Current, Noise and Full Counting Statistics in Superconducting Junctions

• Applicant: Professor Dr. Wolfgang Belzig
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2011 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 191125331

• Final Report Year: 2015

Final Report Abstract

Josephson junctions are electronic elements made by connecting two superconductors through a different nanoscale-sized material. The current flow through such junctions has very peculiar properties, which cannot be found in any other element. First, in thermodynamic equilibrium a current can flow, which depends on the quantum mechanical phase difference between the superconductors. Hence it is an extremely sensitive probe of quantum phenomena such as interference, which is used as the highest sensistive magnetometer, or decoherence, viz. the loss of the phase information due to the influence of an external environment. Second the current-voltage characteristic is highly non-linear. This holds both in the static case, where it can be used for high-resolution spectroscopy, as well as in the dynamic case displaying e.g. characteristics of a nonlinear inductor. In this project we have investigated microscopic as well as stochastic models of such Josephson junctions and calculated their performance parameters relevant for the experimental verification of our predictions. A Josephson junction containing a material with a non-trivial topological band structure can host exotic particles know as Majorana fermions - having no charge and now spin, yet they are real particles. We have proposed a setup which allows to detect the Majorana fermions unambiguously via a cleverly devised electronic circuit through a combined measurement of conductance and current-noise correlations. Such a smoking-gun experiment is worldwide searched for and our proposal could by decisive to detect Majorana particle for the first time. As part of the miniaturization of information storage devices nanoscopic magnetic element play a major role. It is therefore natural to investigate their coupling to superconducting junction and try to determine their potential for spintronics like spin current detection and creation. We have shown that such a junctions can serve as a transducer from external magnetic field to a controllable spin supercurrent. Tayloring the transport by adding a quantum resonance tunable by a gate voltage gives additional functionality such as a free choice of the spin-polarization of the current. Because many real system are far from ideal, basic research has to address the fundamental problem of disorder and its effect on physical properties. Disordered Josephson contacts are some of the best studied systems, since they are at the same time probes of the fundamental quantum mechanical wave nature of electrons. Accordingly it came as big surprise that we discovered a novel spectral gap feature in chaotic Josephson junction which was overlooked in over 40 years of research. The phase-dependent properties of this so-called ’smile’-gap differ from previous studied cases and hence open a new problem field in the theory of disordered systems. For many practical applications the switching behavior of superconducting junctions between the supercurrent and the dissipative state are of fundamental importance. However, even in the regime of classical dissipation, the switching charactierstics were hitherto only poorly understood quantitively. Together with our Czech collaboration partners we have developed an efficient numerical approach to predict the experimentally observed switching. At the same time we could identify - and correct - problems in previously used fitting procedures. Hence, now a theoretically sound modelling with an unprecedented accuracy is possible for this technologically extremely relevant electronic devices. One of the project's publications has been selected as Editor’s Choice and is especially highlighted in Physical Review B.

Publications

• Voltage noise, switching rates, and multiple phase-slips in moderately damped Josephson junctions
  Martin Žonda, Wolfgang Belzig, and Tomáš Novotný
  
• Interferometric and noise signatures of Majorana fermion edge states in transport experiments. Phys. Rev. Lett. 107, 136403 (2011)
  Grègory Strübi, Wolfgang Belzig, Mahn-Soo Choi, and Christoph Bruder
  
• Spin-precession-assisted supercurrent in a superconducting quantum point contact coupled to a single-molecule magnet. Phys. Rev. B 86, 054519 (2012)
  Cecilia Holmqvist, Wolfgang Belzig and Mikhael Foglström
  
• Josephson current through a quantum dot coupled to a molecular magnet Phys. Rev. B 88, 104512 (2013)
  Pascal Stadler, Cecilia Holmqvist, and Wolfgang Belzig
  
• Secondary ”Smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types. Phys. Rev. B 90, 014521 (2014)
  Johannes Reutlinger, Leonid Glazman, Yuli V. Nazarov, and Wolfgang Belzig
  
• ”Smile”-gap in the density of states of a cavity between superconductors. Phys. Rev. Lett. 112, 067001 (2014)
  Johannes Reutlinger, Leonid Glazman, Yuli V. Nazarov, and Wolfgang Belzig