Tunneling density of states in a Luttinger liquid in proximity to a superconductor: Effect of nonlocal interaction

A recent study have shown that it is possible to enhancement, in contrast an expected suppression, tunneling density of states (TDOS) a Luttinger liquid (LL) which solely driven by the non-local density-density interactions. Also, well known LL proximity superconductor (SC) shows enhancement TDOS vicinity junction zero energy limit. In this paper, we interplay nonlocal interaction and superconducting correlations SC-LL junction, where maybe realized on edge integer or fractional quantum Hall state. We show wire (QW) due correlation at can be farther amplified presence appropriate choice parameters, demonstrated through neat algebraic expression weak also that, full parameter regime comprising both local interaction, region enhanced for with "superconducting" boundary condition "non-superconducting charge conserving" (discussed Phys. Rev. B 104, 045402 (2021)) are mutually exclusive. fact understood terms symmetry relation established between non-superconducting sectors theory. compare dependence induced pair potential as function distance $x$ from junction. demonstrate spatial power law exponent `TDOS(x)/TDOS(x -> 0)' `pair-potential(x)/pair-potential(x distinct various implies not directly attributed LL.