Nonuniform superconductivity in wires with strong spin-orbit coupling
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Nonuniform superconductivity in wires with strong spin-orbit coupling Julie Baumard 1,2 , J´erˆ ome Cayssol 1,a , and Alexandre Buzdin 1 1 2
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France Donostia International Physics Center (DIPC), Manuel de Lardizabal 5, 20018 San Sebasti´ an, Spain Received 25 May 2020 / Received in final form 26 May 2020 Published online 13 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We study theoretically the onset of nonuniform superconductivity in a one-dimensional single wire in presence of Zeeman (or exchange field) and spin-orbit coupling. Using the Green’s function formalism, we show that the spin-orbit coupling stabilizes modulated superconductivity in a broad range of temperatures and Zeeman fields. We investigate the anisotropy of the temperature-Zeeman field phase diagram, which is related to the orientation of the Zeeman field. In particular, the inhomogeneous superconducting state disappears if this latter field is aligned or perpendicular to the wire direction. We identify two regimes corresponding to weak and strong spin-orbit coupling respectively. The wave-vector of the modulated phase is evaluated in both regimes. The results also pertain for quasi-1D superconductors made of weakly coupled 1D chains.
1 Introduction Superconducting systems in the presence of Zeeman field and spin-orbit coupling (SOC) exhibit striking spectral and transport properties including modifications in the pairing correlations [1,2], the presence of Majorana zero-modes [3–10], unconventional magnetoelectric effect [11–16], or critical field enhancement [17,18]. This latter feature was first observed in the bulk non-centrosymmetric heavy fermion superconductor CePt3 Si [19] and shortly after in CeRhSi3 [20] and CeIrSi3 [21]. Moreover, it has been predicted that the interplay between an in-plane magnetic field and SOC in a surface superconductor would lead to an inhomogeneous superconducting phase [18,22,23], similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase [24,25]. Low dimensional systems were recently fabricated using strong spin-orbit coupled semiconducting epitaxial InAsSb nanowires coated by an extremely thin layer of superconducting aluminium [8,9] or in 2D platforms suitable for manipulating Majorana end states [10]. Besides the Majorana physics, such lowdimensional systems should also display a superconducting modulated phase. Moreover, such a modulated phase is characterized by the rotation of the superconducting phase along the wire, which produces a ground state with a finite phase difference ϕ0 for a finite length wire used as a weak link [26–29]. Recently such ϕ0 -Josephson junction has been realized experimentally in nanowire quantum dots [30]. a
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The inhomogeneous FFLO state originates from the interaction of the superconducting condensate with a Zeeman field (see [31] as a review). The latter
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