Anomalous Enhancement in Tunneling density of states in a Luttinger liquid : interplay of nonlocal interactions and proximitized superconductivity.

Suppression of local single-electron tunneling density of states (TDOS) in zero bias limit is the hallmark property of Luttinger liquids (LLs) and is due to the fact that there are no electronlike quasi particles in the low-energy excitation spectrum of LL. An exception to this suppression, leading to enhancement in TDOS, is possible if we have an Andreev-reflection (AR) like process at the junction. This can be achieved for a LL in proximity to a superconductor (SC) or due to strong correlations localized at the junction of multiple LLs which can drive the system to a fixed point. All such junction fixed point hosting AR-like process were found to be unstable against relevant perturbations in the RG sense. Here, we report the possibility of having TDOS enhancement along with stable fixed point, for a much simpler junction of two LLs in the presence of non-local interactions. We consider a LL junction with current conserving normal (N) boundary condition (BC) and current non-conserving Superconducting (SC) BC. We establish symmetry relation between the normal and superconducting sectors of the theory. Such a model can be realized on the edge states of a bilayer quantum Hall (QH) system with tunnel (SC pair) coupling such that intralayer and interlayer interactions mimics the local and nonlocal interactions. This study is inspired by the current experimental advances where Large cross Andreev reflection has already been observed for a fractional QH edge in proximity to a superconductor.