Charge and spin transfer statistics in complex nanostructures

• Applicant: Privatdozent Dr. Andreas Komnik
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2009 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 159037256

• Final Report Year: 2012

Final Report Abstract

Due to the rapid progress of microelectronic technology manufacturing of such nanometresized electronic circuitry elements as single-electron quantum dots has become a routine. While the conductance properties of such objects are by now quite well understood, arranging them in more complex geometries has a potential to generate circuits with interesting and potentially very useful properties. Aiming at practical applications it is not only necessary to know the non-linear transport properties of such devices but also to possess detailed information about their noise spectra and, what is even more important, about their charge transfer statistics properties in general. For these reasons the goal of the project was the computation and analysis of the full counting statistics of non-trivial arrangements of several quantum dots in different geometries. One of the simplest representatives of such structures is the double quantum dot in parallel geometry. It turns out that, contrary to the single dot device, such structure possesses a rather wide window of parameters in which one observes a perfect transmission suppression – an antiresonance. Within the project the robustness of this antiresonance with respect to electronic correlations of different strength has been analyzed in full detail. It turns out that the antiresonance is still perfect even for finite interactions in the case the quantum dot is modelled by Anderson impurities but narrows with growing correlations. Qualitatively the same behaviour is observed in the case both quantum dots are in the Kondo state. While in the first realization of the structure perturbative expansion in interaction strength along with effective self-energies were employed, for the Kondo dots an exact analytical solution has been found, which is valid for one (highly non-trivial) point in the parameter space. In the next step the cumulant generating functions of the charge transfer statistics were calculated. While in the double dot realized by Anderson impurities the dominant transport process is always a single-electron process in the case of Kondo double dot both single-electron and electron-pair process contribute equally to the transport. The knowledge of the FCS enabled a calculation and analysis of not only noise but also higher order cumulants of the particle transfer statistics and to make a number of predictions for their qualitative as well as quantitative behaviour in different regimes. As a possible application of the above systems we propose a spin-filtering device which allows for very effective generation or detection of spin-polarized electric currents. It is possible to build such device on the basis of both Anderson impurity as well as Kondo dot based double quantum dot nanostructures.

Publications

• “Spin-polarized current generation and detection by a double quantum dot structure”, Phys. Rev. B 81, 2010, 075110
  J.P.Dahlhaus, S.Maier and A.Komnik
  
• “Transport properties of a molecular quantum dot coupled to one-dimensional correlated electrons”, Phys. Rev. B 82, 2010, 165116
  S.Maier und A.Komnik
  
• Effect of electron-phonon interaction in nanostructures and ultracold quantum gases, Dissertation, Ruprecht-Karls-Universität Heidelberg, 2011
  S.Maier
  
• “Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data”, Phys. Rev. B 83, 2011, 075107
  L.Mühlbacher, D.F.Urban and A.Komnik
  
• “Charge transfer statistics and entanglement in normal-quantum dot-superconductor hybrid structures”, Eur. Phys. J. D 63, 2011, 3
  H.Soller und A.Komnik
  
• “Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction”, Phys. Rev. B 83, 2011, 085401
  S.Maier, T.L.Schmidt and A.Komnik
  
• “Hamiltonian approach to the charge transfer statistics of Kondo quantum dots contacted by a normal metal and a superconductor”, Physica E 44, 2011, 425
  H.Soller and A.Komnik
  
• “Nonequilibrium transport properties of a double quantum dot in the Kondo regime”, Phys. Rev. B 84, 2011, 155305
  D.Breyel and A.Komnik
  
• “Quantum Fluctuation Theorem in an Interacting Setup: Point Contacts in Fractional Quantum Hall Edge State Devices”, Phys. Rev. Lett. 107, 2011, 100601
  A.Komnik und H.Saleur