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@ARTICLE{Kruti:1030127,
      author       = {Kruti, Daniel and Riwar, Roman-Pascal},
      title        = {{I}mpact of evanescent scattering modes and finite
                      dispersion in superconducting junctions},
      publisher    = {arXiv},
      reportid     = {FZJ-2024-05233},
      year         = {2024},
      abstract     = {Superconducting junctions are essential building blocks for
                      quantum hardware, and their fundamental behavior remains a
                      highly active research field. The behaviour of generic
                      junctions is conveniently described by Beenakker's
                      determinant formula, linking the subgap energy spectrum to
                      the scattering matrix characterizing the junction. In
                      particular, the gap closing between bound and continuum
                      states in short junctions follows from unitarity of the
                      scattering matrix, and thus, from probability conservation.
                      In this work, we critically reassess two assumptions: that
                      scattering in short junctions is approximately
                      energy-independent and dominated by planar channels. We
                      argue that strongly energy-dependent scattering follows from
                      finite dispersion of the conductor electrons even when they
                      spend little time within the scattering region, and show
                      that evanescent modes play a central role when cross-channel
                      scattering is important. By generalizing Beenakker's
                      equation and performing a mapping to an effective
                      Hamiltonian, we show that the gap closing is linked to a
                      chiral symmetry. While finite energy-dependence in the
                      scattering breaks the chiral symmetry, we show two distinct
                      mechanisms preserving the gap closing, each connected to new
                      types of constraints on energy-dependent scattering matrices
                      beyond unitarity. If the dispersive mode is planar, the gap
                      closing is still preserved through a time-dependent
                      probability conservation analysis of the scattering process.
                      If the dispersive channel is evanescent, we derive a
                      constraint which, notably, cannot follow from probability
                      conservation. We thus demonstrate that Andreev physics
                      reveal a much wider variety of properties of normal metal
                      scattering than commonly expected. We expect that our
                      findings will have an impact on the dissipative behavior of
                      driven junctions, and offer a new perspective on fundamental
                      properties of scattering matrices.},
      keywords     = {Mesoscale and Nanoscale Physics (cond-mat.mes-hall) (Other)
                      / Other Condensed Matter (cond-mat.other) (Other) /
                      Superconductivity (cond-mat.supr-con) (Other) / FOS:
                      Physical sciences (Other)},
      cin          = {PGI-2},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {5221 - Advanced Solid-State Qubits and Qubit Systems
                      (POF4-522)},
      pid          = {G:(DE-HGF)POF4-5221},
      typ          = {PUB:(DE-HGF)25},
      doi          = {10.48550/ARXIV.2408.07035},
      url          = {https://juser.fz-juelich.de/record/1030127},
}