Insight into the charge density wave gap from contrast inversion in topographic STM images

TL;DR

This study reveals that contrast inversion in STM images of 2D charge density waves occurs at negative bias due to the CDW gap opening away from the Fermi level, providing new insights into the nature of CDWs.

Contribution

It demonstrates the relationship between contrast inversion and the CDW gap position using combined density functional theory and STM analysis in 1T-TiSe2.

Findings

Contrast inversion occurs at negative bias due to the CDW gap location.

The CDW gap shifts to higher binding energy with electron doping.

Contrast inversion helps identify the CDW gap in STM images.

Abstract

Charge density waves (CDWs) are understood in great details in one dimension, but they remain largely enigmatic in two dimensional systems. In particular, numerous aspects of the associated energy gap and the formation mechanism are not fully understood. Two long standing riddles are the amplitude and position of the CDW gap with respect to the Fermi level ($E_F$) and the frequent absence of CDW contrast inversion (CI) between opposite bias scanning tunneling microscopy (STM) images. Here, we find compelling evidence that these two issues are intimately related. Combining density functional theory and STM to analyse the CDW pattern and modulation amplitude in 1$T$-TiSe$_2$, we find that CI takes place at an unexpected negative sample bias because the CDW gap opens away from $E_F$, deep inside the valence band. This bias becomes increasingly negative as the CDW gap shifts to higher binding energy with electron doping. This study shows the importance of CI in STM images to identify periodic modulations with a CDW and to gain valuable insight into the CDW gap, whose measurement is notoriously controversial.