Second harmonic generation in carbon nanotubes induced by transversal electrostatic field

Carbon nanotubes (CNTs) of armchair and zigzag type contain an inversion centre, and are thus intrinsically unable to generate dipole even-order nonlinearities, such as second harmonic generation (SHG). Breaking the inversion symmetry by application of an external voltage transversal to the CNT axis will, however, induce a second harmonic response. Similarly, additional non-vanishing second harmonic tensor elements will be induced in chiral tubes already displaying an intrinsic response. Many geometries realizing such a setup can be envisaged, e.g., an experimental gate setup or deposition of CNTs on, or integration in, strongly polarized host media, perhaps facilitating a tunable second harmonic response. In this work, we calculate the SHG signal from CNTs under transversally applied electric fields based on a tight-binding model.