Secondary electron interference from trigonal warping in clean carbon nanotubes

A. Dirnaichner, M. del Valle, K. J. G. Götz, F. J. Schupp, N. Paradiso, M. Grifoni,
Ch. Strunk, and A. K. Hüttel
Physical Review Letters 117, 166804 (2016)

Imagine a graphene "sheet" of carbon atoms rolled into a tube - and you get a carbon
nanotube. Carbon nanotubes come in many variants, which influence strongly their
electronic properties. They have different diameter, but also different "chiral
angle", describing how the pattern of the carbon atoms twists around the tube axis.
In our work, we show how to extract information on the nanotube structure from
measurements of its conductance. At low temperature, electrons travel ballistically
through a nanotube and are only scattered at its ends. For the quantum-mechanical
electron wavefunction, metallic nanotubes act then analogous to an optical Fabry-
Perot interferometer, i.e., a cavity with two semitransparent mirrors at either end,
where a wave is partially reflected. Interference patterns are obtained by tuning the
wavelength of the electrons; the current through the nanotube oscillates as a
function of an applied gate voltage. The twisted graphene lattice then causes a
distinct slow current modulation, which, as we show, allows a direct estimation of
the chiral angle. This is an important step towards solving a highly nontrivial
problem, namely identifying the precise molecular structure of a nanotube from
electronic measurements alone.