruno-Alfonso, A. Latge, J. Phys. Condens. Matter 14(2), 259–270 (2002)
D. Gridin, A.T.I. Adamou, R.V. Craster, Phys. Rev. B 69(15), 155317 (2004)
A. Lorke, J.R. Luyken, A.O. Govorov, J.P. Kotthaus, J.M. Garcia, P.M. Petroff, Phys. Rev. Lett. 84(10), 2223–2226 (2000)
D.M. Ceperley, Rev. Mod. Phys. 67(2), 279–355 (1995)
B. Baxevanis, D. Pfannkuche, J. Nanoelectron. Optoelectron. 6(1), 76–80 (2011)
M. Takahashi, M. Imada, J. Phys. Soc. Jpn. 53(3), 963–974 (1984)
R. Egger, W. Häusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 83(2), 462 (1999)
R. Pauncz, The Construction of Spin Eigenfunctions: An Exercise Book (Kluwer Academic/Plenum, New York, 2001)
A.P. Lyubartsev, P.N. Vorontsov-Velyaminov, Phys. Rev. A 48(6), 4075–4083 (1993)
M. Hamermesh, Group Theory and Its Application to Physical Problems (Dover, New York, 1989)
L. Wendler, V.M. Fomin, A.V. Chaplik, A.O. Govorov, Z. Phys. B, Condens. Matter 100, 211–221 (1996)
E. Wigner, Phys. Rev. 46(11), 1002–1011 (1934)
M. Koskinen, M. Manninen, B. Mottelson, S.M. Reimann, Phys. Rev. B 63(20), 205323 (2001)
P. Hawrylak, D. Pfannkuche, Phys. Rev. Lett. 70(4), 485–488 (1993)
P.A. Maksym, Phys. Rev. B 53(16), 10871–10886 (1996)
P.A. Maksym, Physica B, Condens. Matter 184(1–4), 385–393 (1993)
R. Courant, D. Hilbert, Methods of Mathematical Physics, vol. I (Interscience, New York, 1953)
C. Herring, Phys. Rev. B 11(5), 2056–2061 (1975)
M. Aizenman, E.H. Lieb, Phys. Rev. Lett. 65(12), 1470–1473 (1990)
E.H. Lieb, D. Mattis, J. Math. Phys. 3(4), 749–751 (1962)
J. Planelles, F. Rajadell, J.I. Climente, Nanotechnology 18(37), 375402–375413 (2007)
A. Bruno-Alfonso, A. Latgé, Phys. Rev. B 77(20), 205303 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Baxevanis, B., Pfannkuche, D. (2014). Coulomb Interaction in Finite-Width Quantum Rings. In: Fomin, V. (eds) Physics of Quantum Rings. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39197-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-39197-2_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39196-5
Online ISBN: 978-3-642-39197-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)