Anomalous Coulomb diamonds and power-law behavior sensitive to back-gate voltages in carbon nanoscale peapod quantum dots

We report anomalous charging effect of single electrons (Coulomb diamonds) observed in carbon nanoscale peapod quantum dots that encapsulate a series of C60 molecules. We find that behaviors of diamonds are anomalously sensitive to back-gate voltages (Vbg), exhibiting two evidently different Vbg regions and a large polarity on Vbg. In particular, we find only a sequence of one large diamond followed by three smaller ones existing around ground state. Magnetic-field dependence indicates the presence of shell filling by spin singlet to doubly degenerate electronic levels for these. The encapsulated- C60 molecules indirectly affect this shell filling at low Vbg possibly via nearly free electrons. In contrast, they act as individual quantum dots coupled in series in high Vbg region. It directly contributes to highly overlapped very large diamonds. Moreover, we report power-law behaviors on conductance versus energy relationships observed in the same carbon nanoscale peapods. We find that the values of powers are also highly sensitive to applied Vbg with three different regions and anomalously high at high source-drain voltages. Because the power laws are found at voltages, which are the nearest outside of the above-mentioned fourfold Coulomb diamonds, correlation of the anomalous powers with orbital-related Tomonaga-Luttinger liquid is discussed.