Highly Conductive Polycrystalline Metallic Ring in a Magnetic Field
Electrical conduction in a quasi-one-dimensional
polycrystalline metallic ring with a long electron phase coherence
length realized at low temperature is investigated. In this situation, the
wave nature of electrons is important in the ring, where the electrical
current I can be induced by a vector potential that arises from a static
magnetic field applied perpendicularly to the ring’s area. It is shown
that if the average grain size of the polycrystalline ring becomes
large (or comparable to the Fermi wavelength), the electrical current
I increases to ~I0, where I0 is a current in a disorder-free ring. The
cause of this increasing effect is examined, and this takes place if the
electron localization length in the polycrystalline potential increases
with increasing grain size, which gives rise to coherent connection
of tails of a localized electron wave function in the ring and thus
provides highly coherent electrical conduction.
[1] M. B¨uttiker, Y. Imry, and R. Landauer, “Josephson behavior in small
normal one-dimensional rings,” Phys. Lett. 96A, 1983, pp.365-367.
[2] Y. Imry and N. S. Shiren, “Energy averaging and the flux-periodic
phenomena in small normal-metal rings,” Phys. Rev. B 33, 1986,
pp.7992-7997.
[3] N. Trivedi and D. A. Browne, “Mesoscopic ring in a magnetic
field: Reactive and dissipative response,” Phys. Rev. B 38, 1988,
pp. 9581-9593.
[4] J. J. Sakurai, Modern Quantum Mechanics, Revised ed., New York:
Addison-Wesley Publishing, 1994. Chap. 2.
[5] L. P. Levy, G. Dolan J. Dunsmuir, and H. Bouchiat, “Magnetization of
mesoscopic copper rings: Evidence for persistent currents,” Phys. Rev.
Lett. 64, 1990, pp. 2074-2077.
[6] D. Mailly, C. Chapelier, and A. Benoit, “Experimental observation of
persistent currents in GaAs-AlGaAs single loop,” Phys. Rev. Lett. 70,
1993, pp. 2020-2023. [7] V. Chandrasekhar, R. A. Webb, M. J. Brady, M. B. Ketchen, W. J.
Gallagher, and A. Kleinsasser, “Magnetic response of a single, isolated
gold loop,” Phys. Rev. Lett. 67, 1991, pp. 3578-3581.
[8] E. K. Riedel and F. von Oppen, “Mesoscopic persistent current in small
rings,” Phys. Rev. B 47, 1993, pp. 15449-15459.
[9] P. Nozieres and D. Pines, The Theory of Quantum Liquids, Vol. 1, 1st
ed., New York: Benjamin, 1966. Chap. 1.
[10] T. Matsubara, “A new approach to quantum-statistical mechanics,” Prog.
Theor. Phys. 14, 1955, pp. 351-378.
[11] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of
Quantum Field Theory in Statistical Physics, 1st ed., New York: Dover,
1975.
[12] S. Washburn and R. A. Webb, “Aharonov-Bohm effect in normal metal
quantum coherence and transport,” Adv. Phys. 35, 1986, pp.375-422.
This paper reports that the measurement of a conductance through an
Au wire or ring at very low temperature (< 1 K) showed a large
conductance fluctuation arising from the electron scattering with disorder
in addition to the average conductance. This also holds in measuring a
current at very low temperature.
[13] A. D. Stone, “Magnetoresistance fluctuations in mesoscopic wires and
rings,” Phys. Rev. Lett. 54, 1985, pp.2692-2695.
[14] P. A. Lee and A. D. Stone, “Universal conductance fluctuations in
metals,” Phys. Rev. Lett. 55, 1985, pp.1622-1625.
[15] G. Bouzerar, D. Poilblanc, and G. Montambaux, “Persistent currents in
one-dimensional disordered rings of interacting electrons,” Phys. Rev. B
49, 1994, pp. 8258-8262.
[16] H. Kato H and D. Yoshioka, “Suppression of persistent currents in
one-dimensional disordered rings by the Coulomb interaction,” Phys.
Rev. B 50, 1994, pp. 4943-4946.
[17] D. Yoshioka and H. Kato, “The effect of the Coulomb interaction on the
mesoscopic persistent current,” Physica B 212, 1995, pp. 251-255. The
Hartree and Fock terms in this paper seemingly give an enhancement
in the current, but actually the Fock term has a different sign from
the Hartree term, so they almost cancel each other in summation, and
eventually the e-e interaction does not contribute to an increase in the
current.
[18] P. M. Th. M. van Attekum, P. H. Woerlee, G. C. Verkade, and A. A. M.
Hoeben, “Influence of grain boundaries and surface Debye temperature
on the electrical resistance of thin gold films,” Phys. Rev. B 29, 1984,
pp. 645-650.
[19] X. Chen, Z. Y. Deng, W. Lu, and S. C. Shen, “Persistent current in
a one-dimensional correlated disordered ring,” Phys. Rev. B 61, 2000,
pp. 2008-2013.
[20] I. Tomita, “Persistent current in a one-dimensional correlated disordered
ring,” Physica A 308, 2002, pp. 1-14.
[21] Y. M. Liu, R. W. Peng, X. Q. Huang, M. Wang, A. Hu, and S. S.
Jiang, “Absence of suppression in the persistent current by delocalization
in random-dimer mesoscopic rings,” J. Phys. Soc. Japan 72, 2003,
pp. 346-351.
[22] P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New
method for a scaling theory of localization,” Phys. Rev. B 22, 1980,
pp.3519-3526.
[1] M. B¨uttiker, Y. Imry, and R. Landauer, “Josephson behavior in small
normal one-dimensional rings,” Phys. Lett. 96A, 1983, pp.365-367.
