Skip to main content
SpringerLink
Log in

Resonances in Electronic Transport Through Quantum Wires and Rings

  • Reference work entry
Encyclopedia of Complexity and Systems Science

  • 99 Accesses

Definition of the Subject

Since the 1980s advances in the growth techniques and new electronic materials developed therefrom have provided almost defect-free electronicdevices, which have dimensions in one or more directions on the quantum scale. New quantum regimes governing such systems of lower dimensionality have ledto novel electronic properties with potential applications. Quantum wells, wires, and dots, which have been implemented in the terminology ofcondensed-matter physics, indicate not only different dimensionality but also exhibit dramatically different electronic properties. Particularly, theelectronic transport properties in lower dimensionality have several important features, which have stimulated a great deal of theoretical andexperimental research. In electronic transport studies, if the size of the sample (or device) is smaller than the phase breaking length, the transport isphase coherent. In this case, electrons have a well-defined phase throughout the device, even...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Scattering:

Scattering is a general physical process whereby some forms of radiation, such as light, sound or moving particles, for example, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which it passes. These non-uniformities are, sometimes, known as scatterers or scattering centers. In quantum transport, a scattering center may be provided by an impurity potential.

Transmission probability:

The transmission probability, denoted by T, for a quantum mechanical particle to pass through a scattering potential is the ratio between the flux of particles that emerges from the potential and the flux that arrives at it. Equivalently, T is the fraction of incident particles that succeed in passing through the scattering potential.

Transmission resonance:

Transmission resonance in electronic transport of quantum wires is an abrupt variation of the transmission probability that occurs over a very small interval the incident electron's energy.

Mode:

In a low-dimensional system where the electrons are confined in one or more directions, the energy eigenstates in the confinement direction(s) represent the modes of the system.

Evanescent mode:

When the electrons are free to propagate in one direction but are confined in the other directions, a mode whose energy is greater than the Fermi energy cannot propagate. This is called an evanescent mode.

Conductance quantization:

To measure the conductance of a sample (such as, a constriction) we divide the current through the sample by the electric potential difference between the reservoirs which are connected to the sample. If N c is the number of occupied subbands, the expression for the conductivity pertaining to the two-terminal measurement is \( { G = 2 \text{e}^2 N_c/h } \). According to this description, the conductance is quantized such that it increases in steps by an amount equal to the quantum of conductance \( { 2 \text{e}^2 / h } \) whenever a new subband opens. This can be achieved either by widening of the constriction (and thus by lowering the subband energies) or by increasing the density of electrons (and thus by raising the Fermi energy).

Bibliography

Primary Literature

  1. Adair RK, Bockelman CK, Peterson RE (1949) Experimental corroboration of the theory of neutron resonance scattering. Phys Rev 76:308–308

    ADS  Google Scholar 

  2. Büttiker M (1988) Symmetry of electrical-conduction. IBM J Res Dev 32:317–334

    Google Scholar 

  3. Büttiker M, Imry Y, Azbel MY (1984) Quantum oscillations in one-dimensional normal-metal rings. Phys Rev A 30:1982–1989

    Google Scholar 

  4. Bagwell PF (1990) Evanescent modes and scattering in quasi-one-dimensional wires. Phys Rev B 41:10354–10371

    ADS  Google Scholar 

  5. Banjamin C, Jayannavar AM (2003) Features in evanescent Aharonov–Bohm interferometry. Phys Rev B 68:085325-1–085325-6

    ADS  Google Scholar 

  6. Bardarson JH, Magnusdottir I, Gudmundsdottir G, Tang CS, Manolescu A, Gudmundsson (2004) Coherent electronic transport in a multimode quantum channel with Gaussian-type scatterers. Phys Rev B 70:245308-1–245308-10

    ADS  Google Scholar 

  7. Benjamin C, Jayannavar AM (2001) Current magnification effect in mesoscopic systems at equilibrium. Phys Rev B 64:233406-1–233406-4

    ADS  Google Scholar 

  8. Cerdeira F, Fjeldly TA, Cardona M (1973) Effect of free carriers on zone-center vibrational modes in heavily doped p-type Si. II. Optical modes. Phys Rev B 8:4734–4745

    ADS  Google Scholar 

  9. Clerk AA, Waintal X, Brouwer PW (2001) Fano resonances as a probe of phase coherence in quantum dots. Phys Rev Lett 86:4636–4639

    ADS  Google Scholar 

  10. Deo PS, Moskalets MV (2000) Features of level broadening in a ring-stub system. Phys Rev B 61:10559–10562

    Google Scholar 

  11. Faist J, Capasso F, Sirtori C, West KW, Pfeiffer LN (1997) Controlling the sign of quantum interference by tunneling from quantum wells. Nature 390:589–591

