The energy of Fermi sea perturbed by an external potential is analyzed with the help of an energy anomaly. Using an example of massive Dirac fermions on a circle, we illustrate how the anomaly accounts for the contribution of the deep-lying states. The energy anomaly is a universal function of the applied field and is related to known field-theoretic anomalies. Applied to the transverse polarizability of carbon nanotubes, the anomaly reveals universality and scale invariance of the response dominated by $\pi$ electrons. The electron band transformation in a strong field-effect regime is predicted.

• Received 18 September 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.036402