[2202.00029] Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Mesoscale and Nanoscale Physics arXiv:2202.00029 (cond-mat) [Submitted on 31 Jan 2022 ( v1 ), last revised 6 Jan 2023 (this version, v2)] Title: Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction Authors: Amulya Ratnakar , Sourin Das View a PDF of the paper titled Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction, by Amulya Ratnakar and Sourin Das View PDF HTML (experimental) 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. Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2202.00029 [cond-mat.mes-hall] (or arXiv:2202.00029v2 [cond-mat.mes-hall] for this version) https://doi.org/10.48550/arXiv.2202.00029 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. B 106, 115412 (2022) Related DOI : https://doi.org/10.1103/PhysRevB.106.115412 Focus to learn more DOI(s) linking to related resources Submission history From: Amulya Ratnakar [ view email ] [v1] Mon, 31 Jan 2022 19:00:07 UTC (5,550 KB) [v2] Fri, 6 Jan 2023 07:41:33 UTC (5,916 KB) Full-text links: Access Paper: View a PDF of the paper titled Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction, by Amulya Ratnakar and Sourin Das View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mes-hall < prev | next > new | recent | 2022-02 Change to browse by: cond-mat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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