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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 arenot fully understood. Two long standing riddles are the amplitude and positionof the CDW gap with respect to the Fermi level ($E_F$) and the frequent absenceof CDW contrast inversion (CI) between opposite bias scanning tunnelingmicroscopy (STM) images. Here, we find compelling evidence that these twoissues are intimately related. Combining density functional theory and STM toanalyse the CDW pattern and modulation amplitude in 1$T$-TiSe$_2$, we find thatCI takes place at an unexpected negative sample bias because the CDW gap opensaway from $E_F$, deep inside the valence band. This bias becomes increasinglynegative as the CDW gap shifts to higher binding energy with electron doping.This study shows the importance of CI in STM images to identify periodicmodulations with a CDW and to gain valuable insight into the CDW gap, whosemeasurement is notoriously controversial.

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