    ADS  Google Scholar 

  12. Fano U (1961) Effects of configuration interaction on intensities and phase shifts. Phys Rev 124:1866–1878

    ADS  MATH  Google Scholar 

  13. Fano U, Cooper JW (1965) Line profiles in the far-uv absorption spectra of the rare gases. Phys Rev 137:A1364–A1379

    ADS  Google Scholar 

  14. Feshbach H (1958) Unified theory of nuclear reactions. Ann Phys 5:357–390

    MathSciNet  ADS  MATH  Google Scholar 

  15. Friedrich H (1990) Theoretical Atomic Physics. Springer, Berlin

    Google Scholar 

  16. Göres J, Goldhaber-Gordon D, Heemeyer S, Kastner MA, Shtrikman H, Mahalu D, Meirav U (2000) Fano resonances in electronic transport through a single-electron transistor. Phys Rev B 62:2188–2194

    Google Scholar 

  17. Jayannavar AM, Deo PS (1994) Persistent currents and conductance of a metal loop connected to electron reservoirs. Phys Rev B 49:13685–13690

    ADS  Google Scholar 

  18. Jayannavar AM, Deo PS (1994) Persistent currents in the presence of a transport current. Phys Rev B 51:10175–10178

    ADS  Google Scholar 

  19. Johnson AC, Marcus CM, Hanson MP, Gossard AC (2004) Coulomb-modified Fano resonance in a one-lead quantum dot. Phys Rev Lett 93:106803-1–106803-4

    ADS  Google Scholar 

  20. Keyser UF, Borck S, Haug RJ, Bichler M, Abstreiter G, Wegscheider W (2002) Aharonov–Bohm oscillations of a tuneable quantum ring. Semicond Sci Technol 17:L22–L24

    ADS  Google Scholar 

  21. Keyser UF, Fühner C, Borck S, Haug RJ, Bichler M, Abstreiter G, Wegscheider W (2003) Kondo effect in a few-electron quantum ring. Phys Rev Lett 90:196601-1–196601-4

    Google Scholar 

  22. Kim CS, Roznova ON, Satanin AM, Stenberg VB (2002) Interference of quantum states in electronic waveguides with impurities. JETP 94:992–1007

    ADS  Google Scholar 

  23. Kim CS, Satanin AM, Joe YS, Cosby RM (1999) Resonant tunneling in a quantum waveguide: Effect of a finite-size attractive impurity. Phys Rev B 60:10962–10970

    ADS  Google Scholar 

  24. Kobayashi K, Aikawa H, Katsumoto S, Iye Y (2002) Tuning of the Fano effect through a quantum dot in an Aharonov–Bohm interferometer. Phys Rev Lett 88:256806-1–256806-4

    ADS  Google Scholar 

  25. Kobayashi K, Aikawa H, Sano A, Katsumoto S, Iye Y (2003) Mesoscopic Fano effect in a quantum dot embedded in an Aharonov–Bohm ring. Phys Rev B 68:235304-1–235304-8

    ADS  Google Scholar 

  26. Kobayashi K, Aikawa H, Sano A, Katsumoto S, Iye Y (2004) Fano resonance in a quantum wire with a side-coupled quantum dot. Phys Rev B 70:035319-1–035319-6

    ADS  Google Scholar 

  27. Landau LD, Lifshitz EM (1965) Quantum Mechanics. Pergamon, New York

    MATH  Google Scholar 

  28. Landauer R (1987) Electrical transport in open and closed systems. Z Phys 68:217–228

    Google Scholar 

  29. Lee M, Bruder C (2006) Spin filter using a semiconductor quantum ring side coupled to a quantum wire. Phys Rev B 73:085315-1–085315-5

    ADS  Google Scholar 

  30. Nöckel JU, Stone AD (1994) Resonance line shapes in quasi-one-dimensional scattering. Phys Rev B 50:17415–17432

    Google Scholar 

  31. Olendski O, Mikhailovska (2003) Fano resonances of a curved waveguide with an embedded quantum dot. Phys Rev B 67:035310-1–035310-13

    MathSciNet  ADS  Google Scholar 

  32. Orellana PA, Pacheco M (2005) Persistent current magnification in a double quantum-ring system. Phys Rev B 71:235330-1–235330-6

    ADS  Google Scholar 

  33. Pareek TP, Deo PS, Jayannavar AM (1995) Effect of impurities on the current magnification in mesoscopic open rings. Phys Rev B 52:14657–14663

