{
  "id": "2202.00029",
  "version": "v1",
  "published": "2022-01-31T19:00:07.000Z",
  "updated": "2022-01-31T19:00:07.000Z",
  "title": "Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction",
  "authors": [
    "Amulya Ratnakar",
    "Sourin Das"
  ],
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "A recent study have shown that it is possible to have enhancement, in contrast to an expected suppression, in tunneling density of states (TDOS) in a Luttinger liquid (LL) which is solely driven by the non-local density-density interactions. Also, it is well known that a LL in proximity to a superconductor (SC) shows enhancement in TDOS in the vicinity of the junction in the zero energy limit. In this paper, we study the interplay of nonlocal density-density interaction and superconducting correlations in the TDOS in the vicinity of the SC-LL junction, where the LL maybe realized on the edge of an integer or a fractional quantum Hall state. We show that the TDOS enhancement in a LL quantum wire (QW) due to superconducting correlation at the junction can be farther amplified in presence of appropriate choice of non-local interaction parameters, which is demonstrated through a neat algebraic expression in the weak interaction limit. We also show that, in the full parameter regime comprising both the local and the non-local interaction, the region of enhanced TDOS for LL junction with \"superconducting\" boundary condition and that of \"non-superconducting charge conserving\" boundary condition (discussed in Phys. Rev. B 104, 045402 (2021)) are mutually exclusive. We show that this fact can be understood in terms of symmetry relation established between the superconducting and non-superconducting sectors of the theory. We compare the dependence of the proximity induced pair potential and TDOS as a function of distance $x$ from the junction. We demonstrate that the dependence of the spatial power law exponent for the `TDOS(x)/TDOS(x -> 0)' and the `pair-potential(x)/pair-potential(x -> 0)' are distinct function of the various local and non-local interaction parameters, which implies that the TDOS enhancement can not be directly attributed to the proximity induced pair potential in the LL.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-31T19:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "luttinger liquid",
      "tunneling density",
      "proximity induced pair potential",
      "non-local interaction parameters",
      "superconductor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}