Enhancement of tunneling density of states at a Y junction of spin-1/2 Tomonaga Luttinger liquid wires

TL;DR

This paper investigates the tunneling density of states at a Y junction of spin-1/2 Tomonaga-Luttinger liquid wires, revealing an anomalous enhancement near the junction due to hole reflection, with implications for STM experiments.

Contribution

It provides the first calculation of TDOS enhancement at a Y junction of spin-1/2 Luttinger liquids, highlighting the physical mechanism and experimental observability.

Findings

TDOS is anomalously enhanced near the junction for certain fixed points.

Enhancement occurs only in the vicinity of the junction, crossing over to suppressed bulk behavior.

The TDOS exponent can be measured via differential tunneling conductance in STM experiments.

Abstract

We calculate the tunneling density of states (TDOS) in a three wire junction of interacting spin-1/2 electrons, and find an anomalous enhancement of the TDOS in the zero bias limit, even for repulsive interactions for several bosonic fixed points. This enhancement is physically related to the reflection of holes from the junction for incident electrons, and it occurs only in the vicinity of the junction ($x < v_{\rm min}/2\omega$ where $v_{\rm min}$ is the minimum of the velocity of charge or spin excitations and $\omega$ is the bias frequency), crossing over to the bulk value which is always suppressed, at larger distances. The TDOS exponent can be directly probed in a STM experiment by measuring the differential tunneling conductance as a function of either the bias voltage or temperature as done in C. Blumenstein et al. Nature Physics 7, 776 (2011).