Presence versus absence of charging energies in PbTe quantum dots

Charging energy ($E_C$) is essential in quantum dot (QD) devices. Previous studies on PbTe QDs have reported both the presence and absence of $E_C$. To resolve this ambiguity, we vary the QD size, i.e. the cross-sectional area of PbTe nanowires, and track the evolution of $E_C$. For large crosssectional areas ($\sim$ 16000 nm$^2$), the PbTe QDs exhibit no measurable $E_C$, while quantized levels are well resolved. Decreasing this area successively to 5000, 1500, and 500 nm$^2$, $E_C$ becomes finite and increases to 80, 160, and 210 $\mu$eV, respectively. We further demonstrate the strong tunability of local gates, which can tune the PbTe device from the QD regime to the regime of ballistic transport. These results address concerns regarding the large dielectric constant of PbTe and provide key insights in engineering advanced PbTe quantum devices.