Excitonic vs Mott insulator in carbon nanotubes: A proposed experimental test

Ultraclean, undoped carbon nanotubes are always insulating, even when the gap predicted by band theory is zero. The residual, intrinsic gap is thought to have a many-body origin, associated with either a Mott¹ or an excitonic phase². Whereas the two scenarios are fundamentally different, as they are driven by the short- and long-range part of Coulomb interaction, respectively, a conclusive experiment has been missing so far.

Here we propose as a unique fingerprint of the excitonic insulator the presence of a cusp in the evolution of the gap with the axial magnetic field, close to the gap mimimum. On the contrary, the Mott phase exhibits a featureless, rounded profile. The non-analytic spike originates from the extreme sensitivity of electron-electron interactions to the Aharonov-Bohm gap modulation, as we demonstrate by combining a first-principles analysis of screening with extensive model calculations for tubes of different size and chirality.

¹Deshpande et al., Science 323, 106 (2009)
²Varsano et al., Nat. Comm. 8, 1461 (2017)