Enhancement in tunneling density of states in a Luttinger liquid: Role of nonlocal interaction

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 "nonsuperconducting 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.

Bipolar Thermoelectricity in Bilayer-Graphene/Superconductor Tunnel Junctions

“…Notwithstanding, a few works [6,7] anticipated that even superconducting systems could exhibit a thermoactive behaviour. Along this route, theoretical [8][9][10][11][12][13][14][15][16] and experimental [17][18][19] research has shown that nonlocality or phase coherence may still trigger intriguing thermoelectric phenomena in superconducting and hybrid systems. Furthermore, some authors even reported the existence of Absolute Negative Conductance (ANC) in superconducting tunnel junctions in out-of-equilibrium conditions or under microwave irradiation [20][21][22][23].…”