[2] Y. Imry and N. S. Shiren, “Energy averaging and the flux-periodic
phenomena in small normal-metal rings,” Phys. Rev. B 33, 1986,
pp.7992-7997.
[3] N. Trivedi and D. A. Browne, “Mesoscopic ring in a magnetic
field: Reactive and dissipative response,” Phys. Rev. B 38, 1988,
pp. 9581-9593.
[4] J. J. Sakurai, Modern Quantum Mechanics, Revised ed., New York:
Addison-Wesley Publishing, 1994. Chap. 2.
[5] L. P. Levy, G. Dolan J. Dunsmuir, and H. Bouchiat, “Magnetization of
mesoscopic copper rings: Evidence for persistent currents,” Phys. Rev.
Lett. 64, 1990, pp. 2074-2077.
[6] D. Mailly, C. Chapelier, and A. Benoit, “Experimental observation of
persistent currents in GaAs-AlGaAs single loop,” Phys. Rev. Lett. 70,
1993, pp. 2020-2023. [7] V. Chandrasekhar, R. A. Webb, M. J. Brady, M. B. Ketchen, W. J.
Gallagher, and A. Kleinsasser, “Magnetic response of a single, isolated
gold loop,” Phys. Rev. Lett. 67, 1991, pp. 3578-3581.
[8] E. K. Riedel and F. von Oppen, “Mesoscopic persistent current in small
rings,” Phys. Rev. B 47, 1993, pp. 15449-15459.
[9] P. Nozieres and D. Pines, The Theory of Quantum Liquids, Vol. 1, 1st
ed., New York: Benjamin, 1966. Chap. 1.
[10] T. Matsubara, “A new approach to quantum-statistical mechanics,” Prog.
Theor. Phys. 14, 1955, pp. 351-378.
[11] A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of
Quantum Field Theory in Statistical Physics, 1st ed., New York: Dover,
1975.
[12] S. Washburn and R. A. Webb, “Aharonov-Bohm effect in normal metal
quantum coherence and transport,” Adv. Phys. 35, 1986, pp.375-422.
This paper reports that the measurement of a conductance through an
Au wire or ring at very low temperature (< 1 K) showed a large
conductance fluctuation arising from the electron scattering with disorder
in addition to the average conductance. This also holds in measuring a
current at very low temperature.
[13] A. D. Stone, “Magnetoresistance fluctuations in mesoscopic wires and
rings,” Phys. Rev. Lett. 54, 1985, pp.2692-2695.
[14] P. A. Lee and A. D. Stone, “Universal conductance fluctuations in
metals,” Phys. Rev. Lett. 55, 1985, pp.1622-1625.
[15] G. Bouzerar, D. Poilblanc, and G. Montambaux, “Persistent currents in
one-dimensional disordered rings of interacting electrons,” Phys. Rev. B
49, 1994, pp. 8258-8262.
[16] H. Kato H and D. Yoshioka, “Suppression of persistent currents in
one-dimensional disordered rings by the Coulomb interaction,” Phys.
Rev. B 50, 1994, pp. 4943-4946.
[17] D. Yoshioka and H. Kato, “The effect of the Coulomb interaction on the
mesoscopic persistent current,” Physica B 212, 1995, pp. 251-255. The
Hartree and Fock terms in this paper seemingly give an enhancement
in the current, but actually the Fock term has a different sign from
the Hartree term, so they almost cancel each other in summation, and
eventually the e-e interaction does not contribute to an increase in the
current.
[18] P. M. Th. M. van Attekum, P. H. Woerlee, G. C. Verkade, and A. A. M.
Hoeben, “Influence of grain boundaries and surface Debye temperature
on the electrical resistance of thin gold films,” Phys. Rev. B 29, 1984,
pp. 645-650.
[19] X. Chen, Z. Y. Deng, W. Lu, and S. C. Shen, “Persistent current in
a one-dimensional correlated disordered ring,” Phys. Rev. B 61, 2000,
pp. 2008-2013.
[20] I. Tomita, “Persistent current in a one-dimensional correlated disordered
ring,” Physica A 308, 2002, pp. 1-14.
[21] Y. M. Liu, R. W. Peng, X. Q. Huang, M. Wang, A. Hu, and S. S.
Jiang, “Absence of suppression in the persistent current by delocalization
in random-dimer mesoscopic rings,” J. Phys. Soc. Japan 72, 2003,
pp. 346-351.
[22] P. W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, “New
method for a scaling theory of localization,” Phys. Rev. B 22, 1980,
pp.3519-3526.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:72289", author = "Isao Tomita", title = "Highly Conductive Polycrystalline Metallic Ring in a Magnetic Field", abstract = "Electrical conduction in a quasi-one-dimensional
polycrystalline metallic ring with a long electron phase coherence
length realized at low temperature is investigated. In this situation, the
wave nature of electrons is important in the ring, where the electrical
current I can be induced by a vector potential that arises from a static
magnetic field applied perpendicularly to the ring’s area. It is shown
that if the average grain size of the polycrystalline ring becomes
large (or comparable to the Fermi wavelength), the electrical current
I increases to ~I0, where I0 is a current in a disorder-free ring. The
cause of this increasing effect is examined, and this takes place if the
electron localization length in the polycrystalline potential increases
with increasing grain size, which gives rise to coherent connection
of tails of a localized electron wave function in the ring and thus
provides highly coherent electrical conduction.", keywords = "Electrical Conduction, Electron Phase Coherence,
Polycrystalline Metal, Magnetic Field.", volume = "10", number = "2", pages = "68-5", }
