Universität Karlsruhe

Institut für Theoretische Festkörperphysik

Electron transport in hybrid nanostructures

Matthias Eschrig, Roland Grein, Georgo Metalidis, Andreas Poenicke, Gerd Schön

Following the progress in fabricating hybrid nanostructures, phase-coherent quasiparticle transport in such systems has attracted considerable theoretical and experimental interest over the past decade. In the associated search for novel devices, particularly promising systems are those involving superconducting materials. By now, the important physics related to heterostructures composed of superconductors and normal metals is well understood [1]. The low-energy (below the superconducting energy gap) quasiparticle transport through a normal metal / superconductor interface can be described in terms of the so-called Andreev reflection process, where an incident electron from the normal metal is phase-coherently reflected back as a hole, transmitting a Cooper pair into the superconductor. A very important feature of this process is that (assuming that the superconductor has a singlet order parameter) the incident electron and the reflected hole occupy different spin bands in the normal metal.

In the past few years, much attention in mesoscopic physics has focussed towards spin-dependent transport phenomena. Accordingly, heterostructures containing ferromagnetic materials as well as superconductors are under active investigation. The spin splitting in the ferromagnet requires modifications to the conventional Andreev-reflection picture. In fact, the process becomes limited by the density of states for the minority spin and, in the context of newly discovered half-metallic (completely polarized) ferromagnets, completely prohibited. On the other hand, new phenomena are expected to arise due to the spin-active nature of the interfaces separating nonmagnetic and magnetic materials [2-5]. Therefore, the rich physics connected with superconductor / ferromagnet interfaces is still a subject of investigation [14-16,20-22].

Quasiclassical theory of superconductivity provides an effective tool of studying superconducting heterostructures [1]. Within this theory, the properties of the interfaces separating different materials appear as effective boundary conditions. Typically these conditions are formulated in terms of a scattering matrix which connects outgoing and incoming waves. However, the resulting boundary conditions for the quasiclassical Green's functions in this approach adopt a fairly inconvenient form, especially in spin-dependent situations. Therefore, we have formulated the necessary conditions in a different but physically equivalent form in terms of a many-body t-matrix [2,6]. This approach can be used to describe both ballistic and diffusive transport through an interface of arbitrary transparency and exhibiting scattering with arbitrary spin dependence, and is valid both in nonequilibrium and equilibrium situations and also in connection with unconventional superconductors [7,8]. In particular, it enables the study of heterostructures involving half-metallic materials [2,10,15].

Using selection rules imposed by the Pauli principle, we classify pairing correlations near interfaces between superconductors and ferromagnets according to their symmetry properties with respect to spin, momentum, and energy [10,15]. We observe that inhomogeneities always leads to mixing of even- and odd-energy pairing components. Spin-active scattering in the interface region induces all of the possible symmetry components. In particular, the long-range equal-spin pairing correlations have odd-frequency s-wave and even-frequency p-wave components of comparable magnitudes.

We analyze the effect of electron-electron interactions on Andreev current and shot noise in diffusive hybrid structures composed of a normal metal attached to a superconductor via a weakly transmitting interface. We demonstrate that at voltages/temperatures below the Thouless energy of a normal metal the Coulomb interaction yields a reduction of both Andreev current and its noise by a constant factor which essentially depends on the system dimensionality. For quasi-1d structures this factor depends on the number of conducting channels and dimensionless conductance of a normal metal. At voltages above the Thouless energy the interaction correction to Andreev current and shot noise acquires an additional voltage dependence which turns out to be a power-law in the quasi-1d limit.[12]

We study the possibility of using a hybrid nanostructure as an entangler, i.e., a device which serves as a source of non-locally entangled states. These states may be useful for quantum communications tasks in a future solid-state based quantum computer. In particular, we propose the use of an angular filter in normal-superconducting structures to generate divergent beams of nonlocally spin-entangled electrons. When the normal etal is a ballistic two-dimensional electron gas, the proposed scheme guarantees arbitrarily large spatial separation of the entangled electron beams emitted from a finite interface [13].
Self-consistently calculated order parameter profiles in a superconductor / half metal / superconductor heterostructure [1].
Yellow: singlet order parameter, red, blue & green: induced triplet correlations.
We predict an indirect Josephson effect, mediated by the (blue) equal-spin triplet pairing component.

Some selected publications
  1. Quasiclassical Green's Function Approach to Mesoscopic Superconductivity
    W. Belzig, F.K. Wilhelm, C. Bruder, G. Schön, and A.D. Zaikin
    Superlattices and Microstructures 25, 1251-1288 (1999).

  2. Theory of Half-Metal/Superconductor Heterostructures
    M. Eschrig, J. Kopu, J.C. Cuevas, and G. Schön
    Phys. Rev. Lett. 90, 137003 (2003).

