| Summary: | 碩士 === 國立臺灣大學 === 應用物理研究所 === 105 === We investigate the quantum and classical effect of capacitance.
For the quantum effect, we predict a periodic capacitance change on multi-walled nanotube due to Aharonov-Bohm (AB) effect. The AB effect will make a single-walled carbon nanotube(SWCNT) becomes metallic as a periodic function quantum flux. We expect each shell of a multi-walled nanotube (MWNT) can have a similar feature of SWCNT, changing between an insulator and a conductor under magnetic field. Correspondingly, the capacitance of a MWNT may have the interesting phenomenon and displays oscillations of capacitance constituting from different shells under magnetic fields. We estimate the maximum change of capacitance is about 40aF. Experimentally, we measured the capacitance of a boron-nitride nanotube (BNNT) with total length 21.51μm (with 17.14μm between the electrode, 4.37μm on the electrode) under a maximum longitudinal magnetic field 8.93T at room temperature. We found that the capacitance change was smaller than 6aF. We also measured the capacitance of a total length 5.118μm MWCNT (with 3.828μm between the electrode, 1.29μm on the electrode) under a maximum longitudinal magnetic field 8.61T. The capacitance change is smaller than 15aF (which is likely to be underestimated because one side of the nanotube was found to be disconnected after the measurement). The experiments put an upper limit for observing Aharonov-Bohm effect on capacitance of MWNT at room temperature.
For the classical effect, we were inspired by a possible effect of capacitance due to the interference of displacement currents. We simulate the resonance frequency of four kinds of split ring resonators (SRRs & DSRRs) and apply an inhomogeneous medium to induce the interference of effective capacitor, hoping to observe a blue-shifted resonance frequency. The most difficult part of the study is to get the same result under different simulation methods and different boundary conditions, and to verify the fake signal. We propose a simple model and find that, in a homogeneous medium, the model can explain the simulated resonance frequencies within 0.15%, thus the effect of fringe field is enough small and can be ignored. However, in an inhomogeneous medium, we find an anomalous red-shift frequency of SRR which cannot be explained by the effect of damping. On the other hand, in an inhomogeneous medium the simple model can still explain the resonance frequency of DSRRs with frequency differences smaller than 0.3%. However, the frequency resolution of the simulation is too low to verify there is a blue shift due to the effect of interference.
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