Universität Karlsruhe

Institut für Theoretische Festkörperphysik

Single-electron tunneling

Jasmin Aghassi, Dmitri Golubev, Matthias Hettler, Stefan Legel, Michael Marthaler, Anna Posazhennikova, Elsa Prada, Pablo San-Jose, Gerd Schön, Andrei Zaikin
(former group members: J. König, H. Schoeller, A. Thielmann, Y. Utsumi)
Electron transport through nanostructures is strongly affected by Coulomb interaction among the electrons. Model systems which define a convenient framework for studying electron-electron interaction in nanostructures are the so-called single-electron box and the single-electron transistor. In these devices, a small metallic island or semiconductor quantum dot is coupled via tunnel contacts to one or several electrodes. Once the energy scale for the charging energy, associated with adding one electron to the island or quantum dot, exceeds temperature and transport voltage, charging effects such as Coulomb blockade appear [1]. Substantial progress in nano-fabrication technology has been achieved in the last few years, which made it possible to fabricate in a controlled way single-electron devices based on metallic tunnel junctions, lateral and vertical semiconductor quantum dots, and even molecular systems.

The regime of weak tunnel coupling between island or quantum dot and lead electrodes is well described by the so-called ``orthodox theory'' of sequential tunneling. With increasing dot-lead tunnel coupling, however, quantum fluctuations become more and more important. This holds for both the linear-response regime and for nonequilibrium physics evoked by a finite transport voltage applied. For a systematic classification and evaluation of different contributions to the transport current, we developed a diagrammatic approach, which is based a real-time analysis of the time evolution of the reduced density matrix [2,3]. Furthermore, we set up a real-time renormalization-group scheme, and employed numerical methods such as quantum Monte Carlo. In our group, we investigate the following subjects:

Quantum dots which are strongly coupled to the lead electrodes exhibit Kondo physics. The latter shows up in the nonlinear current-voltage characteristics as zero-bias anomalies, which is split in the presence of an external magnetic field [4]. Metallic single-electron transistors are related to a different type of Kondo model (multi-channel Kondo). We described these Kondo correlations by the use of a systematic second-order perturbation scheme ("cotunneling") at resonance [5]. Furthermore, we analyzed renormalization effects in metallic single-electron boxes with strong tunnel coupling [6].

The ground state of the dot depends on the spin on the dot and the number of channels in the lead electrodes. For example, when the dot spin is equal to 1, and the leads are one-channel, such a quantum dot can exhibit an interesting non-Fermi liquid behavior at low temperatures, characterized by a singular conductance behavior [7]. The large spin of the dot can be described within Schwinger-boson formalism, and the zero-bias anomaly is analyzed in the large-N approach. The non-Fermi liquid behavior is reproduced analytically both in linear response regime and for finite voltage [7]. On the other hand, when the number of channels of the spin-1 quantum dot is equal to two, due to the channel interference, the conductance is suppressed at zero temperature (manuscript in preparation).

We study charge transport through a chain of quantum dots. The dots are fully coherent among each other and weakly coupled to metallic electrodes via the dots at the interface, thus modelling a molecular wire. If the non-local Coulomb interactions dominate over the inter-dot hopping we find strongly enhanced shot noise above the sequential tunneling threshold. The current is not enhanced in the region of enhanced noise, thus rendering the noise super-Poissonian. In contrast to earlier work this is achieved even in a fully symmetric system. The origin of this novel behavior lies in a competition of "slow" and "fast" transport channels that are formed due to the differing non-local wave functions and total spin of the states participating in transport. This strong enhancement may allow direct experimental detection of shot noise in a chain of lateral quantum dots[8-11].

In order to fully characterize the noise associated with electron transport, with its severe consequences for solid-state quantum information systems, the theory of full counting statistics has been developed. It accounts for correlation effects associated with the statistics and effects of entanglement, but it remains a non-trivial task to account for interaction effects. We evaluate the current distribution for a single-electron transistor with intermediate strength tunnel conductance. Nonequilibrium effects induce a lifetime broadening of the charge-state levels, which suppress large current fluctuations [12,13].

Information about the coherence of transport through quantum dots can be gained from interference measurements in Aharonov-Bohm rings with one or two quantum dots imbedded. We identified coherent transport contributions for weak coupling and in the cotunneling regime, and studied the interplay of Kondo physics and the Fano effect for strong tunnel coupling, as well as low-temperature transport features in double-dot interferometers.

example of a diagram describing the time evolution of the reduced density matrix of a quantum dot

Some selected publications
  1. Quantum Transport and Dissipation
    T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger
    ISBN 3-527-29261-6, Wiley-VCH Verlag (1998)
    Chapter 3: Single-Electron Tunneling (G. Schön), p. 149-212.

  2. Transport Theory of Interacting Quantum Dots
    H. Schoeller
    Habilitationsschrift, Fakultät für Physik, Universität Karlsruhe (1997).

  3. Quantum Fluctuations in the Single-Electron Transistor
    J. König
    ISBN 3-8265-4696-2, Shaker Verlag (1999).

  4. Zero-bias Anomalies and Boson-Assisted Tunneling through Quantum Dots
    J. König, H. Schoeller, and G. Schön
    Phys. Rev. Lett. 76, 1715-1718 (1996).

  5. Cotunneling at Resonance for the Single-Electron Transistor
    J. König, H. Schoeller, and G. Schön
    Phys. Rev. Lett. 78, 4482-4485 (1997).

  6. Strong Charge Fluctuations in the Single-Electron Box: A Quantum Monte Carlo Analysis
    C.P. Herrero, G. Schön, and A.D. Zaikin
    Phys. Rev. B 59, 5728-5737 (1999).

  7. Anomalous conductance of a spin-1 quantum dot
    A. Posazhennikova and P. Coleman
    Phys. Rev. Lett. 94, 036802 (2005)

  8. Co-tunneling current and shot noise in quantum dots
    A. Thielmann, M.H. Hettler, J. König, and G. Schön
    Phys. Rev. Lett. 95, 146806 (2005)

  9. Super-Poissonian noise, negative differential conductance, and relaxation effects in transport through molecules, quantum dots and nanotubes
    A. Thielmann, M. H. Hettler, J. König, and G. Schön
    Phys. Rev. B 71, 045341 (2005)

  10. Strongly enhanced shot noise in chains of quantum dots
    J. Aghassi, A. Thielmann, M. H. Hettler, and G. Schön
    Appl. Phys. Lett. 89, 052101 (2006)

  11. Shot noise in transport through two coherent strongly coupled quantum dots
    J. Aghassi, A. Thielmann, M.H. Hettler, and G. Schön
    Phys. Rev. B 73, 195323 (2006)

  12. Full counting statistics of interacting electrons
    D.A. Bagrets, Y. Utsumi, D.S. Golubev, and G. Schön
    Fortschritte der Physik 54, 917-938 (2006).

  13. Full counting statistics for a single-electron transistor, non-equilibrium effects at intermediate conductance
    Y. Utsumi, D.S. Golubev, and G. Schön
    Phys. Rev. Lett. 96 , 086803 (2006)

Relevant grants and some links

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