An Atlas of Carbon Nanotube Optical Transitions

Feng Wang (UCB) and Alex Zettl (UCB)

Systematic mapping between structure and property of nanomaterials is crucial for nanoscience, because physical properties of nanomaterials depend sensitively on their underlying structures. This is exemplified in single-walled carbon nanotubes (SWNTs), a family of one-dimensional (1D) graphitic tubules with hundreds of different structural forms. Each SWNT structure, uniquely defined by the chiral index (n,m), exhibits distinct optical transitions.

In this project we establish the first comprehensive and precise chiral index-optical transition map for both semiconducting and metallic SWNTs over a broad diameter range. This is achieved by simultaneous determination of chiral indices and optical transitions for over 200 individual SWNTs using combined electron diffraction and Rayleigh scattering measurements on the same suspended nanotubes. This mapping provides the final reference for nanotube spectroscopic characterization. Once we know the optical resonances of a single-walled nanotube, we can reliably identify its chiral index; and vice versa. It also enables the quantitative characterization of photo process in carbon nanotubes, such as quantum efficiency for photocurrent and photovoltaics.

Experimental atlas of SWNT optical transitions. Open circles are our data, which are well reproduced by our empirical formula. Each line corresponds to a family of SWNTs with a constant (2n+m) value.

Exploring the Mechanical Effects of Microwave Photons

Keith Schwab (Caltech) and Michael Roukes (Caltech)

We investigated the back-action of the microwave photons on the nanowire motion. The nanowire is capacitively coupled to the microwave coplanar waveguide resonator. (Fig. a) By applying a red-detuned microwave power to the sample, back-action cooling of the nanowire motion occurs, which can be used to prepare mechanical ground states. The previous work has shown cooling down to 3 mechanical quanta. The cooling was limited by heating, which was not clearly understood, and also the mechanical resonance showed frequency jitters below 100mK. Our effort was identifying the source of heating and jitter and finding out a way to reduce them. With an improved measurement set-up (Fig.b), the mechanical noise thermometry worked down to 50mK with lower jitter (left plot). The back-action cooling worked down to 8 mechanical quanta, and the observed excess heating was found to be consistent with a resonant two-level bath model, which becomes relevant in a few quanta regime (right plot, green line). Our result calls for a study on the mechanical dissipation in low occupation regime and methods to reduce it, in order to reach the goal of achieving mechanical ground states in a back-action cooling scheme.

This work was performed under the auspices of the National Science Foundation by University of California Berkeley under Grant No. 0832819.

Graphene Drums – Measuring Graphene Membrane Vibrations

Alex Zettl (UCB) and Feng Wang (UCB)

Graphene, an atomic sheet of carbon, can be thought as the thinnest drumhead possible. Similarly to macroscopic drums, vibrations on suspended graphene membranes have certain frequencies of oscillation, known as resonance frequencies. We have excited and measured the resonant frequencies of the fundamental and first three excited states of a graphene “drum”.  This graphene drum is much more than a simple nanodrum; the atomically thin oscillator should be an excellent mass sensor. If mass is added to the membrane is will slow the vibration down. The magnitude of this change is proportional to the mass of the membrane. Since the graphene membrane is so light, graphene membranes should have atomic mass resolution.

This work was performed under the auspices of the National Science Foundation by University of California Berkeley under Grant No. 0832819.

TEM image of of a graphene membrane (left). Resonance peaks for the fundamental and first three excited vibrational states of a graphene membrane (right).