Terahertz imaging and spectroscopy of large-area single-layer graphene.

We demonstrate terahertz (THz) imaging and spectroscopy of a 15 × 15-mm2 single-layer graphene film on Si using broadband THz pulses. The THz images clearly map out the THz carrier dynamics of the graphene-on-Si sample, allowing us to measure sheet conductivity with sub-mm resolution without fabricating electrodes. The THz carrier dynamics are dominated by intraband transitions and the THz-induced electron motion is characterized by a flat spectral response. A theoretical analysis based on the Fresnel coefficients for a metallic thin film shows that the local sheet conductivity varies across the sample from σ(s) = 1.7 × 10(-3) to 2.4 × 10(-3) Ω(-1) (sheet resistance, ρ(s) = 420 - 590 Ω/sq).

Determination of electron orbital magnetic moments in carbon nanotubes.

The remarkable transport properties of carbon nanotubes (CNTs) are determined by their unusual electronic structure. The electronic states of a carbon nanotube form one-dimensional electron and hole sub-bands, which, in general, are separated by an energy gap. States near the energy gap are predicted to have an orbital magnetic moment, mu(orb), that is much larger than the Bohr magneton (the magnetic moment of an electron due to its spin). This large moment is due to the motion of electrons around the circumference of the nanotube, and is thought to play a role in the magnetic susceptibility of CNTs and the magnetoresistance observed in large multiwalled CNTs. But the coupling between magnetic field and the electronic states of individual nanotubes remains to be quantified experimentally. Here we report electrical measurements of relatively small diameter (2-5 nm) individual CNTs in the presence of an axial magnetic field. We observe field-induced energy shifts of electronic states and the associated changes in sub-band structure, which enable us to confirm quantitatively the predicted values for mu(orb).

Tuning carbon nanotube band gaps with strain.

We show that the band structure of a carbon nanotube (NT) can be dramatically altered by mechanical strain. We employ an atomic force microscope tip to simultaneously vary the NT strain and to electrostatically gate the tube. We show that strain can open a band gap in a metallic NT and modify the band gap in a semiconducting NT. Theoretical work predicts that band gap changes can range between +/-100 meV per 1% stretch, depending on NT chirality, and our measurements are consistent with this predicted range.

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).