    ADS  Google Scholar 

  34. Park W, Hong J (2004) Analysis of coherent current flows in the multiply connected open Aharonov–Bohm rings. Phys Rev B 69:035319-1–035319-7

    ADS  Google Scholar 

  35. Ryu CM, Cho SY (1998) Phase evolution of the transmission coefficient in an Aharonov–Bohm ring with Fano resonance. Phys Rev B 58:3572–3575

    ADS  Google Scholar 

  36. Satanin AM, Joe YS (2005) Fano interference and resonances in open systems. Phys Rev B 71:205417-1–205417-12

    ADS  Google Scholar 

  37. Tekman E, Bagwell PF (1993) Fano resonances in quasi-one-dimensional electron waveguides. Phys Rev B 48:2553–2559

    ADS  Google Scholar 

  38. Tekman E, Ciraci S (1990) Ballistic transport through a quantum point contact: Elastic scattering by impurities. Phys Rev B 42:9098–9103

    ADS  Google Scholar 

  39. Vargiamidis V, Polatoglou HM (2005) Conductance of a quantum wire with a Gaussian impurity potential and variable cross-sectional shape. Phys Rev B 71:075301-1–075301-16

    ADS  Google Scholar 

  40. Vargiamidis V, Polatoglou HM (2005) Resonances in electronic transport through a quantum wire with impurities and variable cross-sectional shape. Phys Rev B 72:195333-1–195333-12

    ADS  Google Scholar 

  41. Vargiamidis V, Polatoglou HM (2006) Fano resonance and persistent current in mesoscopic open rings: Influence of coupling and Aharonov–Bohm flux. Phys Rev B 74:235323-1–235323-14

    ADS  Google Scholar 

  42. Vargiamidis V, Polatoglou HM (2007) Temperature dependence of the Fano effect in quantum wires with short- and finite-range impurities. Phys Rev B 75:153308-1–153308-4

    ADS  Google Scholar 

  43. Voo KK, Chu CS (2005) Fano resonance in transport through a mesoscopic two-lead ring. Phys Rev B 72:165307-1–165307-9

    ADS  Google Scholar 

  44. Wharam DA, Thornton TJ, Newbury R, Pepper M, Ahmed H, Frost JEF, Hasko DG, Peacock DC, Ritchie DA, Jones GAC (1988) One-dimensional transport and the quantization of the ballistic resistance. J Phys C 21:L209–L214

    ADS  Google Scholar 

  45. Wu HC, Guo Y, Chen XY, Gu BL (2003) Giant persistent current in a quantum ring with multiple arms. Phys Rev B 68:125330-1–125330-5

    ADS  Google Scholar 

  46. Wunsch B, Chudnovskiy A (2003) Quasistates and their relation to the Dicke effect in a mesoscopic ring coupled to a reservoir. Phys Rev B 68:245317-1–245317-9

    ADS  Google Scholar 

  47. Xiong YS, Liang XT (2004) Fano resonance and persistent current of a quantum ring. Phys Lett A 330:307–312

    ADS  Google Scholar 

  48. Yi J, Wei JH, Hong J, Lee SI (2001) Giant persistent currents in the open Aharonov–Bohm rings. Phys Rev B 65:033305-1–033305-4

    ADS  Google Scholar 

  49. van Wees BJ, van Houten H, Beenakker CWJ, Williamson JG, Kouwenhoven LP, van der Marel D, Foxon CT (1988) Quantized conductance of point contacts in a two-dimensional electron gas. Phys Rev Lett 60:848–850

    ADS  Google Scholar 

Books and Reviews

  1. Beenakker CWJ, van Houten H (1991) Quantum transport in semiconductor nanostructures. In: Ehrenreich H, Turnbull D (eds) Solid State Physics, vol 44. Academic Press, New York

    Google Scholar 

  2. Datta S (1995) Electronic Transport in Mesoscopic Systems. Cambridge University Press, Cambridge

    Google Scholar 

  3. Economou EN (1983) Green's Functions in Quantum Physics. Springer, Heidelberg

    Google Scholar 

  4. Imry Y (1986) Physics of mesoscopic systems. In: Grinstein G, Mazenko G (eds) Directions in Condensed Matter Physics. World Scientific Press, Singapore

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Aristotle University, Thessaloniki, Greece

    Vassilios Vargiamidis

Authors
  1. Vassilios Vargiamidis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Vargiamidis, V. (2009). Resonances in Electronic Transport Through Quantum Wires and Rings. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_454

Download citation

Publish with us

Policies and ethics

Search

Navigation