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AIP conference proceedings

Current Amplification by Frequency of the Oscillating Flux in an Aharonov-Bohm Device

Dongkwan Shin, Jongbae Hong

Published Jan 1, 2006• 0 citations
Publisher

Abstract

A connected double‐ring with bias threaded by both static and oscillating magnetic fields, which is called an Aharonov‐Bohm device, is proposed as a new type of transistor amplifying a source‐drain current by changing the frequency of the oscillating field threaded by the rings. The scheme of current amplification is given by disturbing perfect interference in the Aharonov‐Bohm ring, under which no current flows, by applying an oscillating magnetic field.

DOI
10.1063/1.2355229

Related papers

Aptly named Aharonov-Bohm effect has classical analogue, long history

Murray Peshkin

I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.

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Ever since Yakir Aharonov and David Bohm pointed out, in 1959, that electrons propagating around a magnetic field through a field-free vacuum should exhibit a quite surprising interference effect, its experimental and theoretical investigation has been contributing to our understanding of the fundamental character of the quantum theory. The recent appearance of this Aharonov–Bohm effect in a rather different context may eventually have a profound effect on our view of the solid state on a “mesoscopic” scale—between the microscopic and the truly macroscopic.

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We theoretically investigate the transmission probability and the persistent current in an open quantum ring threaded by the magnetic flux. From the numerical results, we find that the two observable quantities both show a periodic characteristic with the increase of the magnetic flux, and they strongly depend on the dimensionless wave vector and the central angle as well as the magnetic flux.

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Technical Physics Letters•Mar 1, 1997•1 citation
A connected double‐ring with bias threaded by both static and oscillating magnetic fields, which is called an Aharonov‐Bohm device, is proposed as a new type of transistor amplifying a source‐drain current by changing the frequency of the oscillating field threaded by the rings. The scheme of current amplification is given by disturbing perfect interference in the Aharonov‐Bohm ring, under which no current flows, by applying an oscillating magnetic field.
I am an author of the 1961 paper that first called the Aharonov-Bohm effect by that name. 1 1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). The term has since appeared in more than 1000 published papers. However, it has been suggested a few times, most recently by Peter Sturrock and Timothy Groves, that the name does not do justice to Werner Ehrenberg and Raymond Siday, who found in 1949 that the motion of electrons can be influenced by magnetic fields confined to regions that the electrons do not enter. 2 2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). I argue that the name Aharonov-Bohm effect is appropriate, although for a reason that I did not fully appreciate in 1961.The 1959 Aharonov-Bohm paper profoundly changed the way we think about electromagnetic fields in quantum mechanics. 3 3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). The gauge-invariant part of the vector potential was promoted to a real physical field, not just a convenient device for summarizing certain information about the electric and magnetic fields. In the words of C. N. Yang, “The electromagnetic field strength fµv in quantum mechanics underdescribes electromagnetism, as the Bohm-Aharonov effect demonstrates … information about the phase factor exp[ie∮(A⋅dx)/ℏc] for all closed loops correctly describes electromagnetism.” 4 4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5.See also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). A century earlier, James Clerk Maxwell changed the way we think about action at a distance by identifying what we now call the Maxwell fields as real physical things that contain energy and momentum and that enable microscopic conservation laws; they are not just mathematical functions that summarize the necessary information about the past motions of charges. Later those physical fields had to be quantized. Yakir Aharonov and David Bohm found that in quantum mechanics the Maxwell fields in a multiply connected region do not contain all the physics; the vector potential must also be endowed with reality to make sense of the subtler interactions in quantum mechanics. Neither Aharonov and Bohm nor Ehrenberg and Siday were the first to observe that magnetic fields in places where a charged particle’s wave function vanishes may influence the motion of that particle. 5 5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) F. London, Nature 140, 793 (1937). Paul Dirac, in his 1931 paper on magnetic monopoles, noted that the electron’s wavefunction must vanish on singular flux lines but said nothing about that raising any question of nonlocality. Fritz London pointed out in the 1930s that the motion of electrons in a superconducting ring depends on an external magnetic flux through the hole in the ring, where the electrons cannot go. He wrote in his 1937 paper, “The most stable state of a ring has no current, unless an external magnetic field is applied.” Like Dirac, he said nothing about a nonlocal action of the magnetic field being surprising or unusual. Of course, London, like Dirac, was focusing on something else.Ehrenberg and Siday were also focusing on something else—electron optics—when they found in 1949 that the motion of an electron can depend on the magnetic field in a region from which the electron is excluded. They chose not to mention that curious phenomenon in the abstract of their paper, although they did explicitly say elsewhere that it was “curious.”None of those earlier authors went on to conclude that such a phenomenon implies that the vector potential has to be seen as a real physical field in quantum mechanics. Only Aharonov and Bohm did that.REFERENCESSection:ChooseTop of pageREFERENCES <<1. M. Peshkin, I. Talmi, L. J. Tassie, Ann. Phys. 12, 426 (1961). Google ScholarCrossref, ISI2. W. Ehrenberg, R. E. Siday, Proc. Phys. Soc. B 62, 8 (1949). Google ScholarCrossref3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959). Google ScholarCrossref, ISI4. C. N. Yang, in Proceedings of the International Symposium on Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1983, S. Kamefuchi et al. , eds., Physical Society of Japan, Tokyo (1984), p. 5. Google ScholarSee also T. T. Wu, C. N. Yang, Phys. Rev. D 12, 3845 (1975). Google ScholarCrossref, ISI5. P. A. M. Dirac, Proc. R. Soc. London A 133, 60 (1931) Google ScholarCrossref F. London, Nature 140, 793 (1937). , Google ScholarCrossref© 2010 American Institute of Physics.
Ever since Yakir Aharonov and David Bohm pointed out, in 1959, that electrons propagating around a magnetic field through a field-free vacuum should exhibit a quite surprising interference effect, its experimental and theoretical investigation has been contributing to our understanding of the fundamental character of the quantum theory. The recent appearance of this Aharonov–Bohm effect in a rather different context may eventually have a profound effect on our view of the solid state on a “mesoscopic” scale—between the microscopic and the truly macroscopic.