  3. Interplay of magnetic and superconducting proximity effects in FSF trilayers
    T. Löfwander, T. Champel, J. Durst, and M. Eschrig
    Phys. Rev. Lett. 95, 187003 (2005)

  4. Switching superconductivity in S/F bilayers by multiple-domain structures
    T. Champel and M. Eschrig
    Phys. Rev. B 71, 220506(R) (2005)

  5. Effect of an inhomogeneous exchange field on the proximity effect in disordered superconductor-ferromagnet hybrid structures
    T. Champel and M. Eschrig
    Phys. Rev. B 72, 054523 (2005)

  6. Quasiclassical description of transport through superconducting contacts
    J.C. Cuevas and M. Fogelström
    Phys. Rev. B 64, 104502 (2001).

  7. Subharmonic gap structure in d-wave superconductors
    A. Poenicke, J.C. Cuevas, M. Fogelström
    Phys. Rev. B 65, 220510(R) (2002).

  8. Shot noise and multiple Andreev reflections in d-wave superconductors
    J.C. Cuevas and M. Fogelström
    Phys. Rev. Lett. 89, 227003 (2002).

  9. Observation of Periodic pi-Phase Shifts in Ferromagnet-Superconductor Multilayers
    V. Shelukhin, A. Tsukernik, M. Karpovski, Y. Blum, K.B. Efetov, A.F. Volkov,
    T. Champel, M. Eschrig, T. Löfwander, G. Schön, and A. Palevski
    Phys. Rev. B. 73, 174506 (2006)

  10. Symmetries of Pairing Correlations in Superconductor-Ferromagnet Nanostructures
    M. Eschrig, T. Löfwander, T. Champel, J.C. Cuevas, J. Kopu, and G. Schön
    J. Low Temp. Phys. 147, 457 (2007).

  11. Proximity effect and multiple Andreev reflections in diffusive SNS junctions
    J.C. Cuevas, J. Hammer, J. Kopu, J.K. Viljas, and M. Eschrig
    Phys. Rev. B 73, 184505 (2006)

  12. Coulomb effects on electron transport and shot noise in hybrid normal-metal--superconducting metallic structures
    A,V. Galaktionov and A.D. Zaikin
    Phys. Rev. B 73, 184522 (2006)

  13. Divergent beams of nonlocally entangled electrons emitted from hybrid normal-superconducting structures
    E. Prada and F. Sols
    New. J. Phys. 7, 231 (2005).

  14. Phase Diagrams of Ferromagnet-Superconductor Multilayers with Misaligned Exchange Fields
    T. Löfwander, T. Champel, and M. Eschrig
    Phys. Rev. B 75, 014512 (2007)
    also in Virtual Journal of Applications of Superconductivity, Vol. 12, Issue 2 (2007).

  15. Triplet Supercurrents in clean and disordered half-metallic ferromagnets
    M. Eschrig and T. Löfwander
    Nature Physics 4, 138-143 (2008)

  16. 0-pi transitions in a superconductor/chiral ferromagnet/superconductor junction
    induced by a homogeneous cycloidal spiral

    T. Champel, T. Löfwander, and M. Eschrig
    Phys. Rev. Lett. 100, 077003 (2008)
    also in Virtual Journal of Applications of Superconductivity, Vol. 14, Issue 5 (2008),
    also in Virtual Journal of Nanoscale Science & Technology, Vol. 17, Issue 9 (2008)

  17. Surface bound states and spin currents in non-centrosymmetric superconductors
    A.B. Vorontsov, I. Vekhter, and M. Eschrig
    Phys. Rev. Lett. 101, 127003 (2008)

  18. Surface states in superconductors with no inversion symmetry
    A. B. Vorontsov, I. Vekhter, and M. Eschrig
    J. Phys. Soc. Jpn. 77, Suppl. A, 165-171 (2008)

  19. Andreev bound states in non-centrosymmetric superconductors
    A. Vorontsov, I. Vekhter, and M. Eschrig
    Physica B 403, 1095 (2008)
    Proceedings for SCES conference in Houston 2007.

  20. Pairing Symmetry Conversion by Spin-Active Interfaces in Magnetic Normal-Metal-Superconductor Junctions
    J. Linder, T. Yokoyama, A. Sudbo, and M. Eschrig
    Phys. Rev. Lett. 102, 107008 (2009)

  21. Coherent conductors at a distance
    M. Eschrig
    Nature Physics (News and Views) 5, (2009)

  22. Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets
    R. Grein, M. Eschrig, G. Metalidis, and Gerd Schön
    accepted for publication in Phys. Rev. Lett.
    arXiv:0904.0149 [cond-mat.supr-con]

Relevant grants

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