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@PHDTHESIS{GonzlezRosado:1025502,
      author       = {González Rosado, Lucía and Hassler, Fabian and Catelani,
                      Gianluigi},
      title        = {{E}lectron-hole diffusion in disordered superconductors},
      school       = {RWTH Aachen},
      type         = {Dissertation},
      publisher    = {RWTH Aachen University},
      reportid     = {FZJ-2024-02903},
      pages        = {pages 1 Online-Ressource : Illustrationen},
      year         = {2021},
      note         = {Dissertation, RWTH Aachen, 2021},
      abstract     = {In a superconductor, the excitations at energies above the
                      gap can be understood as a superposition of electrons and
                      holes. In this work, we study their diffusive behavior in
                      disordered superconductors in an electron-hole basis. That
                      is, we treat electron and hole diffusion as well as
                      electron-hole conversion processes. We refer to this concept
                      as electron-hole diffusion. We develop a formalism based on
                      semiclassical Green's functions in Nambu space that allows
                      us to treat disorder in superconductors, and use said
                      formalism to study diffusive propagation in conventional
                      superconductors. We focus on different properties that
                      relate to electron-hole diffusion in order to understand
                      more in depth the properties of disordered conventional
                      superconductors and their possible applications. We show
                      that the speed of propagation in disordered superconductors
                      is given by the energy dependent group velocity
                      $v_g=v_F\sqrt{E^2-\Delta^2}/E$ and determine that the
                      conditions for the diffusive regime to take place in the
                      superconducting state differ from those in metals. In
                      superconductors there exist two energy scales that determine
                      the onset of the diffusive regime. The first energy scale is
                      given, similar to the normal metal case, by the inverse of
                      the scattering time. The second energy scale does not depend
                      on disorder strength, but instead on the energy carried by
                      the diffusing particle and the strength of the
                      superconducting gap. Two regimes can be defined depending on
                      which energy scale dominates, and a novel energy scale
                      $\varepsilon_*$, that separates these two regimes, emerges.
                      We later study thermal conductivity in superconductors,
                      putting special emphasis in the particular behavior of the
                      weak localization correction. We show that the behavior of
                      the weak localization is temperature dependent. This
                      dependence varies in the two energy regimes defined by
                      $\varepsilon_*$. We discuss its behavior in the different
                      regimes, and highlight the case of a dirty superconductor
                      ($\tau_e \Delta \ll 1$), where we theorize that the novel
                      energy scale $\varepsilon_*$, given in this case by
                      $\varepsilon_*=\sqrt{\Delta/\tau_e}$, could be
                      experimentally measured. We discuss as well the use of
                      disordered superconductors in the field of quantum
                      computation. We build on a proposal where a disordered
                      superconductor is used as a way to extend the exchange
                      interaction between solid-state spin qubits. In the setup,
                      the exchange interaction is possible via virtual propagation
                      through the superconductor at energies below the
                      superconducting gap. We discuss the viability of the setup
                      under different experimental conditions. We show that the
                      effects of external magnetic fields or spin-orbit (SO)
                      coupling in the superconductor decrease the coupling range.
                      We also highlight however the role of the geometry of the
                      superconductor, which has a very strong impact on the
                      coupling range with gains of over an order of magnitude from
                      a 2D film to a quasi-1D strip. We estimate that for
                      superconductors with weak SO coupling (e.g., aluminum),
                      exchange rates of up to $100\,$MHz in the presence of
                      external magnetic fields of up to $100$mT could be achieved
                      over distances of over $1\mu\text{m}$.Finally, we study the
                      density of states anomaly in disordered conventional
                      superconductors. We focus on the two-dimensional case. For
                      energies larger than the superconducting gap we obtain a
                      logarithmic correction in $\tau_e E$ with the leading order
                      correction due to superconductivity proportional to
                      $\Delta^2/E^2$. For energies close to the gap, the behavior
                      of the DOS anomaly is divergent. However, as opposed to the
                      logarithmic divergence encountered in the normal metal state
                      when approaching the Fermi energy, in the superconducting
                      case this divergence is stronger and proportional to
                      $\sqrt{\Delta/(E-\Delta)}$. This divergence shows as a
                      decrease of the superconducting density of states peak as
                      disorder increases.},
      keywords     = {superconductivity ; diffusion ; thermal conductivity ;
                      quantum computation ; spin qubits ; exchange interaction ;
                      transport (Other)},
      cin          = {PGI-11},
      cid          = {I:(DE-Juel1)PGI-11-20170113},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2021-11036},
      url          = {https://juser.fz-juelich.de/record/1025502},
}