Tunneling into a periodically modulated Luttinger liquid

TL;DR

This paper investigates how periodic modulation of electron concentration in a Luttinger liquid affects tunneling, revealing a phase-dependent spectral gap anomaly linked to localized plasmon modes at the edge.

Contribution

It introduces the concept that phase-controlled periodic modulation causes a spectral gap and edge-localized plasmon modes, affecting tunneling density of states.

Findings

Modulation creates a spectral gap in plasmon spectrum.

Anomaly in density of states appears at the gap center.

Anomaly shape depends on the phase of modulation.

Abstract

We study the tunneling into the edge of the Luttinger liquid with periodically modulated concentration of electrons. It is shown that the modulation,by causing a gap in the spectrum of plasmons, leads to an additional anomaly in the density of states at frequency corresponding to the center of the gap. The shape of the anomaly depends strongly on the {\em phase} of the modulation. The sensitivity to the phase is related to the plasmon mode, localized at the edge, its frequency lying within the gap (analog of the Tamm state for an electron in an interrupted periodic potential).