Abstract
The structure factor and correlation energy of a quantum wire of thickness b ≪ a B are studied in random phase approximation (RPA) and for the less investigated region r s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ϵ c (b, r s ) = α(r s )/b + β(r s ) ln(b) + η(r s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.
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References
G.F. Giuliani, G. Vignale, Quantum theory of the electron liquid (Cambridge University Press, Cambridge, 2005)
R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical properties of carbon nanotubes (Imperial College Press, London, 1998)
M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, P.L. McEuen, Nature 397, 598 (1999)
H. Ishii, H. Kataura, H. Shiozawa, H. Yoshioka, H. Otsubo, Y. Takayama, T. Miyahara, S. Suzuki, Y. Achiba, M. Nakatake, T. Narimura, M. Higashiguchi, K. Shimada, H. Namatame, M. Taniguchi, Nature 426, 540 (2003)
M. Shiraishi, M. Ata, Solid State Commun. 127, 215 (2003)
J. Schäfer, C. Blumenstein, S. Meyer, M. Wisniewski, R. Claessen, Phys. Rev. Lett. 101, 236802 (2008)
Y. Huang, X. Duan, Y. Cui, L.J. Lauhon, K.-H. Kim, C.M. Lieber, Science 294, 1313 (2001)
H. Monien, M. Linn, N. Elstner, Phys. Rev. A 58, R3395 (1998)
A. Recati, P.O. Fedichev, W. Zwerger, P. Zoller, J. Opt. B: Quantum Semiclass. Opt. 5, S55 (2003)
H. Moritz, T. Stoferle, K. Guenter, M. Kohl, T. Esslinger, Phys. Rev. Lett. 94, 210401 (2005)
F.P. Milliken, C.P. Umbach, R.A. Webb, Solid State Commun. 97, 309 (1996)
S.S. Mandal, J.K. Jain, Solid State Commun. 118, 503 (2001)
A.M. Chang, Rev. Mod. Phys. 75, 1449 (2003)
A. Nitzan, M.A. Ratner, Science 300, 1384 (2003)
S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950)
J.M. Luttinger, Phys. J. Math. 4, 1154 (1963)
F.D.M. Haldane, J. Phys. C 14, 2585 (1981)
H.J. Schulz, Phys. Rev. Lett. 71, 1864 (1993)
M.M. Fogler, Phys. Rev. Lett. 94, 056405 (2005)
M.M. Fogler, Phys. Rev. B 71, 161304(R) (2005)
M. Fabrizio, A.O. Gogolin, S. Scheidl, Phys. Rev. Lett. 72, 2235 (1994)
S. Capponi, D. Poilblanc, T. Giamarchi, Phys. Rev. B 61, 13410 (2000)
G. Fano, F. Ortolani, A. Parola, L. Ziosi, Phys. Rev. B 60, 15654 (1999)
D. Poilblanc, S. Yunoki, S. Maekawa, E. Dagotto, Phys. Rev. B 56, R1645 (1997)
B. Valenzuela, S. Fratini, D. Baeriswyl, Phys. Rev. B 68, 045112 (2003)
W.I. Friesen, B. Bergersen, J. Phys. C 13, 6627 (1980)
L. Calmels, A. Gold, Phys. Rev. B 56, 1762 (1997)
V. Garg, R.K. Moudgil, K. Kumar, P.K. Ahluwalia, Phys. Rev. B 78, 045406 (2008)
M. Tas, M. Tomak, Phys. Rev. B 67, 235314 (2003)
R. Bala, R.K Moudgil, S. Srivastava, K.N. Pathak, J. Phys.: Condens. Matter 24, 245302 (2012)
R. Bala, R.K. Moudgil, S. Srivastava, K.N. Pathak, Eur. Phys. J. B 87, 5 (2014)
C.R. de Oliveira, A.A. Verri, Ann. Phys. 324, 251 (2009)
L.O. Wagner, E.M. Stoudenmire, K. Burke, S.R. White, Phys. Chem. Chem. Phys. 14, 8581 (2012)
E.M. Stoudenmire, L.O. Wagner, S.R. White, K. Burke, Phys. Rev. Lett. 109, 056402 (2012)
R.M. Lee, N.D. Drummond, Phys. Rev. B 83, 245114 (2011)
M. Casula, S. Sorella, G. Senatore, Phys. Rev. B 74, 245427 (2006)
A. Malatesta, Quantum Monte Carlo study of a model one-dimensional electron gas, Ph.D. thesis, Universita Degli studi Di Trieste, Departmento di Fisica Teorica, 1999
L. Shulenburger, M. Casula, G. Senatore, R.M. Martin, Phys. Rev. B 78, 165303 (2008)
A. Malatesta, G. Senatore, J. Phys. IV 10, 5 (2000)
P.F. Loos, J. Chem. Phys. 138, 064108 (2013)
K. Morawetz, V. Ashokan, R. Bala, K.N. Pathak, to be published
D. Pines, P. Nozieres, The theory of quantum liquids (W.A. Benjamin, Inc., New York, 1966)
V. Ashokan, N.D. Drummond, K.N. Pathak, to be published
R.J. Needs, M.D. Towler, N.D. Drummond, P.L. Ríos, J. Phys.: Condens. Matter 22, 023201 (2010)
Handbook of mathematical functions, edited by M. Abramowitz, I. Stegun (Dover Publications, Inc., New York, 1972), pp. 498 and 260
H. Bateman, A. Erdélyi, Higher transcendental functions (McGrawHill, New York, 1953), Vol. I, p. 206 (see 5.3, Definition of the G-Function)
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Ashokan, V., Bala, R., Morawetz, K. et al. Dependence of structure factor and correlation energy on the width of electron wires. Eur. Phys. J. B 91, 29 (2018). https://doi.org/10.1140/epjb/e2017-80530-8
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DOI: https://doi.org/10.1140/epjb/e2017-80530-8