We report experimental observation of impedance oscillations in single-walled carbon nanotubes measured from 100 MHz to 65 GHz on coplanar wave guides and a power law dependence of the differential conductance with bias voltage. From the crossover of the real and imaginary parts of the complex impedance observed in the range of 10 GHz, we estimate a long lifetime of 15 ps that can support the claim of ballistic transport. By measuring the scattering parameters at high-frequencies of a few aligned single-walled bundles at low temperatures we show that, this observation is strongly influenced by the number of tubes available. __________________________________________________________________________________ a) Author to whom correspondence should be addressed. Electronic mail: Somnath.Bhattacharyya@wits.ac.za
2Over the past few decades there have been both theoretical [1,2] and experimental [3][4][5] efforts to understand one dimensional (1D) transport in DC and high frequency regimes. Calculations based on collective (electron) phenomena have predicted alternative current (AC) response that is chirality dependent in single-walled carbon nanotubes (SWNTs) even in the presence of contact effects and a universal inductive to capacitive transition in the imaginary admittance with increase in contact resistance [6]. On the other hand, a semi-classical model based on a transmission line by Burke et al.has predicted possible Luttinger liquid excitations in metallic CNTs achievable in the gigahertz regime by setting up standing voltage waves in the CNTs [7]. Some experimental RF measurements were done on individual or bundle of SWNTs, double-walled CNT (DWNTs) and multi-walled CNTs (MWNTs) but there has not been experimental evidence of some of the theoretical predictions [8,9]. This motivated us to probe the temperature dependent AC response and extend previous works on CNTs.In the high frequency (HF) regime AC conductance is believed to be equivalent to a transmission line composed of kinetic inductance (L k ) and quantum capacitance (C q ) as additional parameters to the magnetic inductance and electrostatic capacitance [6,8]. If the decay length (of voltage waves) is comparable to the mean free path of the carriers and the intrinsic resistance of material is in the linear response regime, the real and imaginary parts of the impedance will be characterised by an oscillatory behaviour corresponding to resonant peaks of the fundamental waves set by the finite length of the transmission line [6]. Experimentally there were several attempts to collectively excite electrons in CNTs and observe impedance oscillations using high frequency which were unsuccessful due to a couple of reasons such as (i) the weak CNT signal from individual SWNTs making it difficult to resolve from instrument noise or (ii) too many CNTs resulted in average (bulklike) properties instead of the expected quantum effects. It is therefore important that a trade-off point between signal strength and number of CNTs be established without losing the indiv...